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SAD/FFS SADScript Version: 1.1.9.0.1k64, Updated: 08/31/2020
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The FFS commands are shown in uppercases. The minimum abbreviated form of each command is enclosed
in (). Each command can be shorten down to that. The optional arguments for the commands are usually
shown in []. The notation ===> reads "equivalent to" below.
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SAD/FFS Examples
ABORT
APPEND(APP)
ATTRIBUTE(ATTR)
beamline
beamlinefunctions
BeamLine
BeamLineName
ExtractBeamLine
PrintBeamLine
WriteBeamLine
orientationofanelement
BEAMSIZE(BEAM)
BYE
characterstring
FromCharacterCode
StringFill
StringJoin
StringLength
StringMatchQ
StringPart
StringPosition
StringReplace
StringTrim
Symbol
ToCharacterCode
ToExpression
ToString
commandsyntax
components
constants
CALCULATE(CAL)
CHROMATICITY(CHRO)
CLOSE(CLO)
COUPLE(COUP)
datastructure
Extract
Head
Length
List
Part
definingfunctions
dynamics
independentvariable
Lagrangean
Hamiltonian
2ndorderHamiltonian
solutionH2
solutiondH
remarksondynamics
xycoupling
extendedTwissparameters
definitions
synchrotronradiation
equilibriumbeamenvelope
DISPLAY(DISP)
ACCELERATION(A)
ALL
BEAM(B)
DREFERENCE(DRE)
DUMPOPTICS(D)
GAMMA(GA)
GEOMETRY(G)
OGEOMETRY(OG)
ORBIT(O)
patternstring
PHYSICAL(P)
region
REFERENCE(RE)
RMATRIX(R)
Z
DRAW
Draw$Option
DUMP
elements
APERT
BEND
AE1
AE2
ANGLE
DISFRIN
DISRAD
DROTATE
DX
DY
E1
E2
F1
FB1
FB2
FRINGE
K0
K1
L
ROTATE
transformation:BEND
CAVI
DISFRIN
DPHI
DVOLT
DX
DY
FREQ
HARM
L
PHI
ROTATE
V02
V1
V11
VOLT
COORD
defaultkeyword
DECA
DISFRIN
DISRAD
DX
DY
K4
L
ROTATE
transformation:THIN
DODECA
DISFRIN
DISRAD
DX
DY
K5
L
ROTATE
transformation:THIN
DRIFT
L
RADIUS
transformation:DRIFT
keywords
MARK
OFFSET
MULT
K0
SK0
K1
SK1
K2
SK2
K3
SK3
K4
SK4
K5
SK5
K6
SK6
K7
SK7
K8
SK8
K9
SK9
K10
SK10
K11
SK11
K12
SK12
K13
SK13
K14
SK14
K15
SK15
K16
SK16
K17
SK17
K18
SK18
K19
SK19
K20
SK20
K21
SK21
AE1
AE2
ANGLE
DISFRIN
DISRAD
DPHI
DVOLT
E1
E2
F1
F2
FB1
FB2
FREQ
FRINGE
HARM
L
misalignments
multipole_with_nonzero_ANGLE
PHI
RADIUS
VOLT
OCT
DISFRIN
DISRAD
DX
DY
K3
L
ROTATE
transformation:THIN
QUAD
DISFRIN
DISRAD
DX
DY
F1
F2
FRINGE
K1
L
ROTATE
transformation:QUAD
SEXT
DISFRIN
DISRAD
DX
DY
K2
L
ROTATE
transformation:THIN
SOL
BOUND
BZ
DISFRIN
DPX
DPY
DX
DY
F1
GEO
expression
()
(/)
AddTo(+=)
Alternatives()
And(&&)
Apply (@@)
CompoundExpression(;)
Decrement()
DivideBy(/=)
Dot(.)
Equal(==)
Function(&)
)>Greater(>)
= or =>)>GreaterEqual(>= or =>)
Increment(++)
Less(<)
LessEqual(<= or =<)
List({})
Map (/@)
MapAll(//@)
Member(@)
MessageName(::)
Not(~)
Or()
Part([[]])
PatternTest(?)
Plus(+)
Power(^)
Repeated(..)
RepeatedNull(...)
ReplaceAll(/.)
ReplaceRepeated(//.)
)>Rule(>)
)>RuleDelayed(:>)
SameQ(===)
Sequence([])
Set(=)
SetDelayed(:=)
StringJoin (//)
SubtractFrom(=)
TagSet(/:)
Times(*)
TimesBy(*=)
)>Unequal(<>)
)>UnsameQ(<=>)
Unset(=.)
ELSE
ELSEIF
EMITTANCE(EMIT)
END
ENDIF
EXECUTE(EXEC)
EXPAND
flags
ABSW
BIPOL
CALC4D
CALC6D
CELL
CMPLOT
COD
CODPLOT
CONV
CONVCASE
DAMPONLY
DAPERT
DIFFRES
ECHO
EMIOUT
FFSPRMPT
FIXSEED
FLUC
GAUSS
GEOCAL
GEOFIX
HALFRES
IDEAL
INS
INTRA
INTRES
JITTER
LOG
LOSSMAP
LWAKE
MOVESEED
PHOTONS
POL
PRSVCASE
PSPAC
QUIET
RAD
RADCOD
RADLIGHT
RADPOL
RADTAPER
REAL
RELW
RFSW
RING
SELFCOD
SORG
SPAC
STABLE
SUMRES
SUS
TRPT
TWAKE
UNIFORM
UNIPOL
UNSTABLE
WSPAC
functions
DataManipulation
Fit
FitEmit
FitGaussian
NIntegrate
PolynomialFit
Spline
DownhillSimplex
functionaloperations
Apply
Cases
DeleteCases
Difference
FixedPoint
FixedPointList
levelspec
Map
MapThread
Position
Scan
ScanThread
SelectCases
SwitchCases
Thread
FFSdedicatedfunctions
AccelerateParticles
BeamMatrix
DynamicApertureSurvey
Element
keystrings:Element
Emittance
ExternalMap
CompiledMap
FFS
FFS$SHOW
FitValue
FitWeight
GaussianCoulomb
GeoBase
LINE
keystrings:LINE
OptimizeOptics
OrbitGeo
RadiationField
RadiationSpectrum
SetElement
SurvivedParticles
SymplecticJ
SynchroBetaEmittance
TouschekLifetime
TrackParticles
Twiss
VariableRange
VariableWeight
WakeFunction
Graphics
BeamPlot
ColumnPlot
FitPlot
GeometryPlot
HistoPlot
ListContourPlot
ListDensityPlot
ListPlot
OpticsPlot
Plot
Input/Output
$FORM
$Input
$Output
Close
OpenAppend
OpenRead
OpenWrite
PageWidth
Print
Read
ReadString
StandardForm
StringToStream
Write
WriteString
Multiprocessing
Fork
OpenShared
Shared
SharedSize
Objectorientedprograming
Class
Randomnumberfunctions
Random
GaussRandom
ParabolaRandom
SeedRandom
ListRandom
Systeminterface
System
TemporaryName
Utilities
DateString
MemoryCheck
TimeUsed
Timing
TracePrint
FIT
FITPOINTS(FITP)
FIX
FREE
defaultkeyword
geometricfunctions
GO
IF
INPUT(IN)
machineerrorcommands
matchingfunctioncommands
multiturntracking
MATRIX(MAT)
MEASURE(MEA)
offmomentummatching
opticalfunctions
ORG
OUTPUT(OUT)
pattern
MatchQ
physicalconstants
PRINT(PRI)
QUIT
RADINT
READ
RECOVER(REC)
REFERENCE(REF)
referenceoptics
REJECT(REJ)
RENUMBER(RENUM)
REPEAT(REP)
RESET
RESUME(RES)
REVERSE(REV)
setvalueofelement
keywords
defaultkeyword
specialvariables
$Line
CASE
CHARGE
CONVERGENCE
DAPWIDTH
DP
DP0
DTSYNCH
EFFRFFREQ
EFFVC
EFFVCRATIO
ElementValues
EMITX
EMITXE
EMITY
EMITYE
EMITZ
EMITZE
ExponentOfResidual
FFS$NumericalDerivative
FitFunction
FSHIFT
GCUT
InitialOrbits
LOSSAMPL
LOSSDZ
MatchingAmplitude
MatchingResidual
MASS
MINCOUP
MOMENTUM
NBUNCH
NetResidual
NP
NPARA
OffMomentumWeight
OMEGA0
OpticsEpilog
OpticsProlog
PBUNCH
PhotonList
PHICAV
SIGE
SIGZ
SpeedOfLight
StabilityLevel
TITLE
SAVE
SEED
SHOW
SPLIT
STATUS(STAT)
STOP
SUSPEND(SUSP)
TERMINATE(TERM)
TYPE(T)
UNTIL
USE
VARIABLES(VAR)
VARY
VISIT
wildcards
Terminates SAD immediately.
See also:
STOP QUIT SAVE USE VISIT BYE
APP {filename  filenumber} switches the output stream to the specified file or the file number.
The output is appended to the existing file.
See also:
TERMINATE(TERM) CLOSE(CLO) INPUT(IN) READ OUTPUT(OUT)
END
Usage: ATTR elementpattern
prints out the current value, minimum and maximum values, COUPLEd element and its coefficient for
elements which match the elementpattern.
See also:
COUPLE(COUP) setvalueofelement wildcards
A beam line is defined in the MAIN level by LINE command as:
LINE a = ( [n1*][]l1 [ [n2*]l2 ...] ) [b = ( ... )];
where l1, l2 are either an element or a line. n1, n2 are positive integers to repeat the same element.
An optional negative sign in fromt of element means the negative orientation of the element of the
line. A negative orientation of a line is inherited by its elements.
The first element of a beam line must be a MARK element, if it is used by FFS, USE, VISIT.
Please do not confuse the LINE command in the MAIN level with the LINE function in FFS.
A beam line can be accessed within FFS via beamlinefunctions as shown below.
See also:
elements orientationofanelement USE VISIT

Functions/objects to construct/edit beam lines and elements in FFS.

Usage: BeamLine[e1, e2, ...];
where e1, e2 has a form of
[  ][ n* ] x ,
with x being one of
1) a name (either a symbol or a character string) of an element defined in MAIN.
2) a name (either a symbol or a character string) of a LINE defined in MAIN.
3) a BeamLine object.
An optional negative sign specifies the direction and a number n the repetition number in the same
way as MAIN. A BeamLine object is automatically expanded to the lowest level whenever it is evaluated.
Editing of BeamLine can be done using any Listhandling functions such as Join, Insert, Delete, etc.
of FFS.
A BeamLine object can be used for FFS calculation when it is used as the
argument of USE or VISIT commands:
Examples:
1) USE BeamLine[IP,QF,QD]
2) aaa=ExtractBeamLine[];
USE Join[aaa,aaa]
In these cases the new beam line becomes a new LINE in the MAIN level, with a name which is created
automatically.
See also:
ExtractBeamLine PrintBeamLine WriteBeamLine orientationofanelement
USE VISIT

BeamLineName[] returns the name of the current beam line. If a BeamLine object is used by USE or
VISIT, the new beam line becomes a new LINE in the MAIN level, with a name which is created automatically.

Usage: ExtractBeamLine[line]
returns a BeamLine object which represents the expanded form of line which has been defined in MAIN.
If line is omitted, the current line is assumed.
See also:
BeamLine PrintBeamLine WriteBeamLine USE VISIT

Usage: PrintBeamLine[b1,.. ,option]
writes the BeamLine b1,.. to stdout. If b1.. is omitted the current beam line is assumed. If Format>"MAIN"
is given, it writes in the MAINinput format. If Name>{name1,..} is given, names of BeamLines are
also written. The number of Name must be not smaller than number of BeamLines.
See also:
BeamLine ExtractBeamLine WriteBeamLine USE VISIT

Usage: WriteBeamLine[f, b1,.. ,option]
writes the BeamLine b1,.. to file f. If b1.. is omitted the current beam line is assumed. If Format>"MAIN"
is given, it writes in the MAINinput format. If Name>{name1,..} is given, names of BeamLines are
also written. The number of Name must be not smaller than number of BeamLines.
See also:
BeamLine ExtractBeamLine PrintBeamLine USE VISIT

An element with negative orientation means a reversal of the element along the zaxis. Thus all
magnets except for a solenoid does not change the polarity. A solenoid changes the polarity. An RF
cavity should change, however, it does not in the current implementation. The edge angles and fringe
parameters of the entrance and the exit swap.
AX, AY, AZ, EPX, EPY, ZPX, ZPY, R2, R3 of a MARK element are reversed.
The orientation is printed out by DISP. It can be accessed by LINE["DIR"] .
See also:
beamline BeamLine LINE
Calculate the beam size with the current Twiss parameters. The calculation is in 5D and not correct
if the synchrotron motion is significant. Use EMITTANCE(EMIT) with CODPLOT for a 6D calculation.
See also:
DISPLAY(DISP) EMITTANCE(EMIT) CODPLOT
Exits from the current beam line and returns to the original beam line where VISIT command was issued.
All information specific to the beam line, such as matching conditions are restored.
Note that BYE does neither SAVE the values of elements of the leaving beam line, nor RESET the
values of elements of the returning beam line.
See also:
VISIT USE SAVE RESET STOP QUIT ABORT
A characterstring is expressed by enclosing in "". Special characters are expressed using \:
\n new line
\r carriage return
\t tab
\" double quote
\\ backslash
\nnn a character whose octal code is nnn.
If a characterstring is written over multiple lines, \ must be placed at the end of each line.
The length of a characterstring is limited to 2^311.

FromCharacterCode[r_Real] returns a character whose character code is r.
FromCharacterCode[l_List] returns a characterstring whose character codes are l.
See also:
ToCharacterCode

StringFill[s, sf, n] with strings s and sf, n > 0, returns (s//sf//sf...)[1,n] .
StringFill[s, sf, n] with strings s and sf, n > 0, returns (...sf//sf//s)[n,1] .
See also:
StringJoin StringJoin (//) StringPart

StringJoin[s1, s2, [,s3...]] ===> s1 // s2 [//s3...] concatenates strings s1, s2 [,s3...].
See also:
StringJoin (//)

StringLength[s] returns the length of string s.

StringMatchQ[s, spat] returns True/False whether string s matches stringpatten spat.
See also:
wildcards

s_String[n] returns the nth character in s.
s_String[n1, n2] returns the substring from n1th through n2th characters of s.
If n1, n2 are negative, they count from the end of the string.

StringPosition[s, subs] returns a list of positions of subs in string s.
StringPosition[s, subs, n] returns a list of first n positions of subs in string s.
Example: StringPosition["abcbcbcbcb","bcb"] returns {{2,4},{4,6},{6,8},{8,10}}.

StringReplace[s, rules] replaces the parts of string s accoding to rules, which is a Rule or a list
of Rules:
StringReplace["abcbcbcbc","bcb">"xyx"] ===> "axyxcxyxc"
StringReplace["abcbcbcbc",{"bcb">"xy","cbc">"pqrs"}] ===> "axypqrsbc" .

StringTrim[s] removes the leading and trailing spaces and tabs from s.

Symbol[s] returns a Symbol whose name is characterstring s.

ToCharacterCode[s] returns the list of character codes of characterstring s.
See also:
FromCharacterCode

ToExpression[s] converts a characterstring s to an expression and evaluate it.
See also:
ToString

ToString[expr] evaluates an expression expr, then converts to a characterstring.
ToString[expr, [FormatType >] form [, form1...]] converts expr using one or more formats form [,form1...].
Available formats are:
InputForm special characters are quoted with \.
HoldForm converts expr without evaluation.
StandardForm converts with the standard number format and PageWidth.
GenelicSymbolForm do not display the generation ($nnn) of local symbols for Module.
See also:
$FORM PageWidth StandardForm Module ToExpression
The command syntax in FFS is
expression1 [param1..] [;] expression2..
(1) The input is first evaluated as an expression. If the expression returns a Symbol with the same
name as the expression itself, it is interpreted as an FFS command, otherwise the returned value
is printed out unless it is Null.
(2) Each command takes succeeding its parameters if necessary. A command with indefinite number
of parameters can be terminated by semicolon. Most commands terminate itself at the end of line.
(3) A line can be continued to the next line if a backslash is placed at the end of the line.
(4) An expression continues to the next line if it is not closed in the line.
(5) An exclamation mark comments out the rest of the line.
Example: A command line
QF* .1
means the setvalueofelement command as unless the symbol QF has been defined otherwise. If QF
has been defines as a number, such as QF=2.5, the above command line is interpreted as Times[QF,.1]
then returns .25 .
See also:
expression functions
Components are the objects which consist the beam line. A component simulates an individual magnet,
drift space, or rfcavity. The parameters of a component is specified the values in the corresponding
element with the same name as the component, which simulates a power supply. Many components can
be attached to the same element. Parameters of each component may deviate from the corresponding
element if machine errors are given.
A component is specified with the form name[.order][{+}offset], where name is the name of the
component. The number order means the orderth component which belongs to name element, counted from
the beginning of the line starting from 1. Offset is a positive or negative number to specify the
downstream or upstream components from the given component. If order is omitted, the first element
is assumed, and if offset is omitted, zero is assumed. The order can be renumbererd by RENUMBER(RENUM).
The end of line is specified by $$$. The first component can be specified by ^^^.
See also:
elements RENUMBER(RENUM)
There are predefined special symbols for constants in FFS:
symbol value
True 1
False 0
Infinity INF
INF INF
NaN NaN
Pi ArcSin[1]*2
E Exp[1]
I Complex[0,1]
Degree Pi/180
GoldenRatio (1+Sqrt[5])/2
EulerGamma 0.57721566490153286061
See also:
specialvariables physicalconstants flags expression
Usage: (1) CAL [[NO]EXPAND]]
(2) CAL matchingfunction1[] [matchingfunction2[]..]
(1) With no argument or with an option [NO]EXPAND, calculates the optics and the matchingfunctions
using the current values of the components. It prints out the values of the matchingfunctions specified
either by the matchingfunctioncommands or the second usage of CAL, as described below. If an option
EXPAND is given(default), it expands the beam line before the calculation. If NOEXPAND is given,
it calculates without any expansion. FFS["CAL"] and FFS["GO"] returns the result as a list, whose
format is
{dp, kind, reslist, functionvalues},
where
dp: a list contains dp/p0 .
kind: a list of kind of the orbit (usually 0, but 1 to 6 for the finite amplitude matching, see
MatchingAmplitude).
reslist: a list of {residual, xstab, ystab}, where
residual: matching residual,
xstab: True when the matrix is stable in X,
ystab: True when the matrix is stable in Y, for each orbit.
Above are lists with length nf (== number of orbits).
functionvalues: a list of length nc (== number of calculated items). Each element has the form:
{component1, component2, function, listofvalues},
where
component1, component2: fit locations (see FIT).
function: name of the function (see matchingfunctioncommands).
listofvalues: list of the value of the function for each orbit Length nf.
The central orbit comes at the Floor[(n+1)/2]th element.
(2) With matchingfunction names, sets the matchingfunctions at the current fit point to be printed
out after calculation. If the matchingfunction is followed by a minus sign, it suppresses the printout.
\nExample:
CALC BX BY CAL
See also:
GO DISPLAY(DISP) COUPLE(COUP) ATTRIBUTE(ATTR) SHOW FIT
matchingfunctioncommands EXPAND CONV CONVERGENCE MatchingResidual
FFS
CHRO prints out the chromaticity of QUAD and SEXT in the entire beam line using the simplest formula:
xi_{x,y}=Integrate[(K1/L) beta_{x,y}(s) ds] for QUAD,
xi_{x,y}=Integrate[(K2/L) eta_x (s) beta_{x,y}(s) ds] for SEXT.
These formula are not valid when there is xy coupling or vertical dispersion.
CLOSE [INPUT(IN)] closes the current input stream and switches it to the previous input stream.
CLOSE OUTPUT(OUT) suspends the current output and switches it to the previous output stream.
See also:
TERMINATE(TERM) INPUT(IN) READ OUTPUT(OUT) APPEND(APP)
END
Usage: COUP slaveelement masterelement coefficient
sets the value of the defaultkeyword of slaveelement to be equal to coefficient times the value
of the defaultkeyword of masterelement. COUPLE(COUP) cannot be cascaded. The masterelement cannot
be COUPLEd to any other element. To reset COUPLE, say COUP slaveelement slaveelement 1.
Consider ElementValues to define universal coupling for any keywords.
See also:
ATTRIBUTE(ATTR) FREE ElementValues
All data and "programs" in SAD Script are expressed either by an atom or a liststructure:
head[body1 [,body2...]]
where head and body1... are atom or liststructure. Defined atoms are:
Real a real number
Symbol a symbol
String a characterstring
Pattern a pattern structure for argument matching
Currently the lengths of a liststructure, a characterstring, and the name of a symbol are limited
to 2^311. A real number has an accuracy of 8 bytes.
See also:
characterstring pattern

Extract[f, part [,head]]
takes elements specified by part, which is a list of indices or Null. Optional head is applied at
each element before evaluation.
Example: Extract[{a,b,c,d,e},{3}] returns c
Extract[{a,b,c,d,e},{3,4}] is an error
Extract[{a,b,c,d,e},{{3},{4}}] returns {c,d}
Extract[Hold[{a,b,c,d,e}],{1,3}, Hold] returns Hold[c]
See also:
Part

Head[f] takes the head of an expression f.

Length[f] returns the number of elements in the body of a structure f.

List is a special symbol to be the head of generic liststructure.
List[a, b, c, ...] is represented as {a, b, c, ...}.
A list is also used to represent a mathematical vector and matrices.
Most of mathematical functions are operated at each element of a list.

Part[f, a [,b ,...]] ===> f[[a, [,b ...]]]
takes the ath element of structure f. f[[a, b]] is equivalent to f[[a]][[b]].
If a is zero, it takes the head of f.
if a is negative, f[[a]] os equivalent to f[[Length[f] + 1 + a]].
If a is a list of Reals {a1, a2, ...}, f[[a]] returns {f[[a1]], f[[a2]], ...}.
If a is Null, f[[,b]] is returns {f[[1,a]], ..., f[[Length[f], b]]}.
See also:
Length Head Extract
A function is defined by one of the following forms:
f[pat1 [,pat2...]] (:)= body;
f[pat1 [,pat2...]] ^(:)= body;
g/:f[pat1 [,pat2...]] (:)= body;
where pat1 [,pat2...] are patterns (including expressions).
If UpSet(^=) or UpSetDelayed (^:=) is used, the definition is associated with the symbol in the
first level of l.h.s.
If TagSet(/:) is used, the definition is associated with the symbol on the left of /: .
The patters can be an expression including constants. The definition with constant arguments can
be accessed faster than searching a list, in general, so they are suitable for a data base. Definitions
with constant arguments have higher priorities than with patterns.
See also:
UpSet UpSetDelayed TagSet(/:) pattern

See also:
Lagrangean Hamiltonian

See also:
Hamiltonian independentvariable

See also:
Lagrangean independentvariable

See also:
Hamiltonian 2ndorderHamiltonian

See also:
DISPLAY(DISP) opticalfunctions matchingfunctioncommands

A symplectic matrix such as the normal mode matrix can be expressed in terms of the extended Twiss
parameters. In 6 by 6 case, those are
AX BX ZX EX
PSIX ZPX EPX
R1 R2 AY BY ZY EY
R3 R4 PSIY ZPY EPY
AZ BZ
PSIZ .
A(X,Y,Z), B(X,Y,Z) are alphas and betas in the usual sense, after a diagonalization to 2 by 2 submatrices.
PSI(X,Y,Z) are the rotation angle to set one the coordinate to parallel to the (X,Y,Z) axes. R(1,2,3,4)
are the components of the xy coupling matrix (see xycoupling). E(X,PX,Y,PY) are "dispersions"
which decouples synchrobeta coupling terms together with Z(X,PX,Y,PY). Those parameters should agree
with what FFS calculates in the case of no synchrobeta couplings.
See also:
xycoupling opticalfunctions

See also:
RAD RADCOD Hamiltonian BEND F1

See also:
EMITTANCE(EMIT) Emittance INTRA WSPAC MINCOUP
Usage: DISP_LAY [keywords] [patternstring] [region]
Displays values of various optical/geometricfunctions at the components given by the patternstring
in the region (see region) in the current beam line. It has several display modes specified by the
keywords. As the default, it displays AX, BX, NX, EX, EPX, AY, BY, NY, EY, EPY, LENG, the length
and the value of the defaultkeyword of the component. Each line refers to the entrance of each component
of the line. The end of the beam line has the name "$$$". The first component can be specified by
"^^^".
DISP suspends the output to the terminal at every 66 lines, asking (q_uit, c_ontinue, a_ll)?.
The further output depends on the first character of the answer from the terminal input. This dialog
is suppressed by specifying ALL.
DISP does not calculate the functions to be displayed, so CALCULATE(CALC) or GO is necessary whenever
values of components are updated.
See also:
TYPE(T) opticalfunctions geometricfunctions

DISP A displays the nominal energy, energy deviation(DDP), longitudinal position(z), and emittances
for a transport line with accelerating cavities. The flag TRPT must be on.
See also:
TRPT RING elements CAVI specialvariables EMITX EMITY DP

ALL is a word to choose the entire beam line for the region to be displayed. If ALL is given, a dialog
at every 66 lines to control the output to the terminal is suppressed. Thus "DISP ALL e1 e2" works
to suppress the dialog for the output region e1 from e2.
See also:
region patternstring

DISP B displays the beam sizes and the projected Twiss parameters calculated either by Twiss parameters
or the EMIT command with the CODPLOT flag.
Example: EMITX=...; EMITY=...;DP=...;
BEAMSIZE(BEAM)
DISP B
See also:
BEAMSIZE(BEAM) EMITTANCE(EMIT) CODPLOT GAUSS UNIFORM specialvariables
EMITX EMITY DP

Display the difference between the reference optics. (beta  betaR)/betaR are displayed for BX, BY,
BZ.
See also:
referenceoptics REFERENCE(REF) DISPLAY(DISP) REFERENCE(RE)
Twiss OpticsPlot

DISP D displays all matchingfunctions in one line suitable to be read by a spreadsheet program.
See also:
opticalfunctions geometricfunctions matchingfunctioncommands

DISP GA displays gamma functions for x and y, instead of dispersions, as well as gamma*L, which is
nealry equal to the natural chromaticity.

DISP G displays geometric information of the beam line. It shows the geometry of the coordinate.
See also:
geometricfunctions matchingfunctioncommands OGEOMETRY(OG)

DISP OG displays geometric information at the orbit.
See also:
geometricfunctions matchingfunctioncommands GEOMETRY(G)

DISP O displays the orbits DX, DPX, DY, DPY together with the other
opticalfunctions.
See also:
opticalfunctions matchingfunctioncommands

The components in the current region can be selectively displayed by the DISP command using the patternstring.
The patternstring is a character string involving the wildcards to match the name of the components.
Note that the components are chosen in the current region, and the keyword ALL is necessary to extend
it to the entire beam line.
See also:
DISPLAY(DISP) wildcards components region ALL

DISP P displays the physical dispersions PEX, PEPX, PEY, PEP, together with the 1D optical parameters.
See also:
opticalfunctions matchingfunctioncommands

Region for DISPLAY(DISP) is specified as
DISP .... begin [end]
with begin and end having the form name[.order][{+}offset], or the component number (see components).
Example:
DISP ... QF.210 QD+5
DISP ... 100 200
displays functions starting at 10 elements upstream from the entrance of the second QF through 5
elements downstream from the entrance of the first QD. The region for DISP is kept after once set.
It is shown in the second part of the prompt when FFSPRMPT is ON, and also seen by the STATUS(STAT)
command.
If begin points to a component after end, DISP displays from begin to $$$, then from ^^^ to end.
ALL can be specified before the region. In such a case, the dialog for the output control is suppressed.
The components which match the patternstring in DISP are only chosen in the current region.
See also:
ALL patternstring components STATUS(STAT)

Specify the reference optics to be displayed.
See also:
referenceoptics REFERENCE(REF) DISPLAY(DISP) DREFERENCE(DRE)
Twiss OpticsPlot

DISP R displays the components of the xy coupling matrix R together with the 1D optical parameters.
See xycoupling.
See also:
xycoupling opticalfunctions matchingfunctioncommands

DISP Z displays muatching functions related to the Z plane: AZ BZ NZ DZ DDP ZX ZPX ZY ZPY GMZ , which
are obtained by CAL/GO with CALC6D.
See also:
extendedTwissparameters CALC6D CALC4D
Usage: DRAW [begin end] fun1 [fun2..] [& fun11 [fun12..]] [elementpattern]
draws a plot of optical functions in multi columns. It calls OpticsPlot internally. Available functions
are all matchingfunctions (except LENG, TRX, TRY, GX, GY, GZ, CHI1, CHI2, CHI3) and additional functions.
If functions are separated by ampersand (&), these are plotted in a separated window.
Function name preceded by "R" and "D" refer the reference optics and the difference, respectively.
If begin and endcomponents are specified, the plot region is limited between them. If the endcomponent
comes earlier than the begincomponents, it wraps the plot around the beam line.
If the optional elementpattern is given, it draws the beamline lattice with the labels for elements
which match elementpattern. If LAT is specified for elementpattern, the lattice is drawn without
label.
A character string assigned to TITLE is shown as the FrameLabel on the top of the plot.
Example:
TITLE="FCCee_t_202_nosol_16_ipac.sad";
Draw$Option={Thickness>2};
DRAW BX BY & EX EY Q*;
See also:
OpticsPlot specialvariables TITLE matchingfunctioncommands
OUTPUT(OUT) TERMINATE(TERM) GEO DISPLAY(DISP) wildcards

Draw$Option is a list of rules to specify Graphics options for the entire DRAW. If you need option
for each column, use OpticsPlot
See also:
DRAW OpticsPlot Graphics REFERENCE(REF)
Usage: DUMP componentpattern [componentpattern1..]
prints out the current machine errors of components which match componentpattern.
See also:
machineerrorcommands components wildcards
An element in FFS represents an object which has a unique name and several keywords with values.
This simulates a power supply of a magnet. An element has one or more components, which correspond
to individual magnets in a beam line. Each component may have different values from the values of
the corresponding element. This simulates the machine error which varies magnet to magnet
The value of an element can be saved to or recovered from the elementsavebuffer by SAVE or RESET
commands. Different beam lines can share the same element, and their values can be different to each
other, but they have the common elementsavebuffer. Therefore the value of an element can be transferred
between beam lines by SAVE and RESET command through the elementsavebuffer.
An element is created only in SAD MAIN level. In the definition, if a keyword is omitted, the
previous definition is unchanged. All keywords have the default value zero. In FFS, it is only possible
to change their values.
See also:
TYPE(T) setvalueofelement Element

An aperture. Only valid in tracking. A particle with
can pass through the aperture, otherwise it is lost and a message is printed out. If AX or AY is
zero (default), they are interpreted as infinity. If AX <=> 0 && AY <=> 0 and (DX1 == DX2 or DY1
== DY2) then the aperture is only determined by AX and AY.

A bending magnet.

The absolute face angle at the entrance. The effective face angle is E1 * ANGLE + AE1, and a positive
angle at the entrance corresponds to a surface with dx/ds > 0.
See also:
E1 AE2 ANGLE

The absolute faceangle at the exit to the bending angle. The effective face angle is E2 * ANGLE
+ AE2, and a positive angle at the exit corresponds to a surface with dx/ds < 0.
See also:
E2 AE1 ANGLE

The bending angle. If positive, it bends the orbit in xs plane toward negativexdirection. ANGLE
determines the geometry of the beam line, while K0 represents a dipole kick on top of the bending
angle given by ANGLE, i.e., the total deflection of the beam is given of ANGLE + K0.
See also:
K0

If nonzero, the nonlinear Maxwellian fringe is suppressed.

If nonzero, the synchrotron radiation in the particletracking is inhibited.
See also:
RAD

Additional rotation in xy plane to simulate a rotation error. DROTATE does not affect the geometry
of the ring.
See also:
DX DY ROTATE

Horizontal displacement of magnet. This applied before the rotation by ROTATE.
See also:
DY ROTATE DROTATE

Vertical displacement of magnet. This applied before the rotation by ROTATE.
See also:
DX ROTATE DROTATE

The ratio of the faceangle at the entrance to the bending angle. The effective face angle is E1
* ANGLE + AE1, and a positive angle at the entrance corresponds to a surface with dx/ds > 0. For
example, a symmetricallyplaced rectangular magnet has
E1 = 0.5 and E2 = 0.5.
See also:
AE1 E2 ANGLE

The ratio of the faceangle at the exit to the bending angle. The effective face angle is E2 * ANGLE
+ AE2, and a positive angle at the exit corresponds to a surface with dx/ds < 0. For example, a
symmetricallyplaced rectangular magnet has E1 = 0.5 and E2 = 0.5.
See also:
AE2 E1 ANGLE

Length of the slope of the field at the edge as:
By(s)  *******
 *
 *
*
*
*
* 
* 
*******+ s
 
<>
 F1 
Only the effects up to y^4 in Hamiltonian are taken into account. A more rigorous definition is
where integration is done over one fringe.
The transformation of the linear fringe of the entrance of a bend is
where f is the length of fringe given by F1, and rhob bending radius at the design momentum. At the exit, the sign of rhob is chang
ed. This linear fringe also changes the path length in the body of the bend as
to maintain the geometric position of the design orbit, i.e., you have to increase the bend field
a little bit to keep the orbit unchanged. Unlike a quadrupole, the effect of linear fringe is always
applied at both the entrance and the exit, otherwise you cannot obtain a circular design orbit.
Use FB1 and FB2 to specify the values of entrance and exit separately.
See also:
FRINGE FB1 FB2

F1 at the entrance. Actually F1 + FB1 is used at the entrance.
See also:
F1 FB2

F1 at the exit. Actually F1 + FB2 is used at the exit.
See also:
F1 FB1

When FRINGE is nonzero, the effect of the linear fringe F1 is taken into account both at the entrance and the exit.
The transformation of the linear fringe of the entrance of a bend is
where f is the length of fringe given by F1, and rhob bending radius at the design momentum. At the exit, the sign of rhob is chang
ed. This linear fringe also changes the path length in the body of the bend as
to maintain the geometric position of the design orbit, i.e., you have to increase the bend field
a little bit to keep the orbit unchanged. Unlike a quadrupole, the effect of linear fringe is always
applied at both the entrance and the exit, otherwise you cannot obtain a circular design orbit.
Use FB1 and FB2 to specify the values of entrance and exit separately.
See also:
F1

The normal dipole magnetic field component (times the length L).
where L is the effective length of the component. Positive sign means horizontal focusing.
See also:
L

The normal quadrupole magnetic field component (times the length L).
where L is the effective length of the component. Positive sign means horizontal focusing.
See also:
L

The effective length along the arc of the orbit.

Rotation in xy plane. After displacing the magnet by DX and DY, rotate the magnet around the local
saxis by (amount given by ROTATE), then place the component. At the exit rotate back the magnet
around the local saxis at the exit, then take out displacement.
See also:
DX DY DROTATE

The transformation of a bend depends on the value of K1. If K1 is zero, it is a series of transformations:
(transformation due to misalignments)
(drift to the entrance face)
(linear fringe at entrance face)
(nonlinear fringe at entrance)
(body of bend)
(nonlinear fringe at exit)
(linear fringe at exit face)
(drift from the exit face)
(transformation due to misalignments)
If K1 is nonzero, the effects from E1 and E2 are approximated by thin
quadrupoles. Then the body is subdivided into
1 + floor(sqrt(abs(K1 L')/(12 10^5 EPS)))
pieces (EPS = 1 is used when EPS = 0), and the bendbody transformation above is done for each piece
and the kick from K1 is applied alternatively. In FFS optics and Emittance calculations, or when
the synchrotron radiation is turned on, the same algorithm as K1 <> 0 is applied.
See also:
coordinates equilibriumbeamenvelope

Accelerating structure.

If nonzero, the Maxwellian fringe is suppressed. The effects of DISFRIN and FRINGE are summarized
as
DISFRIN=0 DISFRIN<>0
FRINGE=0 entr & exit none
FRINGE=1 entr none
FRINGE=2 exit none
FRINGE=3 entr & exit none
See also:
FRINGE

Relative phase offset. The stable synchrotron phase above the transition is near PHI = 0. The acceleration is given by
where ts is the equilibrium time determined by the valance between the acceleration and the radiation
loss around the ring. DPHI is not taken into account to determine the design momentum p0(s).
See also:
FREQ VOLT DVOLT V1 V20 V11

Additional accelerating voltage to be added to VOLT without affecting the design momentum.
See also:
VOLT

Horizontal displacement of magnet. This applied before the rotation by ROTATE.
See also:
DY ROTATE DROTATE

Vertical displacement of magnet. This applied before the rotation by ROTATE.
See also:
DX ROTATE DROTATE

Rf frequency. If this keyword is nonzero, the keyword HARM is ignored.
See also:
HARM

A harmonic number. This is valid only when FREQ is zero.
See also:
FREQ

The effective length.

Relative phase offset. The stable synchrotron phase above the transition is near PHI = 0. The acceleration is given by
where ts is the equilibrium time determined by the valance between the acceleration and the radiation
loss around the ring.
See also:
FREQ VOLT DVOLT V1 V20 V11

Rotation in xy plane. After displacing the magnet by DX and DY, rotate the magnet around the local
saxis by (amount given by ROTATE), then place the component. At the exit rotate back the magnet
around the local saxis at the exit, then take out displacement.
See also:
DX DY DROTATE

The y^2dependence of the acceleration. Tracking only.
See also:
VOLT DVOLT V1 V20 V11

The linear xdependence of the acceleration. Tracking only.
See also:
VOLT DVOLT V1 V11 V02

The xydependence of the acceleration. Tracking only.
See also:
VOLT DVOLT V1 V20 V02

Accelerating peak voltage in Volt.
where ts is the equilibrium time determined by the valance between the acceleration and the radiation
loss around the ring. (CAVI only) The nonrelativistic corrections
(VOLT+DVOLT)*(2 Pi FREQ/c)^2/(gamma beta)^2/4 are
automatically added to V20 and V02, respectively. The Lorentz factor is evaluated as inverse of average
of 1/(beta gamma) at the entrance and the exit.
CAVI includes the edge effect at the lowest order, given by a Hamiltonian at the entrance edge
at s0:
Hf =  (e (VOLT+DVOLT)/L)(Sin(omega t  dphi) + Sin(dphi)  offset) (x^2+y^2)/4 delta(ss0)
where dphi and offset are determined by the cavity phase and the radiation loss, which is nonzero
only in the case of NORAD. The sign flips at the exit. This Hamiltonian should be consistent with
what Kiyoshi Kubo derived.
See also:
DVOLT

An element for an arbitrary coordinate transformation. This element can be used to express an offaxis element.
Usage: COORD name=(DX=dx DY=dy CHI1=chi1 CHI2=chi2 CHI3=chi3 DIR=dir); .
If dir is zero (default), the transformation of the coordinate by COORD is
and if dir is nonzero,
where {x, y, z}_1 are the new coordinates and
Note that these transformationis are NOT the inverse to each other.
To use this element, you have to calculate the values of those parameters carefully. DISP G may
help you but there is no automatic way to get them. You may also have to be careful when you use
a line with this element in the reverse direction.
A better way to do an equivalent thing in most cases is to use SOL. Unlike COORD, SOL automatically
determines the parameters for the coordinate transformation.
See also:
SOL DISPLAY(DISP)

The default and available nondefault variable keywords are:
type defaultkeyword nondefault variable keyword
DRIFT L 
BEND ANGLE K1,K0,E1,E2
QUAD K1 ROTATE
SEXT K2 ROTATE
OCT K3 ROTATE
DECA K4 ROTATE
DODECA K5 ROTATE
MULT K1 K0,K2..K21,SK0,SK1,SK2..SK21,ROTATE,ANGLE
MARK  AX,BX,EX,EPX,AY,BY,EY,EPY,R1,R2,R3,R4,DETR,
DX,DPX,DY,DPY,DZ,DDP,AZ,BZ,ZX,ZPX,ZY,ZPY
See also:
keywords

A decapole magnet.

If nonzero, the nonlinear Maxwellian fringe is suppressed.

If nonzero, the synchrotron radiation in the particletracking is inhibited.
See also:
RAD

Horizontal displacement of magnet. This applied before the rotation by ROTATE.
See also:
DY ROTATE DROTATE

Vertical displacement of magnet. This applied before the rotation by ROTATE.
See also:
DX ROTATE DROTATE

The normal decapole magnetic field component (times the length L).
where L is the effective length of the component. Positive sign means horizontal focusing.
See also:
L

The effective length.

Rotation in xy plane. After displacing the magnet by DX and DY, rotate the magnet around the local
saxis by (amount given by ROTATE), then place the component. At the exit rotate back the magnet
around the local saxis at the exit, then take out displacement.
See also:
DX DY DROTATE


A dodecapole magnet.

If nonzero, the nonlinear Maxwellian fringe is suppressed.

If nonzero, the synchrotron radiation in the particletracking is inhibited.
See also:
RAD

Horizontal displacement of magnet. This applied before the rotation by ROTATE.
See also:
DY ROTATE DROTATE

Vertical displacement of magnet. This applied before the rotation by ROTATE.
See also:
DX ROTATE DROTATE

The normal dodecapole magnetic field component (times the length L).
where L is the effective length of the component. Positive sign means horizontal focusing.
See also:
L

The effective length.

Rotation in xy plane. After displacing the magnet by DX and DY, rotate the magnet around the local
saxis by (amount given by ROTATE), then place the component. At the exit rotate back the magnet
around the local saxis at the exit, then take out displacement.
See also:
DX DY DROTATE


A drift space.

The length, can be negative.

Radius of the vacuum chamber. Effective when SPAC is ON.
See also:
SPAC

The transformation of a drift is written as
with
See also:
coordinates

Available keywords are:
type keywords
DRIFT L RADIUS
BEND L ROTATE DROTATE DX DY ANGLE K0 K1 E1 E2 AE1 AE2 F1 FB1 FB2 FRINGE DISFRIN DISRAD EPS RANKICK
QUAD L ROTATE DX DY K1 F1 F2 FRINGE DISFRIN DISRAD EPS
SEXT L ROTATE DX DY K2 DISFRIN DISRAD
OCT L ROTATE DX DY K3 DISFRIN DISRAD
DECA L ROTATE DX DY K4 DISFRIN DISRAD
DODECA L ROTATE DX DY K5 DISFRIN DISRAD
MULT L DX DY DZ CHI1 CHI2 ROTATE(=CHI3) K0..K21 SK0..SK21 DISFRIN F1 F2 FRINGE DISRAD EPS VOLT
DVOLT HARM PHI DPHI FREQ RADIUS ANGLE E1 E2 AE1 AE2 DROTATE
SOL BZ DX DY DZ DPX DPY BOUND GEO CHI1 CHI2 CHI3 DBZ DISFRIN
CAVI L ROTATE DX DY VOLT DVOLT V1 V20 V11 V02 FREQ PHI HARM RANVOLT RANPHASE DISFRIN FRINGE
TCAVI L ROTATE DX DY K0 V1 FREQ PHI HARM RANKICK RANPHASE
COORD DX DY CHI1 CHI2 CHI3 DIR
MARK AX BX AY BY EX EPX EY EPY R1 R2 R3 R4 DETR DX DPX DY DPY DZ DDP AZ BZ NZ ZX ZPX ZY ZPY EMITX
EMITY DP AZ SIGZ GEO OFFSET
APERT DX1 DX2 DY1 DY2 DP AX AY DX DY
See also:
defaultkeyword setvalueofelement Element

MARK elements play special roles in FFS:
(1) The first element of the beam line must be a MARK element to be used by FFS. In this case the
MARK element contains the parameters of the incoming beam (see opticalfunctions, specialvariables
EMITX, EMITY, DP).
(2) The calculated optical parameters at a MARK command is saved by SAVE or STOP commands, then
it can be used as the incoming condition of other beam lines which have the same MARK element.
Example: MARK P1 = (EMITX = .. EMITY = .. DP = ..);
LINE A = ( .. P1 ..)
B = (P1 .. );
FFS USE = A;
... do matching on LINE A
SAVE P1 save the parameters at P1
USE B; switch to LINE B
... do matching of LINE B whose entrance is to be
matched P1.
(3) If a MARK element has keyword GEO nonzero, this MARK element becomes the origin of the geometric
rotation after the last SOL element.
(4) The values of opticalfunctions of the MARK element at the beginning of the beam line can be
specified as matching variables by the FREE command.
A MARK elements have all opticalfunctions as its keywords except NX, NY, TRX, TRY, and LENG. Also
it has keywords EMITX, EMITY, and DP which give the values of the corresponding specialvariables.
See also:
SAVE USE opticalfunctions SOL specialvariables EMITX
EMITY DP

OFFSET is a relative position from the current position. A fraction is allowed to specify a location
within an element.
If the MARK at the beginning of a beam line has OFFSET nonzero, the optics calculation starts
from the shifted location. If the last component of a beam line is a MARK with nonzero OFFSET, the
optics calculation stops at the shifted location. The periodic condition is applied between those
shifted locations.
The geometric origin and the origin of LENG shift to the first MARK.
Examples:
(1) LINE A = ( ... QF PQFC ... );
QUAD QF = (L=0.3 K1=0.2);
MARK PQFC = (OFFSET = 0.5);
Here PQFC represents the center of QF.
(2) LINE A = ( ... PQFC QF ... );
QUAD QF = (L=0.3 K1=0.2);
MARK PQFC = (OFFSET = 1.5);
Here PQFC represents the center of QF, too (consider why). The value of OFFSET is interpreted taking
the direction of the LINE into account, i.e., a MARK in a line A represents the same location in
a line A.
Restrictions:
(1) Function TrackParticles does not take OFFSET into account if the start
or stop location is in the midst of a beam line and a Mark with nonzero
OFFSET, in the current version. Tracking for entire beam line or
MEASURE(MEA) command supports OFFSET.
(2) The outputs by DISPLAY(DISP) outside of the narrowed region by OFFSET are
meaningless.

A magnet with multipoles. Note that the reference plane is defined so that the skew quadrupole component
becomes zero.
It can have a nonzero ANGLE to express a combined function bending magnet with multipoles. Note
that the definition of the multipoles with nonzero ANGLE is very special The current version does
not allow nonzero ANGLE inside a solenoid or with acceleration. Also the fringe field and emittance
calculation are not installed properly for nonzero ANGLE.
See also:
multipole_with_nonzero_ANGLE

The normal dipole magnetic field component (times the length L).
where L is the effective length of the component. Positive sign means horizontal focusing.
See also:
L

The skew dipole magnetic field component (times the length L).
where L is the length of the component. Positive sign means a horizontally focusing magnet rotated
around zaxis by 90/1 degree, i.e., ROTATE = 90 DEG .
See also:
L

The normal quadrupole magnetic field component (times the length L).
where L is the effective length of the component. Positive sign means horizontal focusing.
See also:
L

The skew quadrupole magnetic field component (times the length L).
where L is the length of the component. Positive sign means a horizontally focusing magnet rotated
around zaxis by 90/2 degree, i.e., ROTATE = 45 DEG .
See also:
L

The normal sextupole magnetic field component (times the length L).
where L is the effective length of the component. Positive sign means horizontal focusing.
See also:
L

The skew sextupole magnetic field component (times the length L).
where L is the length of the component. Positive sign means a horizontally focusing magnet rotated
around zaxis by 90/3 degree, i.e., ROTATE = 30 DEG .
See also:
L

The normal octupole magnetic field component (times the length L).
where L is the effective length of the component. Positive sign means horizontal focusing.
See also:
L

The skew octupole magnetic field component (times the length L).
where L is the length of the component. Positive sign means a horizontally focusing magnet rotated
around zaxis by 90/4 degree, i.e., ROTATE = 22.5 DEG .
See also:
L

The normal decapole magnetic field component (times the length L).
where L is the effective length of the component. Positive sign means horizontal focusing.
See also:
L

The skew decapole magnetic field component (times the length L).
where L is the length of the component. Positive sign means a horizontally focusing magnet rotated
around zaxis by 90/5 degree, i.e., ROTATE = 18 DEG .
See also:
L

The normal dodecapole magnetic field component (times the length L).
where L is the effective length of the component. Positive sign means horizontal focusing.
See also:
L

The skew dodecapole magnetic field component (times the length L).
where L is the length of the component. Positive sign means a horizontally focusing magnet rotated
around zaxis by 90/6 degree, i.e., ROTATE = 15 DEG .
See also:
L

The normal 14pole magnetic field component (times the length L).
where L is the effective length of the component. Positive sign means horizontal focusing.
See also:
L

The skew 14pole magnetic field component (times the length L).
where L is the length of the component. Positive sign means a horizontally focusing magnet rotated
around zaxis by 90/7 degree, i.e., ROTATE = 12.857142857142856 DEG .
See also:
L

The normal 16pole magnetic field component (times the length L).
where L is the effective length of the component. Positive sign means horizontal focusing.
See also:
L

The skew 16pole magnetic field component (times the length L).
where L is the length of the component. Positive sign means a horizontally focusing magnet rotated
around zaxis by 90/8 degree, i.e., ROTATE = 11.25 DEG .
See also:
L

The normal 18pole magnetic field component (times the length L).
where L is the effective length of the component. Positive sign means horizontal focusing.
See also:
L

The skew 18pole magnetic field component (times the length L).
where L is the length of the component. Positive sign means a horizontally focusing magnet rotated
around zaxis by 90/9 degree, i.e., ROTATE = 10 DEG .
See also:
L

The normal 20pole magnetic field component (times the length L).
where L is the effective length of the component. Positive sign means horizontal focusing.
See also:
L

The skew 20pole magnetic field component (times the length L).
where L is the length of the component. Positive sign means a horizontally focusing magnet rotated
around zaxis by 90/10 degree, i.e., ROTATE = 9 DEG .
See also:
L

The normal 22pole magnetic field component (times the length L).
where L is the effective length of the component. Positive sign means horizontal focusing.
See also:
L

The skew 22pole magnetic field component (times the length L).
where L is the length of the component. Positive sign means a horizontally focusing magnet rotated
around zaxis by 90/11 degree, i.e., ROTATE = 8.181818181818182 DEG .
See also:
L

The normal 24pole magnetic field component (times the length L).
where L is the effective length of the component. Positive sign means horizontal focusing.
See also:
L

The skew 24pole magnetic field component (times the length L).
where L is the length of the component. Positive sign means a horizontally focusing magnet rotated
around zaxis by 90/12 degree, i.e., ROTATE = 7.5 DEG .
See also:
L

The normal 26pole magnetic field component (times the length L).
where L is the effective length of the component. Positive sign means horizontal focusing.
See also:
L

The skew 26pole magnetic field component (times the length L).
where L is the length of the component. Positive sign means a horizontally focusing magnet rotated
around zaxis by 90/13 degree, i.e., ROTATE = 6.923076923076923 DEG .
See also:
L

The normal 28pole magnetic field component (times the length L).
where L is the effective length of the component. Positive sign means horizontal focusing.
See also:
L

The skew 28pole magnetic field component (times the length L).
where L is the length of the component. Positive sign means a horizontally focusing magnet rotated
around zaxis by 90/14 degree, i.e., ROTATE = 6.428571428571428 DEG .
See also:
L

The normal 30pole magnetic field component (times the length L).
where L is the effective length of the component. Positive sign means horizontal focusing.
See also:
L

The skew 30pole magnetic field component (times the length L).
where L is the length of the component. Positive sign means a horizontally focusing magnet rotated
around zaxis by 90/15 degree, i.e., ROTATE = 6 DEG .
See also:
L

The normal 32pole magnetic field component (times the length L).
where L is the effective length of the component. Positive sign means horizontal focusing.
See also:
L

The skew 32pole magnetic field component (times the length L).
where L is the length of the component. Positive sign means a horizontally focusing magnet rotated
around zaxis by 90/16 degree, i.e., ROTATE = 5.625 DEG .
See also:
L

The normal 34pole magnetic field component (times the length L).
where L is the effective length of the component. Positive sign means horizontal focusing.
See also:
L

The skew 34pole magnetic field component (times the length L).
where L is the length of the component. Positive sign means a horizontally focusing magnet rotated
around zaxis by 90/17 degree, i.e., ROTATE = 5.294117647058823 DEG .
See also:
L

The normal 36pole magnetic field component (times the length L).
where L is the effective length of the component. Positive sign means horizontal focusing.
See also:
L

The skew 36pole magnetic field component (times the length L).
where L is the length of the component. Positive sign means a horizontally focusing magnet rotated
around zaxis by 90/18 degree, i.e., ROTATE = 5 DEG .
See also:
L

The normal 38pole magnetic field component (times the length L).
where L is the effective length of the component. Positive sign means horizontal focusing.
See also:
L

The skew 38pole magnetic field component (times the length L).
where L is the length of the component. Positive sign means a horizontally focusing magnet rotated
around zaxis by 90/19 degree, i.e., ROTATE = 4.7368421052631575 DEG .
See also:
L

The normal 40pole magnetic field component (times the length L).
where L is the effective length of the component. Positive sign means horizontal focusing.
See also:
L

The skew 40pole magnetic field component (times the length L).
where L is the length of the component. Positive sign means a horizontally focusing magnet rotated
around zaxis by 90/20 degree, i.e., ROTATE = 4.5 DEG .
See also:
L

The normal 42pole magnetic field component (times the length L).
where L is the effective length of the component. Positive sign means horizontal focusing.
See also:
L

The skew 42pole magnetic field component (times the length L).
where L is the length of the component. Positive sign means a horizontally focusing magnet rotated
around zaxis by 90/21 degree, i.e., ROTATE = 4.285714285714286 DEG .
See also:
L

The normal 44pole magnetic field component (times the length L).
where L is the effective length of the component. Positive sign means horizontal focusing.
See also:
L

The skew 44pole magnetic field component (times the length L).
where L is the length of the component. Positive sign means a horizontally focusing magnet rotated
around zaxis by 90/22 degree, i.e., ROTATE = 4.090909090909091 DEG .
See also:
L

The absolute face angle at the entrance. The effective face angle is E1 * ANGLE + AE1, and a positive
angle at the entrance corresponds to a surface with dx/ds > 0.
See also:
E1 AE2 ANGLE

The absolute faceangle at the exit to the bending angle. The effective face angle is E2 * ANGLE
+ AE2, and a positive angle at the exit corresponds to a surface with dx/ds < 0.
See also:
E2 AE1 ANGLE

The bending angle. If positive, it bends the orbit in xs plane toward negativexdirection. ANGLE
determines the geometry of the beam line, while K0 represents a dipole kick on top of the bending
angle given by ANGLE, i.e., the total deflection of the beam is given of ANGLE + K0.
See also:
K0

If nonzero, the nonlinear maxwellian fringe is suppressed. The effects of DISFRIN and FRINGE are
summarized as
DISFRIN=0 DISFRIN<>0
Nonlinear Linear Nonlinear Linear
FRINGE=0 entr & exit none none none
FRINGE=1 entr entr none entr
FRINGE=2 exit exit none exit
FRINGE=3 entr & exit entr & exit none entr & exit
See also:
FRINGE

If nonzero, the synchrotron radiation in the particletracking is inhibited.
See also:
RAD

Relative phase offset. The stable synchrotron phase above the transition is near PHI = 0. The acceleration is given as
where ts is the equilibrium time determined by the valance between the acceleration and the radiation
loss around the ring. DPHI is not taken into account to determine the design momentum p0(s).
See also:
FREQ VOLT DVOLT V1 V20 V11

Additional accelerating peak voltage to be added to Volt, without affecting the design momentum p0(s).
See also:
VOLT

The ratio of the faceangle at the entrance to the bending angle. The effective face angle is E1
* ANGLE + AE1, and a positive angle at the entrance corresponds to a surface with dx/ds > 0. For
example, a symmetricallyplaced rectangular magnet has
E1 = 0.5 and E2 = 0.5.
See also:
AE1 E2 ANGLE

The ratio of the faceangle at the exit to the bending angle. The effective face angle is E2 * ANGLE
+ AE2, and a positive angle at the exit corresponds to a surface with dx/ds < 0. For example, a
symmetricallyplaced rectangular magnet has E1 = 0.5 and E2 = 0.5.
See also:
AE2 E1 ANGLE

The effects only in the first order of K1 is taken into account.
See also:
F2 FRINGE

The effects only in the first order of K1 is taken into account.
See also:
F1 FRINGE

Linear Fringe length F1 for the K0 component at the entrance.
See also:
BEND F1 FB1

Linear Fringe length F1 for the K0 component at the exit.
See also:
BEND F1 FB2

Rf frequency. If this keyword is nonzero, the keyword HARM is ignored.
See also:
HARM

The effects of the linear fringe (characterized by F1 and F2), and the nonlinear Mexwellian fringe
are controled as:
DISFRIN=0 DISFRIN<>0
Nonlinear Linear Nonlinear Linear
FRINGE=0 entr & exit none none none
FRINGE=1 entr entr none entr
FRINGE=2 exit exit none exit
FRINGE=3 entr & exit entr & exit none entr & exit
See also:
F1 F2 DISFRIN

A harmonic number. This is valid only when FREQ is zero.
See also:
FREQ

The effective length.

Misalignments of a MULT element are expressed by the keywords DX, DY, DZ, CHI1, CHI2, and ROTATE(=CHI3). They specify all misa
lignments of a rigid body, At the entrance of MULT, the coordinates of a particle are transformed as
where c1 and s1 are Cos[CHI1] and Sin[CHI1], etc. The inverse is applied at the exit.
Those misalignments are also valid within a solenoid.
Other straight elements such as QUAD or THIN do not and will not have these full misalignment
specifications, because they can be substituted by MULT.
The geometry of the design orbit is determined by the saved values of CHI1, CHI2, and DZ, while
the current values are used for DX, DY, and ROTATE.

The multipoles in MULT with nonzero ANGLE are defined by
Actually the summation is truncated at n + k <= 21 in the current version. While this definition
converges to the regular one for multipoles when ANGLE > 0, K0 and K1 of MULT are different from
those of BEND.
See also:
ANGLE

Relative phase offset. The stable synchrotron phase above the transition is near PHI = 0.
The acceleration is given as
where ts is the equilibrium time determined by the valance between the acceleration and the radiation
loss around the ring.

Radius of the vacuum chamber. Effective when SPAC is ON.
See also:
SPAC

Accelerating peak voltage in Volt.
where ts is the equilibrium time determined by the valance between the acceleration and the radiation
loss around the ring.
See also:
DVOLT

A octupole magnet.

If nonzero, the nonlinear Maxwellian fringe is suppressed.

If nonzero, the synchrotron radiation in the particletracking is inhibited.
See also:
RAD

Horizontal displacement of magnet. This applied before the rotation by ROTATE.
See also:
DY ROTATE DROTATE

Vertical displacement of magnet. This applied before the rotation by ROTATE.
See also:
DX ROTATE DROTATE

The normal octupole magnetic field component (times the length L).
where L is the effective length of the component. Positive sign means horizontal focusing.
See also:
L

The effective length.

Rotation in xy plane. After displacing the magnet by DX and DY, rotate the magnet around the local
saxis by (amount given by ROTATE), then place the component. At the exit rotate back the magnet
around the local saxis at the exit, then take out displacement.
See also:
DX DY DROTATE


A quadrupole magnet.

If nonzero, the nonlinear maxwellian fringe is suppressed. The effects of DISFRIN and FRINGE are
summarized as
DISFRIN=0 DISFRIN<>0
Nonlinear Linear Nonlinear Linear
FRINGE=0 entr & exit none none none
FRINGE=1 entr entr none entr
FRINGE=2 exit exit none exit
FRINGE=3 entr & exit entr & exit none entr & exit
See also:
FRINGE

If nonzero, the synchrotron radiation in the particletracking is inhibited.
See also:
RAD

Horizontal displacement of magnet. This applied before the rotation by ROTATE.
See also:
DY ROTATE DROTATE

Vertical displacement of magnet. This applied before the rotation by ROTATE.
See also:
DX ROTATE DROTATE

The effects only in the first order of K1 is taken into account.
See also:
F2 FRINGE

The effects only in the first order of K1 is taken into account.
See also:
F1 FRINGE

The effects of the linear fringe (characterized by F1 and F2), and the nonlinear Mexwellian fringe
are controled as:
DISFRIN=0 DISFRIN<>0
Nonlinear Linear Nonlinear Linear
FRINGE=0 entr & exit none none none
FRINGE=1 entr entr none entr
FRINGE=2 exit exit none exit
FRINGE=3 entr & exit entr & exit none entr & exit
See also:
F1 F2 DISFRIN

The normal quadrupole magnetic field component (times the length L).
where L is the effective length of the component. Positive sign means horizontal focusing.
See also:
L

The effective length.

Rotation in xy plane. After displacing the magnet by DX and DY, rotate the magnet around the local
saxis by (amount given by ROTATE), then place the component. At the exit rotate back the magnet
around the local saxis at the exit, then take out displacement.
See also:
DX DY DROTATE

The transformation in a QUAD is a sequence of:
(nonlinear fringe at entrance)
(linear fringe at entrance)
(body of quad)
(linear fringe at exit)
(nonlinear fringe at exit)
See also:
Hamiltonian 2ndorderHamiltonian solutionH2 solutiondH

A sextupole magnet.

If nonzero, the nonlinear Maxwellian fringe is suppressed.

If nonzero, the synchrotron radiation in the particletracking is inhibited.
See also:
RAD

Horizontal displacement of magnet. This applied before the rotation by ROTATE.
See also:
DY ROTATE DROTATE

Vertical displacement of magnet. This applied before the rotation by ROTATE.
See also:
DX ROTATE DROTATE

The normal sextupole magnetic field component (times the length L).
where L is the effective length of the component. Positive sign means horizontal focusing.
See also:
L

The effective length.

Rotation in xy plane. After displacing the magnet by DX and DY, rotate the magnet around the local
saxis by (amount given by ROTATE), then place the component. At the exit rotate back the magnet
around the local saxis at the exit, then take out displacement.
See also:
DX DY DROTATE


A solenoid. Unlike other elements, SOL elements inserted at boundaries or of a solenoid or at where
the field changes. Between SOL elements DRIFT, BEND(straight bend only), QUAD, and MULT elements
can be inserted. The longitudinal field of the solenoid overlaps on those elements.
In a SOL region, the coordinate is shifted on the axis of the solenoid, no matter how the design
orbit bends there. The xdirection of the coordinate in a solenoid is so chosen as to CHI3 = 0. At
the exit of a solenoid, the coordinate is shifted back to the design orbit, but the value of CHI3
is so determined as to set CHI3 zero at the nearest MARK element which has GEO = 1 after the exit.
The offset and orientation of the design orbit can be given by keywords DX, DY, DPX, DPY at a SOL
element with GEO = 1. SOL can be used to shift the coordinate to the actual orbit even without BZ.
It is useful to define the coordinate with magnets with DX and DY.
See also:
geometricfunctions MARK

BOUND = 1 must be given at both sides of the boundaries of a solenoid, otherwise SOL only specifies
the change of BZ

The longitudinal field of a solenoid. If a SOL is used with BOUND = 0 (default), only BZ is used
to change the field, and no coordinate transformation is applied.


An offset of the design ORBIT angle CHI1 relative to the solenoid axis at SOL with GEO = 1.
See also:
GEO DX DY DPY CHI1

An offset of the design ORBIT angle CHI2 relative to the solenoid axis at SOL with GEO = 1.
See also:
GEO DX DY DPX CHI2

An xoffset of the design ORBIT relative to the solenoid center at SOL with GEO = 1.
See also:
GEO DY DPX DPY

A yoffset of the design ORBIT relative to the solenoid center at SOL with GEO = 1.
See also:
GEO DX DPX DPY

The length of fringe of the solenoid field. It affects only the EMITTANCE calculation. If F1 = 0
(default), no radiation arises at the fringe.

One of boundaries (with GEO = 1) of a solenoid must have GEO = 1 to specify the alignment of the
design orbit. At a SOL element with GEO = 1, the design orbit is determined by DX, DY, DPX, DPY parameters
See also:
DX DY DPX DPY geometricfunctions DISPLAY(DISP) GEOMRTRY(G) OGEOMETRY(OG)
An expression in FFS consists of a symbol, constants, and operators.
>>> A symbol is a characters of any length starting with an alphabet or $.
>>> There are two kinds of constants, real number and characterstring.
real number is a number in fortranline format.
characterstring is a set of characters surrounded by "" or ''.
specialcharacters can be specified with backslash.
>>> Available operators are (in the order of the priority):
#,##,
?,
::,
@,
[],
++, ,
/@, //@, @@,
.,
^,
*, /,
+, ,
==, <>, >, <, >=, =>, <=, =<,
===, <=>,
~,
&&,
,
.., ...,
,
:,
>, :>,
/., //.,
+=, =, *=, /=,
&,
//,
/:,
=, :=, ^=, ^:=, =.
;,
{}
An operator with higher priority is operated first. An expression enclosed in () is evaluated first.
Most mathematical operations are threaded into a list, i.e., {a,b} + {c,d} gives {a + b,c + d}, etc.
Each operators can be used as a function using its name. For example, Plus[x,y] gives the same
result as x + y.
See also:
constants functions commandsyntax characterstring

operator for subtraction or unary minus.

operator for division.

a+=b is equivalent to a=a+b .

a  b  ... represents a pattern which matches one of patterns a, b, ...

a && b returns True(==1) when both a and b are nonzero real, False(==0) otherwise. b is not evaluated
when a is zero.

f@@a applies function f to subexpressions of a. f@@[a,level] specifies a levelspec to apply by level.
See also:
Apply

a ; b evaluates a, then evaluates b and returns its result.

a decrements a by 1, returning the old value of a. a decrements a by 1, returning the new value
of a.

a/=b is equivalent to a=a/b.

a . b returns the inner product of a and b.

a == b returns True(==1) if a and b are both Real with the same value or a String with same length
and value. If one of a or b is a list, or both are lists with same size, returns a list of elementwise
results.

a & is a purefunction whose argument is specified #, #n, ##, ##n.
See also:
Slot(#) SlotSequence(##) functions Function(&)

If both a and b are real, a > b returns True if a is greater than b, False otherwise. If one of a
or b is a list, or both are lists with same size, returns a list of elementwise results.

If both a and b are real, a => b returns True if a is greater than or equal to b, False otherwise.
If one of a or b is a list, or both are lists with same size, returns a list of elementwise results.

a++ increments a by 1, returning the old value of a. ++a increments a by 1, returning the new value
of a.

If both a and b are real, a < b returns True if a is less than b, False otherwise. If one of a or
b is a list, or both are lists with same size, returns a list of elementwise results.

If both a and b are real, a <= b returns True if a is less than or equal to b, False otherwise. If
one of a or b is a list, or both are lists with same size, returns a list of elementwise results.

{a,b,c...} is a list structure.

f/@a maps function f to subexpressions of a. f/@[a,level] specifies a levelspec of map by level.
See also:
Map

f//@a maps function f to all subexpressions of a. f//@[a,Heads>True] maps including the heads of
a and its subexpressions.

f@a refers the member a of an instance or a class f. Otherwise it is same as f[a]. f@g@h means (f@g)@h,
and f@g[h] (f@g)[h].

symbol::tag returns a message associated with symbol and tag
symbol::tag = message sets a message identified by symbol

~a returns True(==1) when a is zero, False(==0) when a is a nonzero real.

a  b returns True(==1) when a is nonzero real or b is nonzero real, False(==0) otherwise. b is
not evaluated when a is nonzero.

a[[b,..]] is a subexpression of an expression a.
If an index is omitted or Null like as a[[,b]], Part returns a list of elements whose corresponding
index takes the entire range. For instance,
{{1, 2}, {3, 4}, {5, 6}}[[,2]] gives {2, 4, 6}.
See also:
Part

pattern?test matches to an object which matches pattern then test[object] gives True.

a + b returns the sum of a and b. If one of a or b is a list, or both are lists with same size, returns
a list of elementwise results.

a ^ b returns the power of a to b. If one of a or b is a list, or both are lists with same size,
returns a list of elementwise results.

p.. matches sequence of one ore more expressions, each matching p.

p... matches sequence of zero ore more expressions, each matching p.

expr/.rule replaces all subexpressions of expr using rule.

expr//.rule replaces all subexpressionso of expr using rule, while a replacement is performed.

pattern>expr represents a rule for ReplaceAll.

pattern:>expr represents a rule for ReplaceAll, where expr is kept unevaluated until the replacement.
See also:
Literal

a === b returns True(==1) if a and b have the same type and same value, False(==0) otherwise.

a[b,c,..] means a list of b, c,.. with the head a. It is evaluated as a functionreference when a
is a function or a definedfunction. When a is a list with head List, it is interpreted as a part
specification of a list. When a is a characterstring, it is interpreted as a substring specification.
When a is an operator, it is an expression b (a) c (a) .. . When a is Null, it means a sequence.

a = value sets the value b to the symbol a. {a,b,..}={v1,v2,..} sets a,b,c simultaneously. a[b,c,..]=v1
sets the part of a[b,c,..] if a is a list. a[b,c,..] = expression defines the value a[b,c,..] if
a is not a list.

same as Set but the right hand side is not evaluated when it is set.
See also:
Set(=)

a // b converts a and b to characterstrings, then join them.
See also:
StringJoin

a=b is equivalent to a=ab .

symb/:lhs = rhs sets rhs to lhs, associated with symbol symb. symb/:lhs := rhs sets rhs to lhs unevaluated,
associated with symbol symb. symb/:lhs =. unsets lhs, associated with symbol symb.

a * b returns the product of a and b. If one of a or b is a list, or both are lists with same size,
returns a list of elementwise results.

a*=b is equivalent to a=a*b .

a <> b returns True(==1) if a and b are both Real with different values or a String with different
length or values. If one of a or b is a list, or both are lists with same size, returns a list of
elementwise results.

a <=> b returns True(==1) if a and b have the different types or different values. False(==0) otherwise.

a=. clears the definition assigned to a.
See also:
Clear
Usage: IF expr1 body1 [ELSEIF expr2 body2 [ELSEIF ..]] [ELSE body3] ENDIF
This is a FORTRAN77 like IFstructure. If the expression expr1 is True(==1) or nonzero, executes
commands in body1. If it is False(==0), skip commands until ELSE, ELSEIF or ENDIF appears at the
same level of the IFstructure, and executes commands after ELSE or ENDIF, or executes the ELSEIF
command. If expr1 is not a real number, an error message is printed and ignores the command line.
See also:
If ELSEIF ENDIF
Usage: IF expr1 body1 [ELSEIF expr2 body2 [ELSEIF ..]] [ELSE body3] ENDIF
This is a FORTRAN77 like IFstructure. If the expression expr1 is True(==1) or nonzero, executes
commands in body1. If it is False(==0), skip commands until ELSE, ELSEIF or ENDIF appears at the
same level of the IFstructure, and executes commands after ELSE or ENDIF, or executes the ELSEIF
command. If expr1 is not a real number, an error message is printed and ignores the command line.
See also:
IF ELSE ENDIF
Usage: (1) EMIT
(2) EMIT dp
(1) EMIT calculates the closed orbit, the normal coordinate, and the equilibrium emittance assuming the current beam line is a posi
tron ring. One of EMITTANCE(EMIT), the Emittance[] function, or the EMIT command in the MAIN level are necessary to be done in prio
r to multiturn tracking. See multiturntracking.
(2) EMIT dp, where dp is df_rf/f_rf/(alpha_p == momentum compaction), does EMIT for five rf frequencies:
then prints out a table of the dependences of various quantities on the frequency shift.
The results of EMITTANCE(EMIT) are affected by flags COD, RADCOD, RFSW, INTRA, WSPAC, EMIOUT,
CODPLOT and specialvariables MOMENTUM, CHARGE, FSHIFT, MINCOUP, PBUNCH. The flag TRPT or RING affects
only Emittance[], as EMITTANCE(EMIT) automatically set RING.
EMITTANCE(EMIT) returns the equilibrium emittances in variables EMITX, EMITY, EMITZ, and the equilibrium
bunch length in SIGZ, the relative momentum spread in SIGE, and the longitudinal equilibrium position
DTSYNCH.
The map used in EMIT is slightly different from that used in the tracking. For instance, the edge
angle of a bend is approximated by a thin quad. If the edge angle is large and the curvature is small,
EMIT may give a wrong answer. This will be corrected in near future.
See also:
multiturntracking extendedTwissparameters COD RADCOD
RFSW INTRA EMIOUT WSPAC CODPLOT TRPT MOMENTUM CHARGE FSHIFT
MINCOUP PBUNCH EMITX EMITY EMITZ SIGE SIGZ DTSYNCH Emittance
equilibriumbeamenvelope
Closes the current outputstream and set the output stream to the standard output(6). It also suspends
all the input streams and switches to the standard input(5). Since this command affects all input
and output streams, you may consider to use TERMINATE(TERM) or CLOSE(CLO) to suspend or close them
selectively.
See also:
TERMINATE(TERM) CLOSE(CLO) INPUT(IN) READ OUTPUT(OUT)
APPEND(APP)
Usage: IF expr1 body1 [ELSEIF expr2 body2 [ELSEIF ..]] [ELSE body3] ENDIF
This is a FORTRAN77 like IFstructure. If the expression expr1 is True(==1) or nonzero, executes
commands in body1. If it is False(==0), skip commands until ELSE, ELSEIF or ENDIF appears at the
same level of the IFstructure, and executes commands after ELSE or ENDIF, or executes the ELSEIF
command. If expr1 is not a real number, an error message is printed and ignores the command line.
See also:
IF ELSE ELSEIF
Usage: EXEC characterstringexpression
executes the characterstringexpression as FFS commands.
See also:
expression FFS ToExpression
EXPAND distributes all variable keys to each corresponding components. Individual deviations (machine
errors) are cleared.
See also:
GO CALCULATE(CAL) EMITTANCE(EMIT)
Usage: [NO]flag
turns the flag on. If NO is prepended to flag, the flag is turned off. Some flags have antonym which
works in the opposite way. Flags can be accessed in the functionsyntax with the form ?flag, which
returns True (=1) when the flag is on, or False (=0) otherwise. Some flags can be accessed by the
ON/OFF commands at the MAIN level.
Status of all flags are displayed by the STATUS(STAT) command.
See also:
STATUS(STAT) PatternTest(?)

ABSW or NORELW sets the weights of variable elements independent from their values in the matching.
Otherwise they are weighted relatively.
See also:
RELW

BIPOL or NOUNIPOL allows the change of sign of the value of the element during the matching. It affects
the default keywords of all elements. This is overridden by MIN, MAX specification or VariableRange
of each element.
See also:
UNIPOL defaultkeyword setvalueofelement VariableRange

If CALC4D is on, the optics calculation in CAL and GO performs a 4x5 calculation (4D + dispersion).
The antonyms is CALC6D. The Default is CALC4D.
See also:
CALC6D CALCULATE(CAL) GO

If CALC6D is on, the optics calculation in CAL and GO performs full 6D calculation, which may takes
RADCOD into account. The antonyms is CALC4D. The Default is CALC4D.
See also:
CALC4D CALCULATE(CAL) GO

CELL or NOINS sets the periodic condition in calculating the opticalfunctions.
See also:
INS CALCULATE(CAL) GO opticalfunctions matchingfunctioncommands

CMPLOT enables the shift of the center of mass at the beginning of the tracking. This is almost obsolete.

COD turns on finding the closedorbit in the emittance calculation. Accessible in MAIN level.
See also:
EMITTANCE(EMIT)

CODPLOT lets the emittance calculation return the information on the closedorbit, extended Twiss
parameters, and the beam size along the beam line into the FFS optics buffer, which can be shown
by DISPLAY(DISP) or DRAW commands as well as Twiss and OpticsPlot functions.
See also:
EMITTANCE(EMIT) DISPLAY(DISP) DRAW WSPAC RADTAPER

CONV is a flag set by the CALCULATE(CAL) or GO commands. It becomes True when MatchingResidual is
less than CONVERGENCE.
See also:
CALCULATE(CAL) GO MatchingResidual CONVERGENCE

When CONVCASE is on, FFS command line parser converts the input characters to the upper case.(Default
on) CONVCASE actions for the element names and patterns CAN be overridden by PRSVCASE flag.
See also:
PRSVCASE

DAMPONLY is the antonym of FLUC.
See also:
FLUC

DAPERT enables the DAPERT procedure in the multiturn tracking to obtain the dynamic aperture diagram.
Accessible in the MAIN level.
See also:
functions DynamicApertureSurvey

In the case of CELL, if the total tune deviates across a difference resonance, it is counted as unstable.
The default is NODIFFRES.
See also:
INTRES HALFRES SUMRES STABLE

ECHO enables the echo of the main input in the MAIN level.

EMIOUT turns on the extended output of emittance calculation.
Accessible in the MAIN level.
See also:
EMITTANCE(EMIT)

When FFSPRMPT is off(default) the input prompt is In[n]:= , where n is $Line+1. Otherwise the prompt
is the traditional FFS prompt, showing the FIT location and the DISP range.
See also:
$Line LOG

FIXSEED or NOMOVESEED disables the change of the seed of the random number generator after the particle
tracking.
See also:
MOVESEED MEASURE(MEA) SEED

FLUC or NODAMPONLY enables the diffusion due to synchrotron radiation in the particle tracking. Otherwise
only the damping is enabled when RAD is ON.
See also:
DAMPONLY RAD RADCOD

GAUSS or NOUNIFORM sets the momentum distribution of the incoming beam to be Gaussian, otherwise
uniform(square) distribution is assumed. It affects the beam size calculated by Twiss parameters.
See also:
UNIFORM MEASURE(MEA) BEAMSIZE(BEAM) specialvariables
DP

When GEOCAL is on(default), the geometry of the beam line is always updated by CALCULATE(CAL) or
GO commands using the current values of components. The coordinate transformation by SOL is also
updated. When GEOCAL is off, the geometry is never updated. It is useful to simulate misalignments
within a solenoid, etc.
See also:
GEOFIX CALCULATE(CAL) GO SOL

GEOFIX is the antonym of GEOCAL.
See also:
GEOCAL

In the case of CELL, if the total tune deviates across a halfinteger resonance, or the traces is
less than 2, it is counted as unstable (~?STABLE). Otherwise the optics is recognized as STABLE.
The default is HALFRES.
See also:
INTRES SUMRES DIFFRES STABLE

IDEAL or NOREAL inhibits to use the componentspecific deviations in the optics calculation.
See also:
REAL CALCULATE(CAL) GO

INS is the antonym of CELL.
See also:
CELL

INTRA turns on the calculation of intrabeam scattering in the emittance calculation. Accessible
in MAIN level.
See also:
EMITTANCE(EMIT) Emittance equilibriumbeamenvelope

In the case of CELL, if the total tune deviates across an integer resonance, or the trace is larger
than 2, it is counted as unstable (~?STABLE). Otherwise the optics is recognized as STABLE. The default
is INTRES.
See also:
HALFRES SUMRES DIFFRES STABLE

JITTER or NOQUIET allows jitter of the centerofmass of the incoming beam in the case of TRPT. Otherwise
the centerofmass statistically fluctuates depending on the number of particles.
See also:
QUIET MEASURE(MEA) TRPT

LOG enables the echo of all inputs in the MAIN level. Also suppresses the prompt in FFS.
See also:
ECHO

If LOSSMAP is on, TrackParticles returns the location and turn where the particle lost is detected,
in the 7/9th and 8/10th element of the result, for NOPOL/POL, respectively. The default is NOLOSSMAP
See also:
TrackParticles POL

LWAKE turns on optics calculation with Longitudinal WakeFunction
See also:
WakeFunction TrackParticles InitialOrbits TWAKE

MOVESEED is the antonym of FIXSEED.
See also:
FIXSEED

When PHOTONS is ON (default is OFF), with RAD and FLUC, TrackParticles generates a list of all photons
radiated through the tracking. The list is assigned to a symbol PhotonList.
See also:
PhotonList TrackParticles RAD FLUC

POL turns on spin tracking and the calculation of equilibrium polarization in EMIT/Emittance[].
See also:
RADPOL EMITTANCE(EMIT) Emittance TrackParticles

When PRSVCASE is on, FFS command line parser preserves the input characters for the element names
and patterns.(Default off)
See also:
CONVCASE

When on, performs spacecharge simulation in a "ParticleInCell" method. PSPAC is effective in tracking
only.
Do not confuse PSPAC with SPAC/WSPAC.
See also:
PSPACNX PSPACNY PSPACNZ PSPACDX PSPACDY PSPACDZ

QUIET is the antonym of JITEER.
See also:
JITTER

RAD turns on the synchrotron radiation in the particletracking. Accessible in the MAIN level.
See also:
RADCOD FLUC

RADCOD turns on the energy loss due to synchrotron radiation at the closedorbit in the emittance
calculation. Also turns off the implicit acceleration in the tracking to compensate the energy loss
automatically, in the case that TRPT is ON. Accessible in MAIN level.
See also:
RAD FLUC TRPT

When RADLIGHT is on, the function TrackParticles returns a list of trajectories which are used to
calculate the synchrotron radiation field.
See also:
TrackParticles RadiationField RadiationSpectrum

If POL is on, RADPOL turns on SokolovTernov effect in tracking.
See also:
POL

Scales all magnets except for solenoids according to the local momentum (DDP) of the closed orbit.
It uses the average of DDPs at the entrance and the exit. For tracking, RADCOD and ( CAL/GO with
CALC6D or EMIT(Emittance[]) ) is necessary. CAL/GO with CALC4D will clear the necessary information
for tracking with RADTAPER.
RADTAPER sets the momentum deviation of the closed orbit to DP0, which is an arbitrary choice of
an underdeterministic problem of tapering. Thus the difference in the path length around the ring
is adjusted by automatically updating FSHIFT.
See also:
RADCOD CALC6D CALC4D EMITTANCE(EMIT) CALCULATE(CAL) GO
DP0 FSHIFT

REAL is the antonym of IDEAL.
See also:
IDEAL

RELW is the antonym of ABSW.
See also:
ABSW

RFSW turns on the acceleration by CAVI and TCAVI element in the particletracking and the emittance
calculation. Accessible in MAIN level, but FFS always turns RFSW on at the beginning of the session.

RING is the antonym of TRPT.
See also:
TRPT

When on with WSPAC, in tracking, the space charge force is calculated relative to the center of mass
of the current set of particles each time. Otherwise(default) it is calculated relative to the closed
orbit given by EMIT. SELFCOD is useful when the closed orbits given by EMIT and TRACK are different.
See also:
WSPAC

SORG sets the origin of S (design orbit length) at the location set by ORG.
See also:
ORG

When SPAC is on, tracking is done with space charge effect. The actual number of particles in the
beam and the number of macro particles are given by PBUNCH and NP, respectively. This calculation
assumes a cylindrical symmetry of the chamber whose radius is given by RADIUS of DRIFT and MULT elements.
If RADIUS is positive, an aperture is also set at RADIUS to make particle loss. If RADIUS is zero,
no space charge calculation is done. If RADIUS is negative, no space charge effect is taken, but
the aperture is set at RADIUS.
Do not confuse SPAC with WSPAC.
See also:
NP PBUNCH WSPAC

STABLE is a flag set by the CALCULATE(CAL) or GO commands in the case of CELL. It becomes True when
the closed orbit is found and the optics is stable in both x and y.
See also:
CALCULATE(CAL) GO INTRES HALFRES SUMRES DIFFRES

In the case of CELL, if the total tune deviates across a sum resonance, it is counted as unstable.
The default is SUMRES.
See also:
INTRES HALFRES DIFFRES STABLE

If OFF, SUSPEND(SUSP) and END commands have no action. The default is ON.
See also:
SUSPEND(SUSP) END

TRPT or NORING declares that the beam line is a transport line, not a part of a storage ring. The
nominal momentum be changed in the beam line due to acceleration. The default momentum distribution
becomes uniform distribution. The default is RING or NOTRPT. TRPT affects Emittance[] to ignore equilibrium
calculation for a transport line.
See also:
DISPLAY(DISP) RING UNIFORM GAUSS

TWAKE turns on optics calculation with Transverse WakeFunction
See also:
WakeFunction TrackParticles InitialOrbits LWAKE

UNIFORM is the antonym of GAUSS. It assumes the momentum distribution to be a uniform(square) within
+DP.
See also:
GAUSS TRPT

UNIPOL is the antonym of BIPOL.
See also:
BIPOL

UNSTABLE is the antonym of STABLE.
See also:
STABLE

When on, performs spacecharge simulation in a "strongweak" mode. The beam size through the beam
line is to be calculated by EMIT with CODPLOT. The spacecharge force is calculated assuming Gaussian
distribution in all dimensions, and particles/bunch given by PBUNCH. WSPAC is effective in optics
and emittance calculations and tracking.
Do not confuse WSPAC with SPAC.
See also:
EMITTANCE(EMIT) PBUNCH CODPLOT MINCOUP SELFCOD SPAC equilibriumbeamenvelope
FFS functions:
Constants:
Degree GoldenRatio I INF* Infinity NaN* Pi SpeedOfLight
Elementaryfunctions:
ArcCos ArcCosh ArcSin ArcSinh ArcTan ArcTanh Cos Cosh Exp Log Sin Sinh
Sqrt Tan Tanh
Specialfunctions:
BesselI BesselJ BesselK BesselY BesselJZero Erf Erfc Factorial
Gamma LogGamma LogGamma1 GammaRegularized GammaRegularizedQ*
GammaRegularizedP* GaussianCoulomb* GaussianCoulombU*
GaussianCoulombFitted* LegendreP*
Numericalfunctions:
Abs Ceiling Floor Max Min MinMax* Mod Negative NonNegative Positive
Round Sign FractionalPart
Matrixoperations:
Det Eigensystem IdentityMatrix Inner LinearSolve Outer SingularValues*
Transpose
Randomnumber:
GaussRandom* Random* SeedRandom
Complex:
Arg Complex ComplexQ Conjugate Im Re
Rational:
Rational FromRational ContinuedFraction FromContinuedFraction SmallPrime
Numerator Denominator
FourierTransformation:
Fourier InverseFourier
DataManipulation:
FindRoot Fit* NIntegrate* PolynomialFit* Spline*
Calculus:
D NIntegrate
Minimization:
DownhillSimplex*
Listmanipulations:
Append Complement Delete Depth Difference* Dimensions Drop Extract Flatten
FlattenAt HeldPart Insert Intersection Join Length Part Partition Prepend
Product Range ReplacePart Rest Reverse RotateLeft RotateRight Select
Sort Sum Take Table Union
Characterstrings:
FromCharacterCode CharacterPosition Characters DigitQ LetterQ StringDrop
StringFill* StringInsert StringLength StringPosition StringTrim*
Symbol SymbolName ToCharacterCode ToLowerCase ToUpperCase ToExpression
FunctionalOperations:
Apply Cases Count DeleteCases Identity FixedPoint* FixedPointList*
Fold Function Level Map MapAll MapAt MapIndexed MapThread Nest Position
Replace Scan ScanThread* SelectCases* SwitchCases* Thread
Objectoriented programing and context:
Begin BeginPackage Class* End EndPackage
FlowControl:
Break Catch Check Continue Do For Goto If Label Return Switch Throw Which
While
Tests:
AtomQ ComplexQ DirectoryQ* EvenQ FileQ* MatchQ MatrixQ MemberQ NearlySameQ*
Negative NonNegative NumberQ OddQ Order Positive RealQ StringQ* VectorQ
BoundQ* FBoundQ*
Input/Output:
Close Flush* Get OpenRead OpenWrite OpenAppend Print Put Read ReadString SeekFile*
Short* StringToStream Write WriteString
File System:
CopyDirectory CopyFile CreateDirectory DeleteDirectory DeleteFile
DirectoryName FileByteCount FileDate FileNames FileType
RenameDirectory RenameFile SetFileDate ToFileName
Scoping:
Block Module With*
Attributes:
Attributes* Clear Evaluate Head Hold Literal Protect ReleaseHold
SetAttributes* Unevaluated Unprotect
GUI Widget:
Window* PanedWindow* Frame* LabelFrame* Canvas* TextLabel* TextMessage*
Button* CheckButton* RadioButton* Menu* OptionMenu* MenuButton*
Entry* SpinBox* ListBox* ScrollBar* Scale* TextEditor*
Graphics:
BeamPlot* ColumnPlot* HistoPlot* ListContourPlot ListDensityPlot
ListPlot Plot Show FitPlot* GeometryPlot* OpticsPlot* TkPhotoPutBlock*
System Interface:
Directory Environment GetEnv* GetGID* GetPID* GetUID* ProcessStatus*
SetDirectory SetEnv* System* TemporaryName* MkSecureTemp* RealPath*
Multiprocessing:
BiPipe* Fork* OpenShared* Shared* Wait*
Utilities:
Date DateString* Definition* FromDate* ToDate ToDateString* Pause
MemoryCheck* Message Off On Sleep TimeUsed Timing TracePrint
Functions listed above work basically in the same way as Mathematica's
except those marked by *.
FFSdedicatedfunctions:
BeamMatrix CalculateOptics DynamicApertureSurvey Element Emittance FFS
FitValue FitWeight GeoBase LINE OptimizeOptics OrbitGeo RadiationField
RadiationSpectrum SymplecticJ SetElement TrackParticles Twiss VariableRange
SynchroBetaEmittance TouschekLifetime WakeFunction
Beamlinefunctions:
BeamLine BeamLineName ExtractBeamLine PrintBeamLine WriteBeamLine
See also:
expression constants physicalconstants beamlinefunctions


Usage: Fit[data, expr, var,
{par1, ini1, [{min1, max1}] }, .. ,{parn, inin, [{minn, maxn}]},
[options..] ]
performs a nonlinear fitting of data with an expression expr.
data: list of {xi,yi}, {xi,yi,dyi}, or {xi,yi,dxi,dyi}, where dxi and dyi
are the standard deviation of the ith point.
expr: an expression containing var as the xvariable, and
parameters par1,..,parn explicitly. Use Evaluate[fun] if an implicit
expression is necessary.
var: a symbol to express the xaxis variable.
par: parameter symbol to be varied in the fitting.
ini: initial value of the parameter. It must be specified.
(min, max}: optional range of parameter.
Fit returns the result as a list:
{par1 > v1, .., parn>vn, ChiSquare > chisq, GoodnessOfFit > good,
ConfidenceInterval > {c1, .., cn}, ConvarianceMatrix > cov},
where v1,..,vn are the values of the parameters which minimizes chisquare, chisq is the resulting
minimum value of the total chisquare (when no error is given for yi, variance is returned), good
is a number given by GammaRegularized[(ndatanpara)/2,chisq/2] to represent the goodness of the fit,
c1, .., cn are the estimated errors in parameters, and cov is the covariance matrix. A typical criterion
of the goodness is (good > 0.1).
Options are
MaxIterations Maximum number of iterations.
D If True (default), tries to use analytical derivative.
Cutoff If nonzero, set the saturation point for each data as:
chisuare = Sum_i ( Min[Cutoff, Max[Cutoff, (d_i  f_ i) / sigma_i]]^2 ) ,
which is a sort of robust MEstimates. By Cutoff, the fit
tends to ignore tail data which are beyond Cutoff.
If Cutoff is zero (default), it is ignored.
See also:
FitPlot

Obtain the emittance, beta, alpha, etc. from data of particles x and px using FitGaussian.
FitEmit[x, px] ,
where x and px are the lists of data of the particles in the phase space, returns a list
{{xmean, pxmean, alpha, beta, emittance},
{xmean, pxmean, alpha, beta, emittance}_conf},
where the second component is the confidence intervals of the results.
See also:
FitGaussian

Performs Gaussian fit of 1D list data:
FitGaussian[data, [opt, ...]]
returns a list
{sigma, mean, {sigma_conf, mean_conf}, chisq} ,
where sigma_conf and mean_conf are the confidence interval of the results sigma and mean, respectively.
The arguments opt... are options for Fit. If Plot > True is specified as the option, a plot of the
fitting will be made.
See also:
Fit FitEmit

NIntegrate returns numerical integration of a Real or Complex
function
Usage: NIntegrate[f, {x, x0, x1}, options]
where f is a function containing Symbol x as the independent variable. The integral range is from
x0 and x1. The function f must contain the symbol x explicitly.
Options Default Description

AccuracyGoal 1e13 Relative accuracy
InitialPoints 20 Number of initial points where
the function is evaluated.

Usage: PolynomialFit[data, n]
performs a 1D linear regression of data.
data: list of {xi,yi}
n: the order of the polynomial
Fit returns the result as a list:
{{c0, .., cn}, {Residual > res}} ,
where c0 .. cn are the coefficients of the fitted polynomial, y = c0 + c1 x + .. + cn x^n . Res is
the rms residual of the fit.
See also:
FitPlot

Spline returns data for cubicspline interpolation.
Usage: sp = Spline[list, [Derivative>{dy1,dy2}] ]
where list contains data in the form as {{x1,y1}, ..} or {{x1,{y11, y12, ..}}, ..}.
Complex number can be allowed for y, but not for x.
This spline assumes y''=0 at the boundary, unless Derivative>{dy1,dy2} is specified to constrain
the derivative at each end to dy1 or dy2. They can be Null to unspecify the constraint at one of
the boundary. The resulting data of the spline is assigned sp as a SplineData object. Then one can
calculate the interpolated data by
sp[x] value of y at x.
Derivative[1][sp][x] value of y' at x.
Derivative[2][sp][x] value of y'' at x.
Integrate[sp[x],{x, x0, x1}] integral of sp[x] from x0 to x1.
Example:
sp=Spline[{{1,2},{3,5},{4,2},{5,7}}];
Plot[{sp[x],Derivative[1][sp][x],Derivative[2][sp][x],Integrate[sp[y],{y,1,#}]&[x]}, {x,1,5},
FrameLabel>{"x"}, Thickness>2, Legend>{"sp[x]","sp'[x]","sp''[x]","Int sp[x]"}];
Update[];
See also:
definingfunctions Plot NIntegrate

Usage: DownhillSimplex[initial, f, options]
minimizes a function f by the downhill simplex method, starting from an initial simplex initial.
Suppose f is a function of n variables. Then initial is a list of n+1 elements, each of which
is a list of the form
{f[vi], vi} ,
where vi is a list of n values corresponding to each variable. The initial must be sorted in ascending
order of f, i.e.,
initial=Sort[Map[{f[#],#}&,vlist]]
generates initial from a list of variables vlist.
DownhillSimplex returns the final simplex in the same form as initial.
Options:
VariableRange > {{min1 .. minn}, {max1 .. maxn}} gives the range of n
variables. The default is Infinity to Infinity for all variables.
MaxIteration > maxi gives the limit of number of iterations. The
default is Max[100, 10*(n+1)].
Output > lfn sets the output file number for the intermediate results.
the default is 6 (stdout).
Tolerance > tol sets the tolerance to judge the local minimum.
If (fmaxfmin)/(abs(fmax)+abs(fmin)) becomes less than tol, the
iteration loop terminates. The default is 10^6.
Examples:
f:=Apply[Function[{x,y},((x^2+y^2)1)*(x^2+y^2)(x.5)/3.],#]&;
v={{1.,1.},{0.,1.},{0.,1.}};
limit={{0.5,1.5},{0.65,1.5}};
p=Sort[Map[{f[#],#}&,v]]
DownhillSimplex[p,f,MaxIteration>100,
Tolerance>1e4,VariableRange>limit]
See also:
FFSdedicatedfunctions:OptimizeOptics


Apply[f, x [, level]] or f@@x [f@@[x, level]]
takes the bod of a list x as the argument sequence of f, and returns the result:
f@@{a, b, c} ===> f[a, b, c]
An optional argument specifies the levelspec.
See also:
Apply (@@) Map Scan MapThread levelspec

Cases[l, pat [, level [,n]]]
returns a list of parts of l, which match a pattern pat. Optional levelspec l and the maximum number
of results n can be specified.
See also:
levelspec pattern Position Deletecases

DeleteCases[l, pat [, level [,n]]]
returns a list of parts of l, which do not match a pattern pat. Optional levelspec l and the maximum
number of results n can be specified.
See also:
levelspec pattern Cases Position

Difference[list] returns Rest[list]  Drop[list, 1] .

FixedPoint[f, e] starts from f[e] then applies f repeatedly until the result no longer changes. FixedPoint[f,
e, n] specifies the maximum number of iterations by n. An option SameTest>s specifies the test function.
Threshold>re, and AbsoluteThreshold>ae set the relative and absolute accuracy, respectively, when
SameTest>NearlySameQ (default).
See also:
FixedPointList

FixedPointList[f, e] returns the intermediate values of FixedPoint[f, e] as a list. FixedPointList[f,
e, n] and options for FixedPoint are valid.
See also:
FixedPoint

Functions Map, Apply, Scan, Cases, Position, Count, Level, DeleteCases takes an optional argument
level to specify which level to operate:
value operates
n_Real from level 1 through level n
{n_Real} only on level n
{n1_Real, n2_Real} from leveln1 through level n2
If n is negative, it counts from the deepest level of each element.
Examples: f@@[{{a, b}, {c, d}}, {1}] ===> {f[a, b], f[c, d]}
See also:
Map Apply Scan Cases Position Count Level DeleteCases

Map[f, x [, level]] or f/@x [f/@[x, level]]
operates f over each element of a list x and returns the result as a list:
f/@{a, b, c} ===> {f[a], f[b], f[c]}
An optional argument specifies the levelspec.
See also:
@/ Scan Apply MapThread levelspec

MapThread[f, l] ===> f@@[Thread[l], {1}]
Example: MapThread[f, {{1, 2}, {3, 4}}] ===> {f[1, 3], f[1, 4]}
See also:
ScanThread Thread Map Apply

Position[l, pat [, level [,n]]]
returns a list of indices of parts of l, which match a pattern pat. Optional levelspec l and the
maximum number of results n can be specified.
See also:
levelspec pattern Cases DeleteCases

Scan[f, x [, level]]
operates f over each element of a list without returning the result:
Scan[f, {a, b, c}] ===> {f[a], f[b], f[c]};Null
An optional argument specifies the levelspec.
See also:
Map Apply MapThread levelspec

ScanThread[f, l] ===> (f@@[Thread[l], {1}];Null) ,
which is equivalent to MapThread without returning the results.
See also:
MapThread Thread Map Apply

Usage: SelectCases[list, {test1,..}]
returns a list {list1, .. }, where list1 is a list of subexpressions which makes test1 True, etc.
If the second argument is like {c1, .. , True&}, the last of the returned list contains subexpressions
which make none of c1, ... True.
See also:
SwitchCases

Usage: SwitchCases[list, {case1,..}]
returns a list {list1, .. }, where list1 is a list of subexpressions which match case1, etc. SwitchCases
does what are done by Cases and DeleteCases simultaneously. If the second argument is like {c1, ..
, _}, the last of the returned list contains subexpressions which match none of c1, ...
See also:
SelectCases

Thread[l] returns a threaded list of l:
Thread[{{1, 2}, {3, 4}}] ===> {{1, 3}, {2, 4}}
Thread[{{1, 2}, {3, 4}, 5}] ===> {{1, 3, 5}, {2, 4, 5}}
If an optional second argument h is given, Thread operates only over on a structure whose head is
h:
Thread[{{1, 2}, {3, 4}} , f] ===> {{1, 2}, {3, 4}}
Thread[{f[1, 2], f[3, 4]} , f] ===> f[{1, 3}, {2, 4}]
Thread[f[f[1, 2], f[3, 4]] , f] ===> f[f[1, 3], f[2, 4]]
Thread is equivalent to Transpose if l is a matrix.
See also:
MapThread Transpose

Functions dedicated to the optics calculations and simulations in FFS.

AccelerateParticles does TrackParticles with acceleration in a ring for a given number of turns.
The adiabatic damping is automatically taken cared.
Usage: AccelerateParticles[beam_,mom_,{n_Symbol,nturn_},opt___]
where beam is a list of beam coordinates in the same format for TrackParticles. mom is an expression
to determine MOMENTUM in each turn as a function of turn number n. nturn is the total number of turns.
An option Synchronize specifies a routine to be executed at every turn of the tracking (e.g. changing
voltages and magnet settings, or storing the results.)
Example:
AccelerateParticles[
beam,
Which[
n < 100, 1e9,
n <= 200, 1e9 + (n  100) * 1e7,
True, 2e9],
{n, 300},
Synchronize :> ((
d = {d, MOMENTUM/1e9 * (1 + #2[[2,6,1]])})&)];
See also:
TrackParticles

BeamMatrix[i] returns a 6 by 6 beammatrix (i.e., ) at location i. The index i can have
a fraction to specify intermediate numbers (see LINE or Twiss). The calculation is based on linear
4 by 5 calculation in the present version, so the zdirection is meaningless. Flag GAUSS affects
the result.
See also:
LINE Twiss GAUSS

Usage: DynamicApertureSurvey[range,nturn,options]
where
range: a list of {xrange,yrange,zrange}, with
xrange: {xmin, xmax},
yrange: {ymin, ymax},
zrange: {zmin, zmax},
and for the horizontal plane, specified by the Axes option,
the corresponding range must be given as {v1, ..., vn}.
These values are the initial amplitude divided by the equilibrium
values, i.e., Sqrt[2Jx,y/(EMITX+EMITY)], Sqrt[2Jz/EMITZ].
See EMITTANCE(EMIT) command or Emittance function.
nturn: number of turns to track.
options: Output>lfn : output to the unit lfn (see OpenWrite).
Axes>axes : one of "XY", "XZ", "YX", "YZ", "ZX", "ZY",
where the first character specifies the horizontal axis, and
the second the vertical, respectively. The default is "ZX".
ReferenceOrbit>{x0, px0, y0, py0, z0, dp0} : Survey is done around
this orbit.
PhaseX>phix : The initial amplitude is rotated in (X, PX) phase space
by phix. Default is zero.
PhaseY>phiy : The initial amplitude is rotated in (Y, PY) phase space
by phiy. Default is zero.
PhaseZ>phiz : The initial amplitude is rotated in (Z, PZ) phase space
by phiz. Default is Pi/2.
ExpandElementValues>True(default) : set the values of the components
according to the values of elements. Machine errors may be reset.
See machineerrorcommands, CALCULATE(CALC).
DynamicApertureSurvey returns the result as a list:
{score,{{{xmin, xmax},{ymin, ymax},{z1, z2, .., zn}},
{{z1,score1,{turn1_1,..,turn1_50}},..,
{zn,scoren,{turnn_1,..,turnn_50}}}}} ,
where score = Sum[scorei,{i,n}], scorei is the "score" of ith momentum, and turni_j is the lost
turn of the particle with ith momentum and jth initial amplitude.
DynamicApertureSurvey tracks number of particles with different initial conditions in the range
given by range. It outputs a zx diagram of the dynamic aperture of the ring. Fifty one initial conditions
are chosen in the range xrange for each point of zrange. The initial yamplitude is linearly dependent
on the xamplitude. It tracks from xmax to downward for each zamplitude zn, until the particles
turns nturn with successive DAPWIDTH xamplitudes. The default DAPWIDTH is 7.
DynamicApertureSurvey does parallel processing up to NPARA processes.
See also:
NPARA DAPWIDTH EMITTANCE(EMIT) Emittance

Element[keystring, {elementpatternstring  elementposition}] returns values for keystring of
elements which match elementpatternstring or located at elementposition. It returns a list if
more than one elements match. The keystring and elementpatternstring can be symbols, unless values
are not assigned to them.
If the second argument is omitted, it means all elements.
The elementposition can be known by Element["POSITION"].
Keystrings "VALUE" and elementkeywords allows to be set (i.e., Element[a,b] = v) when elementpatternstring
chooses only one element. If a value is set to Element, it is automatically distributed to all components
those belong to the element. If the keyword is the default variable, the error given by machineerrorcommand
DK is applied.
The arguments of Element can be lists. It automatically maps as
Element[{a,b,c..},y] means {Element[a,y],Element[b,y],Element[c,y]..}
Element[x,{a,b,c..}] means {Element[x,a],Element[x,b],Element[x,c]..},
where both x and y can be also a list.
If an option Saved>True is given, Element refers the savebuffer which can be transferred to
other beam lines. Otherwise values set by Element are not saved when FFS is stopped, unless they
are the defaultkeyword or keywords once used in matching.
See also:
elements wildcards components LINE SetElement

The keystring is not casesensitive. Available keystrings are:
"LENGTH" Number of elements in the beam line. No second argument.
"POSITION" Position of the element in the elementlist.
"NAME" Name of the element.
"VALUE" Current value of the default keyword of the element.
"KEYWORDS" List of available keywords of the element.
"DEFAULT" The default keyword of the element
"TYPE" The internal codenumber of the type of the element.
"TYPENAME" The name of the type of the element.
keyword If keyword is the default keyword, it means the current value. If not, it means the saved
value. Changing the nondefault keyword by Element does not affects the current setting
of the components.
"EXPAND" Distribute the value of the defaultkeywords and the keywords used in the matching to
all components in the beam line. No second argument.
Setting by Element["VALUE",..] or Element[keyword,..] to the DEFAULT keyword or a matchingvariable
keyword changes the current value, and distributed to the components in the succeeding calculation.
See also:
setvalueofelement elements keywords defaultkeyword
components

Emittance[option] returns a set of rules as
{keyword1>value1, keyword2>value2, ..} .
Its options and default values are Matrix(False), Orbit(False), OneTurnInformation(False), Emittance(True),
ExpandElementValues(True), SaveEMIT(False), InitialOrbit(Null), InitialBeamMatrix(Null), Region({1,1}),
and Output(0).
If Emittance>False is specified, the resulting keywords are:
Stable True if all modes are stable and the closed orbit is found.
Region The region {begin, end} to calculate.
Tunes {nux, nuy, nuz} .
EnergyLossU0 One turn energy loss in eV.
RfVoltageVc The effective RF voltage (V).
EquilibriumPosition dz in meter.
MomentumCompaction dz/dp
OrbitDilation ds in meter.
BucketHeight dV/E0
HarmonicNumber The effective harmonic number
OrbitAtExit physical c.o.d. at the end of line.
If None of the options is given, the following keywords are added:
DampingRate {T0/taux, T0/tauy, T0/tauz}
Emittances {emitx, emity, emitz} *1)
MomentumSpread sigma p/p0
BunchLength sigma_z
Polarization equilibrium polarization, if POL is on
Polarization2 equilibrium polarization by up to 2nd order calculation
Polarization4 equilibrium polarization by up to 4th order calculation
Polarization6 equilibrium polarization by up to 6th order calculation
PolarizationVector direction of polarization AppendTo the entrance of the beam line
SpinTune spin tune on the closed orbit
NominalSpinTune spin tune calculated by MOMENTUM and electron g2
TuneShiftByRadiation {dnux, dnuy, dnuz}
If OneTurnInformation>True, or Orbit>True, or Matrix>True, the followings are added.
OrbitAtEntrance physical c.o.d. at the entrance of the ring.
OneTurnTransferMatrix symplectic part of the oneturn transfer matrix.
OneTurnDampingMatrix deviation of transfer matrix due to radiation.
NormalCoordinates conversion matrix from physical to normal coords.
OneTurnExcitation excitation matrix by radiation and intrabeam scattering (with INTRA).
EquilibriumBeamMatrix equilibrium beam matrix.
ExtendedTwissParameters list of rules giving the extended Twiss parameters at the entrance of the
ring.
If Orbit>True or Matrix>True, the following is added:
ClosedOrbit List of physical closed orbit at every element in the ring.
If Matrix>True, the followings are added:
TransferMatrices List of physical transfer matrix from the beginning of the beam line to all
elements.
IntrabeamExcitation List of the change of the 6 x 6 beam matrix due to the intrabeam scattering
(only when INTRA), converted to the beginning of the beam line.
If the flag TRPT or NORING is set, the calculation assumes a transport line so that several quantities
such as damping rate, eigen modes, equilibrium beam matrix, etc. are meaningless. Use RING or NOTRPT
for such calculation. In the case of TRPT or NORING, the incoming beam envelope must be given by
the option InitialBeamMatrix with a 6 x 6 symmetric matrix. TRPT is useful for calculation of space
charge and intrabeam in a transport line.
Please do not forget to put semicolon at the end of Emittance[] function, otherwise the output
will be huge especially when Orbit or Matrix is True.
If ExpandElementValues>False, calculation is made using the present values of each component (i.e.,
including machine errors).
If SaveEMIT>True, the calculated values of emittances are stored in variables EMITX, EMITY, EMITZ,
SIGE, SIGZ. The default is SaveEMIT>False.
InitialOrbit>{x0,px0,y0,py0,z0,dp0/p0} specifies the incoming orbit which is valid when NOCOD is
set. The option Output>filenum enables the print out of EMITTANCE(EMIT) to filnum.
If Region is not the entire ring, parameters such as Emittances and DampingRate, etc., are not calculated,
and return NaNs.
*1) The values of Emittances with INTRA and MINCOUP correspond to the equilibrium with intrabeam
scattering weakened by MINCOUP.
See also:
EMITTANCE(EMIT) SymplecticJ COD EMITX EMITY EMITZ SIGZ SIGE
POL MINCOUP equilibriumbeamenvelope

With MAP elements, ExternalMap defines a userdefined map of particles. It also allows a user to
do anything (doing statistics, etc.) at any point of a beam line during a tracking.
Usage: First define a MAP element at MAIN level:
MAP name=(L=leng);
Currently L is the only keyword. Insert it at the location(s) where you want to use it.
1) Tracking
In FFS, define the function ExternalMap as
ExternalMap["TRACK",n,nt_,x_]:=body;
The second argument n is the position of MAP counting from the beginning, which can be obtained using
LINE["POSITION","name.m"]. The third argument nt_ is used to receive the number of turns which is
incremented by the tracking. The last argument x_ is used to receive the coordinates of particles.
It is a (7 or 9, np) list of real numbers. The elements (1..8, i) are (x, px ,y ,py ,z ,dp/p0, sy,
sarg) of the ith particle. The (1, i) element is True(==1) if the ith particle has been survived,
and False(==0) if it has been lost. The spin coordinates sy and sarg are only valid with the POL
flag.
You can define ExternalMap to change the coordinates of each particle as you like by returning a
new x in the same format as above. If you do not return it or you return in a different format, the
tracking routine does not change the particle coordinates. You can neither rebirth a lost particle
nor kill a surviving particle.
After defined ExternalMap, tracking calls it in every turn.
Example:
MAP P1=();
....
LINE A=(... P1 ... P1 ...);
....
FFS USE=A;
ExternalMap["TRACK",LINE["POSITION","P1.2"],nt_,x_]:=
(Print[x];x*(Print[x];x*2);
.... ....
TRACK USE=A ....;
This example defines ExternalMap to print out the coordinates of all particles at the second
P1 in the line A. It also makes all coordinates of all particles twice in every turn.
Optionally a compiled module CompiledMap can be used for ExternalMap["TRACK"] (see below).
2) Emittance
In FFS, define the function ExternalMap as
ExternalMap[ExternalMap["EMIT",n,cod_]:=body;
The second argument n is the position of MAP counting from the beginning, which can be obtained
using LINE["POSITION","name.m"]. The last argument cod_ is used to receive the orbit
at the entrance of the element, as a list of 6 real numbers. ExternalMap must return
a list, either {cod1, trans} or {cod1, trans, dtrans, dbeam}, where cod1 is the orbit
at the exit, trans is the 6 by 6 transfer matrix of this element, dtrans is the radiation
damping part of the transfer matrix (6 by 6), and dbeam is the radiation excitation of
the beam matrix (6 by 6). Only j >= i parts of dbeam[[i, j]] are taken into account.
Example: Example:
ExternalMap[ExternalMap["EMIT",LINE["POSITION","P1"],cod_]:=(
Print[cod]; Print[cod];
{cod+{0,0.00{cod+{0,0.001,0,0,0,0},IdentityMatrix[6]});
3) Optics
In FFS, define the function ExternalMap as
ExternalMap[ExternalMap["OPTICS",n,cod_]:=body;
The second argument n is the position of MAP counting from the beginning, which can be obtained
using LINE["POSITION","name.m"]. The last argument cod_ is used to receive the orbit
at the entrance of the element, as a list of 6 real numbers. ExternalMap must return
a list {cod1, trans}, where cod1 is the orbit at the exit and trans is the 6 by 6 transfer
matrix of this element. In the case of CACL4D (== ~CALC6D), only the 4 by 5 transfer
matrix is effective.
Example: Example:
ExternalMap[ExternalMap["OPTICS",LINE["POSITION","P1"],cod_]:=(
Print[cod]; Print[cod];
{cod+{0,0.00{cod+{0,0.001,0,0,0,0},IdentityMatrix[6]});
4) Geometry
In FFS, define the function ExternalMap as
ExternalMap[ExternalMap["GEO",n,geo_,pos_]:=body;
The second argument n is the position of MAP counting from the beginning, which can be obtained
using LINE["POSITION","name.m"]. The argument geo_ receives the geometry of the beam
line at the MAP element, in the same format as LINE["GEO",n], i.e., {{GX,GY,GZ},{CHI1,CHI2,CHI3}}.
The last argument pos_ receives the orbit length S at the element. ExternalMap must return
an updated list {geo1, pos1}, as { {{GX,GY,GZ},{CHI1,CHI2,CHI3}}, S} as the values at
the exit of the element.
Example: Example:
ExternalMap[ExternalMap["GEO",LINE["POSITION","P1"],geo_,pos_]:=(
Print[cod]; Print[cod];
{ {geo[[1]]+{1,0,0}, geo[[2]]}, pos+0.1})
See also:
MAP CALC4D POL CompiledMap

Usage:
ExternapMa["TRACK", n, nt_, x_]:=CompiledMap[nt, x, src, prm, opt___];
where n is the location number, nt the number of turns, x the particle coordinates with the alive
flag, as described for ExternalMap. It takes options of Rules as shown below. A charachter string
src is the source code for the map, which completes a subroutine having a header:
implicit none;
integer,intent(in):: np,nprm,nt,n;
real(kind=8),intent(inout):: x(np),px(np),y(np),py(np),z(np),dp(np),&
sy(np),sarg(np),flag(np),prm(nprm);
where np is the number of particles, and prm is a list of reals of any length. The spin coordinates
sy and sarg are meaningless without the flag POL. The src must ends with "return;end" to complete
the subroutine, and more routines can be inserted if needed. Currently gfortran in free format is
available for the compiler, and gcc will be supported in future.
Example:
src = "flag = flag * merge(1.d0, 0.d0, x<prm(1) .or. x>prm(2) .or. (y>prm(3) .and. y<prm(4)));return;end";
prm
= {0.001, 0.001, 3e4, 3e4};
ExternalMap["TRACK", LINE["POSITION","M1.2"], nt_, x_]:=CompiledMap[nt, x, src, prm];
works as a special colimation at a MAP element M1.2, resulting:
(Actually the example above can be performed also by SADScript:
ExternalMap["TRACK", LINE["POSITION","M1.2"], nt_, x_]:=Append[Drop[x, 1],
x[[1]] < prm[[1]]  x[[1]] > prm[[2]]  (prm[[3]] < x[[3]] < prm[[4]])];
which runs even FASTER than the compiled one!!)
Options Defaul Description

Single False If True, the map is called once for the entrire particles even for NPARA
> 1.
Completion Null A completion SADScript to be called after the map with the arg {x, prm}.
See also:
ExternalMap MAP POL

FFS[commandstring] executes commandstring as FFS commands. Any commands can be used. Some commands
CALCULATE(CAL), GO, VARIABLES(VAR), SHOW returns their result, otherwise Null is returned. All outputs
of the commands are suppressed.
FFS[commandstring,lo] directs the output of the commands to filenumber lo. The filenumber lo
may be given by OpenWrite or OpenAppend.
The IF structure and REPEAT(REP) loop must complete within a single FFS.
See also:
Input/Output OpenWrite OpenAppend

FFS["SHOW"] or FFS$SHOW[] returns the current matching conditions as a list. Each element has
a form of
{component1, component2, function, goalvalue, numberofmomentums, scale},
which corresponds to the format of the printout by SHOW.
See also:
SHOW

Usage:
(1) FitValue[component, function, {id_,dp_}, goal_, now_] := body
modifies the goal of the matching of function at component. The argument id_ is the orbit id for
MatchingAmplitude or InitialOrbits. The argument dp_ receives the value of dp/p0. The argument goal_
is the value of the goal of the matching set by matchingfunctioncommands. The argument now_ is
the current value of function.
Example: FitValue["$$$", "NX", {_,dp_}, goal_, now_] := goal + dp * xix * 2 * Pi
sets the tune NX to have chromaticity xix.
(2) FitValue[component1, component2, function, {id_,dp_}, goal_, now1_, now2_] := body
modifies the value of the function at component1 for a twocomponent matching. Component1 is assumed
upstream in the beam line. The value of body is used in place of the current value, now1. The argument
id_ is the orbit id for MatchingAmplitude or InitialOrbits. The argument dp_ receives the value of
dp/p0. The argument goal_ is the value of the goal of the matching set by matchingfunctioncommands.
The argument now1 and now2 are the current values of the function at component1 and component2, respectively.
Example:
FitValue["QF1", "QF2", "NX", _, goal_, now1_, now2_] :=
If[Abs[now2(now1+goal)] < 0.01*2*Pi , Null, now1]
sets the tune difference between QF1 and QF2 gaol + 0.01.
During the matching process the matching routine calls FitValue with arguments, then if body returns
a number, it overrides the goal give by matchingfunctioncommands. If body returns Null, the matching
of function is ignored.
The matchingfunctioncommand is necessary besides FitValue to perform the matching. Only defining
FitValue does not do the matching.
FitValue is cleared by USE. It is hidden by VISIT and restored by BYE
See also:
matchingfunctioncommands offmomentummatching

A defined function to modify the weight of matching of particular function at particular component
with particular momentum offset.
Usage: FitWeight[component, function, {id_,dp_}, default_] := weight;
where
component is the name of the location of the fit, like "QF.2", etc.
function is the name of the matchingfunction, like "BX", "LENG", etc.
id_ is the id number of the orbit for MatchingAmplitude or InitialOrbits.
dp_ is a variable to receive the momentum deviation of the fit.
default_ is a variable to receive the default fit weight.
weight is an expression which returns the desired weight.
Example: FitWeight["$$$","LENG",{_,dp_},ws_]:=ws*10;
makes the weight of LENG at $$$ 10 times (100 times in MatchingResidual) bigger than the default.
See also:
matchingfunctioncommands specialvariables MatchingResidual


GeoBase[{chi1, chi2, chi3}] converts the rotation angles of the coordinate base vectors to a transformation
matrix {{x_gx,x_gy,x_gz}, {y_gx,y_gy,y_gz}, {z_gx,z_gy,z_gz}}
See also:
GEO OrbitGeo

LINE[keystring, {componentpatternstring  componentposition}]
returns values for keystring of components which match componentpatternstring or located at componentposition.
It returns a list if more than one components match. The keystring and componentpatternstring
can be symbols, unless values are not assigned to them. The second arg can be a fractional number
to denote an intermediate value of two components.
If the second argument is omitted, it means all components.
The componentposition can be known by LINE["POSITION"].
Keystrings "DIR" and componentkeywords allows to be set (i.e.,
LINE[a,b] = v) when componentpatternstring chooses only one component.
The arguments of LINE can be lists. It automatically maps as
LINE[{a,b,c..},y] means {LINE[a,y],LINE[b,y],LINE[c,y]..}
LINE[x,{a,b,c..}] means {LINE[x,a],LINE[x,b],LINE[x,c]..},
where both x and y can be also a list.
See also:
components wildcards elements Element

The keystring is not casesensitive. Available keystrings are:
"LENGTH" Number of components in the beam line. No second argument.
"POSITION" Position of the component in the beam line.
"NAME" Name of the component.
"TYPE" The internal codenumber of the type of the component.
"TYPENAME" The name of the type of the component.
"ELEMENT" The name of the corresponding element.
"DIR" The orientation of the component, +1.
"S" The orbit length to the entrance from the beginning of the beam line.
"LENG" Same as "S".
"GEO" Geometricfunctions at the entrance of the component, {{GX, GY, GZ}, {GCHI1, GCHI2,
GCHI3}}.
"OGEO" Geometricfunctions of the orbit at the entrance of the component, {{OGX, OGY, OGZ},
{OCHI1, OCHI2, OCHI3}}.
"GAMMA" Lorentz factor gamma.
"GAMMABETA" Lorentz factor gamma*beta = Sqrt[gamma^2  1].
"SIGab" Beam matrix component, where a and b are one of X, PX, Y, PY, Z, DP. If b is omitted
it returns Sqrt[SIGaa] is returned. Just "SIG" returns the entire 6 by 6 beam matrix.
"SIZEab" Beam matrix component calculated by (CODPLOT;EMIT), where a and b are one of X, PX,
Y, PY, Z, DP. If b is omitted it returns Sqrt[SIZEaa] is returned. "SIZE" returns the
entire 6 by 6 beam matrix.
"MULT" The ordered number of each component belonging to the same element, starting from 1.
keyword The value of the keyword of the component (see below).
"EXPAND" Distribute the value of the defaultkeywords and the keywords used in the matching to
all components in the beam line. No second argument.
"GX", "GY", "GZ" Geometric functions for the coordinate GX, GY, GZ.
"GCHI1", "GCHI2", "GCHI3" Geometric functions for the coordinate CHI1, CHI2, CHI3
"OGX", "OGY", "OGZ", "OCHI1", "OCHI2", "OCHI3" Geometrical functions for the orbit.
Setting by LINE[keyword,..] to the DEFAULT keyword for the FIRST component changes the current value
of the corresponding element, because the value of an element is stored in the first component.
See also:
components geometricfunctions elements keywords defaultkeyword
Element

Usage: OptimizeOptics[options]
optimizes (1 + MatchingResidual) or any function using DownhillSimplex with variables specified by
FREE. Unlike GO, any keyword of any element can be a variable.
OptimizeOptics returns the final simplex. The variables are set to the values which give the minimum
of the function so far at the end.
Options:
All options for DownhillSimplex are valid.
OptimizeFunction > fun is the function to be minimized. The default is
((FFS["CALC"];1+MatchingResidual)&).
InitialSimplex > initial sets the initial simplex to initial. The
default is Null, which mean to create initial from the current value
of the variables. Its format is same as for initial of
DownhillSimplex
SimplexSize > size is the initial size of the simplex. Each variable
is relatively shifted by this amount from the current value.
Example:
free Q* Q* L
fit nx .3 ny .2
OptimizeOptics[]
optimizes the optics by changing the lengths of quads which are not allowed by GO, as well as K1
of quads.
See also:
DownhillSimplex

OrbitGeo[location] returns the geometry {GX, GY, GZ} of the current (not design) orbit.
See also:
GEO GeoBase

To calculate the field of the synchrotron radiation from particles, first record trajectories of
particles. This is done by the function TrackParticles with a new flag RADLIGHT on. When RADLIGHT
is on, TrackParticles returns a list
{beam, trajectory} ,
where beam is a list as {location, coordinates}, and trajectory is a list
{ {t1 .. tm}, {x1 ..xm}, {y1 .. ym}, {z1 .. zm} }, ..
where {t,x,y,z}_i is the coordinates of the particle at ith point in the trajectory. The origin
and the direction of the spatial coordinates are the same as GEO coordinate {GX, GY, GZ}. One can
track many particles at the same time by TrackParticles, so the trajectory has the dimensions {np,
m}, where np is the number of particles.
After the trajectory is obtained, one can calculate the field in time domain
at any observation point. This is done by the function RadiationFiled as
field = RadiationField[ trajectory[[i]], obs];
where trajectory[[i]] is the trajectory of the ith particle, and obs is the spatial coordinate of
the observation point in the GEO coordinate. The output field is a list
{ {tau1 .. taum},
{Ex1 .. Exm}, {Ey1 .. Eym}, {Ez1 .. Ezm},
{Hx1 .. Hxm}, {Hy1 .. Hym}, {Hz1 .. Hzm},
{Sx1 .. Sxm}, {Sy1 .. Sym}, {Sz1 .. Hzm} }
where H = (n x E)/(c mu0) and S = E x H , and tau is the observation time.
RadiationField uses the FeynmannHeviside formula
E = (mu0 e*CHARGE/4pi) (c^2n/R^2 + R/c d(c^2n/R^2)/dt + d^2n/dt^2) ,
where n and R are the direction vector and the distance from the electron at the retarded time to
an observation point.
The derivatives in the above formula is calculated using the spline
interpolation.
Next one can calculate the spectrum of the field by RadiationSpectrum as
spect = RadiationSpectrum[ {field[[1]], field[[k]]},
{lambda1, lambda2, dlambda} ] ,
where filed[[k]] is one of the fields calculated by RadiationField. The range of the wavelength is
given as a list above. The output spectrum spect is a list as
{ {k1 .. kk}, {c1 .. ck}, {s1 .. sk} } ,
where k1 .. kk is the wave number k = omega/c, c1 .. ck and s1 .. sk are the cosine and sine integrals
of the field in tau1 .. taum , i.e.,
ck + I sk = Integrate[ field[tau] Exp[I c k tau] dtau] .
An example is seen in $(SAD_ROOTPATH)/sad/examples.sad .
See also:
TrackParticles RADLIGHT

To calculate the field of the synchrotron radiation from particles, first record trajectories of
particles. This is done by the function TrackParticles with a new flag RADLIGHT on. When RADLIGHT
is on, TrackParticles returns a list
{beam, trajectory} ,
where beam is a list as {location, coordinates}, and trajectory is a list
{ {t1 .. tm}, {x1 ..xm}, {y1 .. ym}, {z1 .. zm} }, ..
where {t,x,y,z}_i is the coordinates of the particle at ith point in the trajectory. The origin
and the direction of the spatial coordinates are the same as GEO coordinate {GX, GY, GZ}. One can
track many particles at the same time by TrackParticles, so the trajectory has the dimensions {np,
m}, where np is the number of particles.
After the trajectory is obtained, one can calculate the field in time domain
at any observation point. This is done by the function RadiationFiled as
field = RadiationField[ trajectory[[i]], obs];
where trajectory[[i]] is the trajectory of the ith particle, and obs is the spatial coordinate of
the observation point in the GEO coordinate. The output field is a list
{ {tau1 .. taum},
{Ex1 .. Exm}, {Ey1 .. Eym}, {Ez1 .. Ezm},
{Hx1 .. Hxm}, {Hy1 .. Hym}, {Hz1 .. Hzm},
{Sx1 .. Sxm}, {Sy1 .. Sym}, {Sz1 .. Hzm} }
where H = (n x E)/(c mu0) and S = E x H , and tau is the observation time.
RadiationField uses the FeynmannHeviside formula
E = (mu0 e*CHARGE/4pi) (c^2n/R^2 + R/c d(c^2n/R^2)/dt + d^2n/dt^2) ,
where n and R are the direction vector and the distance from the electron at the retarded time to
an observation point.
The derivatives in the above formula is calculated using the spline
interpolation.
Next one can calculate the spectrum of the field by RadiationSpectrum as
spect = RadiationSpectrum[ {field[[1]], field[[k]]},
{lambda1, lambda2, dlambda} ] ,
where filed[[k]] is one of the fields calculated by RadiationField. The range of the wavelength is
given as a list above. The output spectrum spect is a list as
{ {k1 .. kk}, {c1 .. ck}, {s1 .. sk} } ,
where k1 .. kk is the wave number k = omega/c, c1 .. ck and s1 .. sk are the cosine and sine integrals
of the field in tau1 .. taum , i.e.,
ck + I sk = Integrate[ field[tau] Exp[I c k tau] dtau] .
An example is seen in $(SAD_ROOTPATH)/sad/examples.sad .
See also:
TrackParticles RADLIGHT

Create/set/read a MAINlevel element.
Usage: SetElement[ elementname, elementtype, options]
where
elementname: name of the element, either a symbol or a string
elementtype: type of the element, a symbol, a string, or a number
options: one or more rules or list of rules of the form
keyword > value or keyword :> value, to set the corresponding
value of keyword of the element.
SetElement returns a list of information of the element, in the suitable form for applying SetElement
again.
You can define a new element by SetElement.
You can change the values of keywords of the element.
You cannot, however, change the type of an existing element, nor cannot delete the element.
The elementtype can be Null. If so, a null type is assumed for a new element.
Examples:
LINE A = ( .. );
QUAD QF = (K1 = 0.2);
...
FFS USE = A;
...
SetElement["QF"] ! reads values of QF.
SetElement["QF","QUAD"] ! same as above.
SetElement["QF","BEND"] ! error because QF is QUAD.
SetElement["QF",,{"K1">0.1}] ! set K1 of QF to 0.1 .
SetElement["QF","QUAD",{"K1">0.1}] ! same as above.
!Assuming QF1 and QF2 are undefined yet:
SetElement["QF1","QUAD",{"K1">0.1}] ! create a new QUAD QF1 with K1=0.1 .
SetElement["QF2",,{"K1">0.1}] ! error because no type with key.
SetElement["QF2"] ! This is OK.
SetElement["QF2","QUAD"] ! Now the type of QF2 is defined.
See also:
elements keywords Element

SurvivedParticles[x]
returns the list of 6 coordinates and the flag of the survived particles in x. The form of x is {x,
px/p0, y, py/p0, z, dp/p0, flag}, where each is a list of length of the number of particles. If all
particles are lost, it is a list of seven null lists.
See also:
TrackParticles

SymplecticJ[n] returns an n by n symplectic matrix:

SynchroBetaEmittance calculates equilibrium emittance under influence of synchrotron motion and chromaticity.
Usage:
SynchroBetaEmittance[{nus0, nus1, dnus},options]
or
SynchroBetaEmittance[nus0,options]
where nus0, nus1, and dnus are the starting, ending and step size of synchrotron tune, respectively.
If only nus0 is given, calculation is done only for nus0. The returned value is a list:
{{nus, emitx, emity, emitxp, emityp, conv}, ... }
where nus, emitx, emity, emitxp, emityp, conv are the synchrotron tune, equilibrium horizontal and
vertical emittances, horizontal and vertical projected emittances, and the convergence, respectively.
When conv is negative, calculation failed to converge, and the returned emittances are not reliable.
Options
Type Default Meaning

AzimuthalModes Real 9 Number of azimuthal modes
See also:
SYNCHTOBETA(SYNCHROB) equilibriumbeamenvelope

TouschekLifetime interpolates the data calculated by EMIT or Emittance[]. There are three ways of
usage:
TouschekLifetime[Infinity, Infinity, nz]: Touschek lifetime in seconds
with momentum aperture nz * SIGE.
TouschekLifetime[nx, Infinity, nz]: Touschek lifetime in seconds
with acceptance 2Jx/(nx * (EMITX+EMITY)) + 2Jz/(nz * EMITZ) < 1.
TouschekLifetime[Infinity, ny, nz]: Touschek lifetime in seconds
with acceptance 2Jy/(ny * (EMITX+EMITY)) + 2Jz/(nz * EMITZ) < 1.
EMIT or Emittance[] with INTRA must precede TouschekLifetime.
See also:
EMITTANCE(EMIT) Emittance INTRA MINCOUP equilibriumbeamenvelope

TrackParticles[beam, destinationcomponent, nbegin, nend]
returns a beam after the tracking at the entrance of the destination component. The destination
can be specified by the name of the component or by a number obtained by LINE["POSITION", component].
If destination is omitted, the end of the line is assumed.
The argument nbegin is the initial turn number to be passed to tracking to indicate it is in the
nth turn. The number is increased by 1 when it passes the end of beam line. If nbegin is omitted,
1 is assumed.
The argument nend is the last turn number. The default is nbegin.
The variable beam and also the result of TrackParticles are lists of the form
{location, coordinates}
where location is the positionnumber of the starting point. If location is same as or in the downstream
of destination, the tracking is done by folding across the beginning of the beam line. The coordinates
are in a list of {7 or 9, np} form, where np is the number of particles. The first 6 or 8 elements
of coordinates specifies either
{x, px/p0, y, py/p0, z, dp/p0} (NOPOL)
{x, px/p0, y, py/p0, z, dp/p0 sy, sarg} (NOPOL)
bin this order. The {1, i} is the flag which is True(==1) when the particle is alive, and False(==0)
when lost.
If the flag POL is on, TrackParticles performs spin tracking. Then the coordinates has two more
components sy and sarg, which correspond to the ycomponent of the classical spin vector and the
angle ArcTan[sx, sz], respectively. If POL is on, another flag RADPOL turns on the SokolovTernov
effect.
When a flag RADLIGHT is on, TrackParticles returns the trajectories of particles which are used
to calculate the radiation fields. See RadiationField and RadiationSpectrum.
When PHOTONS is ON (default is OFF), TrackParticles generates a list of all photons radiated through
the tracking. The list is assigned to a symbol PhotonList.
When LOSSMAP is ON (default is OFF), TrackParticles returns the component and the turn where the
loss of each particle is detected.
See also:
components LINE PHOTONS PhotonList RADLIGHT TouschekLifetime
WakeFunction SurvivedParticles LOSSMAP POL RADPOL

Twiss[opticalfunction, component] returns the value of the opticalfunction at the entrance of
component. The values are those calculated by the last CALCULATE(CALC) or GO commands, or CalculateOptics
function.
The second argument, component can be a name of component, a component number, or a list of them.
If the number has a fraction, the intermediate value in the component is calculated.
Twiss["ALL",component] or Twiss["*",component] returns all 28 opticalfunctions at the entrance
of component as a list:
{AX, BX, GMX, NX, AY, BY, GMY, NY, EX, EPX, EY, EPY, R1, R2, R3, R4, DETR, DX, DPX, DY, DPY, DZ,
DDP, AZ, BZ, GMZ, NZ, ZX, ZPX, ZY, ZPY},
which can be directly used in CalculateOptics. In the current version, however, parameters after
AZ are uninteresting, because it always returns 1 for BZ and zeros for the others. "R"//opticalfunction
refers the reference optics. "D"//opticalfunction refers the difference between the current and
the referece optics. "RALL" and "DAL" mean the all optical functions for the reference optics and
the differences, respectively.
Keywords "PEX", "PEPX", "PEY", "PEPY", "PZX", "PZPX", "PZY", "PZPY" return dispersions in the
physical coordinate.
Keywords "LENGTH", "GAMMA", "GAMMABETA", "S", "SIGab" return the same results as for the function
LINE.
The units of NX, NY, NZ are in radian.
See also:
DRAW opticalfunctions extendedTwissparameters CalculateOptics LINE
referenceoptics

Usage: VariableRange[element, keyword ,v_] := expression
where the current value of the element:keyword is passed in v_, and expression should give False
when the value is out of range.
Example: VariableRange["QF","ROTATE",v_]:= 0.1 < v < 0.1;
This restricts the range of the rotation angle of QF within +100 mrad.
VariableRange[_,"ROTATE",v_]:= 0.1 < v < 0.1;
This specifies the same for all elements.
The expression can also return the range as a list {vmin, vmax}, which may give more chance of
solutionfinding for the matching routine.
VariableRange only acts for variables used in the matching with the FREE command.
See also:
FREE setvalueofelement

Usage: VariableWeight[element, keyword ,v_] := expression
where the default weight for matching with element:keyword is passed in v_, and expression should
return a modified value of weight. If nonreal is returned, the default weight is used.
Example: VariableWeight["QF","K1",v_]:= 0.1*v;
reduces the weight of QF1:K1 to 1/10 of the default value.
The weight also affects the step size of the numerical derivative of the response. A smaller weight
makes the step size larger.
VariableWeight only acts for variables used in the matching with the FREE command.
See also:
FREE setvalueofelement

WakeFunction[Longitudinal, comp]={{z1, wl1}, ..., {zn, wln}};
WakeFunction[Transverse, comp]={{z1, wt1}, ..., {zn, wtn}};
specify longitudinal and transverse dipole wake functions at a component comp (string). Each functions
is a list of {z, w} where z is the distance (z>=0) and w is the value of the wake, in the unit of
either V/C or V/C/m.
The wake functions are applied at the component comp, giving kicks to each orbit whose initial
conditions are given by InitialOrbits. The sufficient number of orbits depends on the situation.
WakeFunction is valid only when TRPT and INS, and also either TWAKE or LWAKE is ON.
For tracking, it is only valid in TrackParticles.
See also:
TrackParticles TRPT INS TWAKE LWAKE

Graphics represents an object for 2D graphics with the form
Graphics[primitives, options]. Up to now available primitives are:
Circle[{cx,cy},rx, options] : Circle.
Circle[{cx,cy},{rx,ry}, options] : Oval.
Points[{{x1,y1} .. {x2,y2}}, options] : Points.
Points[{{x1,y1,dx,dy} .. {x2,y2,dx,dy}}, options] : Points with error bars.
Line[{{x1,y1} .. {x2,y2}}, options] : Line.
Line[{{x1,y1,dx,dy} .. {x2,y2,dx,dy}}, options] : Line with error bars.
Rectangle[{x1,y1}, {x2,y2}] : A box.
Rectangle[{x1,y1}, {x2,y2}, graphic] : Graphics in a box.
Polygon[{{x1,y1} .. {x2,y2}}, options] : Polygon.
Text[{string, {x,y}}, options] : Textstring at {x,y}.
Possible options and their defaults values of Graphics are:
option default optional values

AspectRatio GoldenRatio any positive number
DisplayFunction $DisplayFunction Identity or Null to suppress display
Detach False True to run tdr asynchronously
Epilog {} List of primitives
Frame True False to erase outline, ticks, ticklabels.
FrameClick True to allow click on frame to change options.
FrameLabel {"","","",""} List of strings
FrameTicks {Both,Both,Ticks,Ticks}
None to turn off ticks and labels
Both to turn on ticks and labels
Ticks to turn on ticks only
<< For bottom tick >>
False is same as Ticks
True is same as Both
<< For top tick >>
False is same as None
True is same as Ticks
<< For left & right ticks >>
False is same as None
True is same as Both
If a form {___, _List} is given where
the List is a list of {coord, label, opt___}
label is displayed at coord with option opt.
If a form {___, fun} is given and
fun[coord,exp,org] returns a list of options
for Canvas[Create$Text], it is displayed at major
ticks at coord. exp is the exponent and org is the
original label.
GridLines Automatic Automatic to draw grid lines at major ticks
{Automatic,None} for only x
{None,Automatic} for only y
Both, Minor, and Major can be also used.
PlotLabel "" string
PlotRange Automatic {ymin,ymax} or {{xmin,xmax},{ymin,ymax}}
Prolog {} List of promitives
Scale {Linear,Linear} Log, Date
TickSize 1 relative size of ticks.
FrameThickness Automatic thickness of the frame line incl. ticks.
Legend "" shows legendstring.
FontScale 1 Relative size of fonts for FrameLabel, FrameTicks.
FrameFontScale 1 Relative size of fonts for FrameLabel.
If Real, applied to all frames. If List, applied to
bottom, left, top, right, supplemented 1s to the right.
TickFontScale 1 Relative size of fonts for FrameTicks.
If Real, applied to all frames. If List, applied to
bottom, left, top, right, supplemented 1s to the right.
LegendFontScale 1 Relative size of fonts for Legend.
Options for primitives:
For Text:
option default optional values

TextAlign "" "CENTER"
TextCases "" string to represent CASES of TopDrawer
TextPosition "" "DATA" to represent the position by data
coordinates
TextRotate 0
TextSize 1 relative size of a character
PlotColor "Black" one of "White", "Black", "Red",
"Green","Blue","Yellow",
"Magenta","Cyan"
For Point
option default optional values

PointSize 1 relative size of a point
PointSymbol "1O" Symbol for PLOT of TopDrawer, or Bar
"6O","7O","8O","9O" are triangles
in CanvasDrawer.
PlotColor "Black" one of "White", "Black", "Red",
"Green","Blue","Yellow",
"Magenta","Cyan"
ErrorBarTickSize 1 length of error bar ticks.
For Line
option default optional values

Dashing "1" character string or a list of numbers to
represent the dashing of the line.
Plot True whether plot symbols at data points.
If True, PointSize and PointSymbol are
effective (see above).
PlotColor "Black" one of "White", "Black", "Red",
"Green","Blue","Yellow",
"Magenta","Cyan"
ErrorBarTickSize 1 length of error bar ticks.
Thickness 1 thickness of line
For Polygon
option default optional values

Plot False whether plot symbols at data points.
If True, PointSize and PointSymbol are
effective (see above).
PointSize 1 relative size of a point
PointSymbol "1O" Symbol for PLOT of TopDrawer, or Bar
"6O","7O","8O","9O" are triangles
in CanvasDrawer.
PointColor "forest green" point fill color.
PointBorderColor Automatic point border color.
Automatic measn PointColor.
PointTags Null points tag string or list of tag strings.
PlotJoined True whether plot border line of polygon.
Thickness 1 thickness of border line
Dashing "1" character string or a list of numbers to
represent the dashing of the line.
PlotColor "black" border line color.
LineTags Null border line tag string.
FillColor Null polygon fill color.
Null means empty polygon.
Tags False polygon tag string.
ListPlot accepts options for Graphics, Point, and Line. Show accepts
options for Graphics. The output is written to file #9 (fort.9 in OSF1 and
ftn09 in HPUX) in TopDrawer commands. If SAD is running on X, the plot is
also done immediately.
Examples:
g1=ListPlot[{{1,2},{10,20}},Scale>Log,PlotJoined>True,
DisplayFunction>Identity];
g2=ListPlot[{{1,15},{10,3}},Scale>Log,PlotJoined>True,Dashing>"1 0.3",
DisplayFunction>Identity,Plot>False];
g3=ListPlot[{{1,2.5},{5,10},{10,12}},Scale>Log,
DisplayFunction>Identity];
Show[g1,g2,g3,FrameLabel>{"X (mm)","Log(Y)"},PlotLabel>"Test Plot",
AspectRatio>1];

Usage: BeamPlot[loc, axes, options]
plots a beam ellipse at a location loc, for axes. Axes are given by a list
{ax, ay}, where ax and ay are one of "X", "PX", "Y", "PY", "Z", "DP".
The beam envelope should be calculated by (CODPLOT;EMIT) or BEAM commands before
BeamPlot.
options defaults

Orbit True Uses Twiss["DX",loc], etc. as the center of
ellipse.
SizeFunction "SIZE" If "SIG", LINE["SIG"] is used.
LINE["SIZE"] is the default.
AspectRatio 1
DataRange Default If Default, PlotRange becomes square for
axes = {"X", "Y"} or {"PX", "PY"}
See also:
BEAMSIZE(BEAM) EMITTANCE(EMIT) CODPLOT

Usage: ColumnPlot[data, options, ...]
plots a column plot.
1) If data is a 1D vector, it makes a simple column plot.
2) If data is a 2D matrix, it makes a multiplecolumn plot.
3) If data is a 3D list, it makes a stacked, multiplecolumn plot.
Besides options common for all plotting functions, ColumnPlot has its own
options:
Option Value Default Action

ColumnOffset 0 < number < 1 0.15 Ratio of spacing of columns
Reference number 0 Where column starts
Orientation Vertical Vertical Orientation of columns
Horizontal
ColumnLabel List of Str. Automatic Labels for each column
Function Scale for column number
None No labels
FillColor color Colors to fill columns
list of colors
MeshStyle bitmap Bitmap to fill columns
list of bitmaps to distinguish stacking
TextSize positive number 1 relative label size
PlotNull True or False False plot a minimal rect for 0 occurrence
Example:
g=ColumnPlot[{{{1,1,2},{2,2,3}}, {{1,4,2},{2,2,3}}, {{1,3,2},{2,2,3}}}, Orientation>Horizontal];
Update[];
See also:
Graphics

Usage: FitPlot[data, fun, var, {par1,ini1}, .. , {parn, inin}, opt].
See also:
Fit

Usage: GeometryPlot[options]
plots a geometry of beam line.
options defaults

Region {1,LINE["LENGTH"]} {begin, end}, begin and end can be strings.
Both begin and end point of drawing region
could be given by "S" unit by using S[beginend] form.
Names "*" A pattern of component names to be plotted.
See also:
Graphics OpticsPlot

Usage: HistoPlot[data, options, ...]
plots a histogram using ColumnPlot(default) or ListPlot.
Data can be a single list, or list of lists, which results in a multicolumn histogram on a common
axis.
Besides options common for all plotting functions and ColumnPlot, it has its own options:
Option Value Default Action

Bins number Automatic number of bins
BinRange {min,max} Automatic Range of bins
PlotStyle ColumnPlot ColumnPlot plot function
ListPlot
FitPlot
Orientation Vertical Vertical orientation of columns
Horizontal
FitParameters args for FitPlot in a list
See also:
Graphics ColumnPlot ListPlot FitPlot

Usage: ListContourPlot[list, options, ...]
plots a contour plot by list which is a 2D List of Real data.
Option Value Default Action

Contours Real 10 number of contours
PlotRange {min,max}, {prxy, prz}, or {prx, pry, prz}
Automatic depth of contours (prz) and PlotRange for xy (prxy)
AspectRatio
Real 1
MeshRange ({x1,xn},{y1,yn}} or {{x1,..,xn},{y1,..,y1n}}
Automatic Range of x and y axes
ColorFunction Color scheme (Blue, Purple, Pink, Yellow, Green, Cyan),Function, or String
Blue Null or None means "white"
ContourColorFunction
Function or String
Automatic Null or None to hide
ColorScale True or False True displays a color scale on the right
Smoothing integer >= 0 1 number of linear interpolations
Example:
xr0=0;xr=Table[xr0+=Sin[i*Pi/21],{i,20}];xr=(xr[[1]]+xr[[1]])/2;
yr=xr;
table=Outer[Cos[Sqrt[(#^2+#2^2)/2]]&,xr,yr];
gc=Graphics[MapThread[
Rectangle[#2,#3,
ListContourPlot[table, MeshRange>{xr, yr}, AspectRatio>1,
DisplayFunction>Identity, ColorFunction>#,
FrameLabel>{"x", "y", ToString[#]}]]&,
{{ Blue, Pink, Green, Purple, Yellow, Cyan},
{{0.15,0.65},{0.25,0.65},{0.65,0.65},{0.15,0 },{0.25,0 },{0.65,0}},
{{ 0.2, 1.1 },{0.6, 1.1 },{1, 1.1 },{ 0.2, 0.45},{0.6 ,0.45},{1.0, 0.45}}}]];
Show[gc];Update[];
See also:
Graphics ListPlot ListDensityPlot

Usage: ListDensityPlot[list, options, ...]
plots a density plot by list which is a 2D List of Real data.
Option Value Default Action

PlotRange {min,max}, {prxy, prz}, or {prx, pry, prz}
Automatic depth of contours (prz) and PlotRange for xy (prxy)
AspectRatio
Real 1
MeshRange ({x1,xn},{y1,yn}} or {{x1,..,xn},{y1,..,y1n}}
Automatic Range of x and y axes
ColorFunction Color scheme (Blue, Purple, Pink, Yellow, Green, Cyan),Function, or String
Blue Null or None means "white"
Mesh True or False False True to draw mesh
MeshColor Function or String
Automatic Null or None to hide
ColorScale True or False True displays a color scale on the right
Smoothing integer >= 0 1 number of linear interpolations
Example:
data = Table[Sin[x]/Cos[x^2 + y^2], {x, 2, 2, 0.1}, {y, 2, 2, 0.1}];
ListDensityPlot[data,PlotRange>{5,5}, MeshRange>{{2,2},{2,2}}, FrameLabel>{"x","y"}];
Update[];
See also:
Graphics ListPlot ListContourPlot

Usage: ListPlot[{{x1,y1},..,{xn,yn}}, options]
makes a graphic with points.
ListPlot[{y1,..,yn}, options] assumes 1,..n for the xxoordinate.
ListPlot[{{x,y,dy}, ..}, options ] plots error bars of length dy in y.
ListPlot[{{x,y,dx,dy}, ..}, options ] plots error bars in x and y.
option default optional values

PlotJoined False True
Step
StepRatio 1 ratio of stepping position
between two data points
Type ? to see other options for Graphics.
Example:
data1={{1,2},{3,5},{4,1}};
data2={{1,4},{2,2},{3.5,3},{5,3}};
g1=ListPlot[data1, PointColor>"dark slate blue",PlotJoined>True, Thickness>2, PlotColor>"dark
slate blue", FrameLabel>{"x","y"}, Legend>"data1", DisplayFunction>Identity];
g2=ListPlot[data2, PointColor>"tomato", Legend>"data2", DisplayFunction>Identity];
Show[g1,g2];
Update[];
See also:
Graphics Plot

Usage: OpticsPlot[fun_list, options]
makes a plot of builtin optical functions, userdefined functions, or
list of data at components on the beam line. The parameters are:
fun_list: a list of objects to be plotted in a window. The number of windows in a plot is the length
of fun_list object plotted in a window MUST have same dimensions. An element of fun_list
is one of fun_label, fun, list_data or a list as {object, options}, where
fun_label: one of "AX", "BX", "GMX", "NX", "EX", "EPX", "DX", "DPX", "AY", "BY", "GMY", "NY", "EY",
"EPY", "DY", "DPY", "R1", "R2", "R3", "R4", "DETR", "AZ", "BZ", "GMZ", "NZ", "ZX", "ZPX",
"ZY", "ZPY", "DZ","DDP","PEX", "PEPX", "PEY", "PEPY", "GAMMA", "GAMMABETA","SIGab", where
a and b in "SIGab" are one of X, PX, Y, PY, Z, DP. "R"//fun_label refers the reference
optics. "D"//fun_label refers the difference between the current and reference optics.
fun: Any function of the component number. A fractional number may be used to obtain the
intermediate value.
list_data: a list of {{pos1, val1}..{posn,valn}}.
options defaults

Region {1,LINE["LENGTH"]} {begin, end}, begin and end can be strings.
Both begin and end point of drawing region
could be given by "S" unit by using S[beginend] form.
Lattice True False to turn of drawing lattice
LatticeRegion Automatic {low,high}, the region where lattice is drawn
FrameHeight Automatic List of relative heights of each frame
InfoLabel False If True, pressing Button shows Twiss, etc.
Names "*" A pattern of component names to be plotted.
RemoveOverlap "L$NAME" If not "L$NAME", overlapping of lattice names
remain untouched.
Tags False True to attach tags "C$"//(component name)
to each rectangle for the lattice, and
"L$"//(component name) to the component
label (CanvasDrawer only).
Legend False If Automatic, Legend is composed from FrameLabel
Automatically.
options in a fun_list element:
options defaults

Unit 1 Unit of the object. "Meter", "InvMeter",etc.
FrameLabel "" Left frame label.
Legend False If Automatic, Legend is composed from FrameLabel
Automatically.
Example:
p2=OpticsPlot[{{"BX","BY"}, {"DX",{{{10,0.001},{20,0.002}}, FrameLabel>"DX meas.", Unit>Meter,
Thickness>2, Names>"Q*"}}}];
Update[];
See also:
Graphics ListPlot Twiss referenceoptics

Usage: Plot[fun, range, options] or Plot[{fun1, .. }, range, options],
where fun is a function and range is a list given as {x, xmin, xmax}.
options defaults

MaxBend 0.04
PlotPoints 25
PlotDivision 250
Dashing {"1","0.8 0.24","0.4 0.12","0.2 0.08","0.1 0.08",
"0.8 0.08 0.08 0.08","0.4 0.08 0.08 0.08"}
Options for ListPlot and Graphics are also available
The independent variable should have been cleared (i.e., no value should
not be set) when Plot is called.
Example:
ff[x_]:=Sin[x]/x;
ff[0]=1;
Plot[{Cos[x],ff[x]}, {x,0,10}, Thickness>2];
Update[];
See also:
Graphics ListPlot


$FORM is a characterstring to specify the format of the output of a real number.
Usage: $FORM="w.f"
$FORM="Sw.f"
$FORM="Fw.f"
$FORM="Mw.f"
where w is the width of the output, and f is the length of the fractions. If S is attached, trailing
zeroes are omitted. If F is attached, it becomes same as FORTRAN's Fformat. If M is attached, the
exponent is expressed as 10^n. If w and f are omitted, 17.15 is assumed.
The default is S17.15 .

$Input holds the file number for console input stream. The default is 1.
See also:
$Output

$Output holds the file number for console output. The default is 1.
See also:
$Input

Close[f] closes file number [f]. It is necessary to complete the output to an external file.
Close[f1, ...] and Close[{f1, ...}] close all files f1, ...
See also:
OpenRead OpenWrite OpenAppend OpenShared StringToStream

f = OpenAppend[file]
opens file (_String) for write and returns the file number (_Real)
See also:
Close OpenRead OpenWrite

f = OpenRead[file]
opens file (_String) for read and returns the file number (_Real)
See also:
Close OpenWrite OpenAppend

f = OpenWrite[file]
opens file (_String) for write and returns the file number (_Real)
See also:
Close OpenRead OpenAppend

PageWidth is the number of columns of the output. The default is set from GetEnv["WIDTH"].

Print[expr1 [,expr2 ...]]
converts expr1... to _String then write them to $Output. A newline character is appended at the end.
See also:
Write WriteString

Read[f, item [, item1...] [, opts..]]
reads item from file number f. If f is $Input, it reads from the current input stream. item can be
one of or a list of:
Word a word, delimited by WordSeparators
Real a real expression
Expression an expression
Character a single character
A format n*item is possible with a positive integer n.
A list {item1,.., itemn} is possible. The result is also a list.
opts are options given by a Rule:
Option Value Default Effect
WordSeparator _String " ,\t" the delimiters for Word
ReadNewRecord True/False True If true, read the next record of the file beyond the end of
line
NullWords True/False False If True, "" is returned when the input contains adjavent word
separators
See also:
OpenRead Close

ReadString[f]
reads the next record from file number f, and returns it as a _String.
See also:
Read OpenRead Close

StandardForm[expr]
resets $FORM and PageWidth to their defaults, then evaluate expr, returns the result, and resets
$FORM and PageWidth to those at the beginning of StandardForm.
See also:
$FORM PageWidth

f = StringToStream[string]
opens a character string for read and returns the file number (_Real)
See also:
Close

Write[f, expr1 [,expr2 ...]]
converts expr1... to _String then write them to file number f. A newline character is appended at
the end.
See also:
WriteString Print OpenWrite OpenAppend Close $FORM PageWidth
StandardForm

WriteString[f, expr1 [,expr2 ...]]
converts expr1... to _String then write them to file number f. No newline character is appended.
See also:
Write OpenWrite OpenAppend Close $FORM PageWidth StandardForm


Forks the process into a parent and a child processes.
Fork[]
returns 0 and the child's pid for the child and the parent, respectively.

Allocated shared memory of n bytes.
s = OpenShared[n] ,
where s is a file number to be used by Shared function. The allocated memory can be released by Close[s].

Read/Write to the shared memory.
Shared[s]
Shared[s] = x
Shared[s] := x
where s is given by OpenShared, and x is Real, builtin function, String, defined symbol, or list
of them.

Returns the size of an object for OpenShared.
n = SharedSize[x]

Environment for an objectorientedprogramming is supplied by:
Class: The function to define a class.
context: A class defines a context to define its all symbols for
the variables and methods within the context.
This automatically avoids conflicts of symbols between
classes, Global, and System. When c = Class[ ... ] is
done, a context c` is defined.
members: The set of Members of a class is a union of class variables,
instance variables, and class methods of the class.
operator @: A special operator to access class member. In a notation
f@g, g's context defaults the class of the class of f.
f@g@h[x] is recognized as ((f@g)@h)[x] , thus the context of
h defaults the class of f.
superclasses: A class inherits all class variables, instance variables,
class methods from its superclasses which are give by the
first argument of Class. If a null list is given, Object`
is set as the default superclass. Multiple inheritance is
allowed.
class variable: Class variables are given by the second argument of Class
as a list of symbols. They are unique in the class.
They can be initialized by declaring in a way such as
{a=1, {b, c} = {2, 3}} like Module. A form like
{a = b = c =1} is allowed.
instance variable:
Instance variables are given by the third argument of Class
as a list of symbols. An instance has those symbols
separately. They can be initialized by declaring in a way
such as {a=1, {b, c} = {2, 3}} like as Module. A form like as
{a = b = c =1} is allowed. Also they
are initialized at the creation of instance by rules as
x = c[ a>1, b:>Print[d]], etc.
class methods: Class methods are given by the fourth(last) argument of
Class. They must be in the form of either one of
f_[arg___] := g_;
With[_, f_[arg___] := g_];
With[_, f_[arg___] := g_; .. ];
If[_,
ft_[argt___] := gt_; ..,
ft_[argf___] := gf_; ..,];
h_[f_[arg___], b___] ^:= g_; .
where f is the symbol for the method to be defined.
Set may be used instead of SetDelayed if necessary.
This: A symbol This in the definition of the method, it is
translated to the object (the instance or the class) which
refers the member.
default reference:
In the definition of the class methods, whenever a member of
the class is appeared, it is recognized as This@member.
When a symbol of the member conflicts the symbol in System`,
the system symbol should be wrapped by Literal.
reference of member of superclasses:
Members of the superclasses (denote cc) are referred by
cc`member in the definition of the method.
copying an instance:
An instance c of a class can be copied to another symbol
by c1 = c. After the copying, c1 and c refer the identical
instance. Destructing one of them by such as c1=. clears
the instance and also all the assigned symbols.
Constructor: When an instance is defined, by x = c[arg], a method
x@Constructor[arg] is always invoked.
In evaluation of instance definition under class scope,
class member symbol appeared 1st slot of Rule or RuleDelayed
argument is sent to Constructor of new class instance
without evaluation. (In other term, class member symbol on
1st slot of Rule or RuleDelayed argument behaves like
evaluating with implicit Literal[]) One can configure
Constructor[] in the definition of the class.
x = c[arg] returns the returned value of Constructor[arg].
The rules in the argument work in two ways: (1) A rule for an
instance variable or a class variable sets the initial value
of the variable, (2) Other rules are stored in an instance
variable Options as a list.
Destructor: An instance x is cleared by (x=.), which invokes
x@Destructor[]. The default Destructor is Object`Destructor,
but one can reconfigure it in the definition of the class.
Short: When an instance x is returned as the result of expression
for Out[], x@Short[] is invoked to show the result. The
default Short is Object`Short, but one can reconfigure it
in the definition of the class.
other methods: Class[] gives the class of the instance.
Parents[] gives the immediate superclasses.
AllParents[] gives the all superclasses.
Members[] gives a list of class variables, class methods,
and instance variables of the class.
AllMembers[] gives a list of class variables, class methods,
and instance variables of the class and its all parents.
See also:
Member(@)

Class sets up a class of objects.
Usage: a = Class[
list of superclasses,
list of classvariables,
list of instancevariables,
classmethods];
Example: a = Class[
{aa, bb}, (* aa and bb are superclasses *)
{a1, a2}, (* classvariables *)
{v1, v2}, (* instancevariables *)
Constructor[arg__] := (Print[{arg}]; v1 = Plus[arg]);
sum[] := v1 + v2 (* defining Constructor and method "sum"*)
];
a1 = a[1, 2] (* creating an instance of a *)
a1@v1 (* accessing an instance variable *)
a1@v2 = 3 (* setting an instance variable *)
a1@sum[] (* calling a method "sum" *)
a1=. (* delete an instance *)

The random number functions use common seed given by SEED command or SeedRandom function. It has
an initial value 17 at the beginning of FFS. The cutoff value of GaussRandom[] is given by variable
GCUT.
See also:
specialvariables: GCUT

Random[] gives a uniform random number between 0 and 1.
Random[n] gives a list of n uniform random numbers.
Random[n1, n2, ..] gives a (n1 * n2 * .. ) tensor of uniform random numbers.
See also:
GaussRandom ParabolaRandom SeedRandom

GaussRandom[] gives a Gaussian random number with average 0,
standard deviation 1, cutoff at GCUT.
GaussRandom[n] gives a list of n Gaussian random numbers.
GaussRandom[n1, n2, ..] gives a (n1 * n2 * .. ) tensor of Gaussian random
numbers.
See also:
Random ParabolaRandom SeedRandom

ParabolaRandom[] gives a parabola random number between 1 and 1.
ParabolaRandom[n] gives a list of n parabola random numbers.
ParabolaRandom[n1, n2, ..] gives a (n1 * n2 * .. ) tensor of parabola random
numbers.
See also:
Random GaussRandom SeedRandom

SeedRandom[plugin_String] selects new pseudo randomnumber generator
plugin named as plugin.
SeedRandom[seed_Real] initializes the internal state of the current
pseudo randomnumber generator plugin by seed.
SeedRandom[{seeds__Real}] initializes the internal state of the current
pseudo randomnumber generator plugin by {seeds}.
SeedRadnom[state_List] restores both the selection of the pseudo randomnumber
generator plugin and the internal state of the selected
plugin by using state dumped by SeedRandom[].
SeedRandom[] returns List containing both the current selected pseudo
randomnumber generator plugin name and its internal state.
See also:
ListRandom Random GaussRandom ParabolaRandom

ListRandom[] returns List of available pseudo randomnumber generator plugins.
See also:
SeedRandom



DateString[] returns the current date and time as string "mm/dd/CCYY HH:MM:SS".
DateString[date] converts date to string as above. The date can be either a real number (in second,
date=0 is 1/1/1900 0:0:0) or a list of 6 reals {Y,m,d,H,M,S}.

MemoryCheck[n]
checks the consistency of the memory allocation by SAD. The range of the check and the output depend
on n:
MemoryCheck[] : checks the consistency of the free area and returns the allocation info,
MemoryCheck[1] : checks the consistensy of the free and used areas. Returns the allocation info.
MemoryCheck[2] : checks the consistensy of the free and used areas. Returns the allocation info.
and a list of free segments.
The returned value is {used, allocated from system, # of free segments, missing size[, list of free
segments]} in units of word (= 8 bytes).
If an inconsistency is found, messages are printed out.

TimeUsed[] returns the cputime since the start of SAD in seconds.
See also:
Timing

Timing[fun]
evaluates fun and returns {cputime, result}. cputime is in seconds.
See also:
TimeUsed

TracePrint[fun]
prints out all function calls and each expression compound in ";" in the evaluation of fun.
Usage: (1) FIT [component]
(2) FIT component1 component2
sets the current location where the matching condition is applied. The component is given with the
form name[.order][{+}offset] (see components). If component is omitted, the end of the beam line
is chosen.
If two components are given, it means a relativefitting or zonefitting. If the fitting condition
is not maximumfitting, the condition means to make values at two components equal (for AX, BX, GMX,
AY, BY, GMY, EX, EPX, EY, EPY, R1, R2, R3, R4, DX, DPX, DY, DPY, PEX, PEPX, PEY, PEPY, CHI1, CHI2,
CHI3), or have the specified difference (for NX, NY, LENG, GX, GY, GZ). If the fitting condition
is maximumfitting, the condition means a zonefitting (for AX, BX, GMX, AY, BY, GMY, EX, EPX, EY,
EPY, R1, R2, R3, R4, DX, DPX, DY, DPY, PEX, PEPX, PEY, PEPY, CHI1, CHI2, CHI3), which suppress the
maximum of the function in the region between component1 and component2, or maximumfitting for the
difference of the function (for NX, NY, LENG, GX, GY, GZ). The fit region is shown in the first
part of the prompt when FFSPRMPT is ON.
Examples: (1) FIT QF.210
sets the current fit point at 10 components upstream from the entrance of the second QF.
(2) FIT QF QD NX 0.5 BXM 10
sets the twopoint fitting between QF and QD, then set the difference of NX between QF and QD to
be 0.5, and the maximum of BX to be 10 in the region between QF and QD.
See also:
matchingfunctioncommands components SHOW GO CALCULATE(CAL)
Usage: FITP n
sets n to the number of offmomentum points in the offmomentum matching. If the fitting condition
is onmomentum only, it is not affected.
See also:
matchingfunctioncommands
Usage: (1) FIX elementpattern [keyword] [elementpattern1 [keyword1]..]
removes elements which match elementpattern from the matching variables. The optional keyword specifies
the nondefault variables. If the keyword is omitted, all keywords are removed.
For the MARK element at the beginning of the beam line, a special form can be used for the FIX
command. That is a form < matchingfunction>> I (appending "I" to a matchingfunction name).
Example: FIX AXI BXI AYI BYI
removes incoming AX, BX, AY, and BY from the matching variables.
Usage: (2) FIX
sets the standard optics for the orbit correction commands.
See also:
FREE FIT SHOW GO CALCULATE(CAL) wildcards elements
Usage: FREE elementpattern [keyword] [elementpattern1 [keyword1]..]
specifies elements which match elementpattern as the matching variables. The optional keyword specifies
the nondefault variables. See defaultkeyword.
For the MARK element at the beginning of the beam line, a special form can be used for the FREE
command. That is a form < matchingfunction > I (appending "I" to a matchingfunction name)
which means the incoming condition of the matchingfunction is varied in the matching.
Example: FREE AXI BXI AYI BYI
changes incoming AX, BX, AY, and BY to find the solution.
See also:
FIX FIT SHOW GO CALCULATE(CAL) wildcards elements

The default and available nondefault variable keywords are:
type defaultkeyword nondefault variable keyword
DRIFT L 
BEND ANGLE K1,K0,E1,E2
QUAD K1 ROTATE
SEXT K2 ROTATE
OCT K3 ROTATE
DECA K4 ROTATE
DODECA K5 ROTATE
MULT K1 K0,K2..K21,SK0,SK1,SK2..SK21,ROTATE,ANGLE
MARK  AX,BX,EX,EPX,AY,BY,EY,EPY,R1,R2,R3,R4,DETR,
DX,DPX,DY,DPY,DZ,DDP,AZ,BZ,ZX,ZPX,ZY,ZPY
See also:
keywords
Available geometricfunctions are:
GX geometrical coordinate xi
GY geometrical coordinate eta
GZ geometrical coordinate zeta
CHI1 geometrical rotation angle ch1_1
CHI2 geometrical rotation angle ch1_2
CHI3 geometrical rotation angle ch1_3
The geometrical coordinate {xi, eta, zeta} is set by the ORG command, and its default origin is at
the entrance of the beam line, and the default directions are xi in sdirection, eta in (xdirection),
and zeta in (ydirection) at the entrance. The set {xi, eta, zeta} forms a righthand system.
The rotation angles are defined so as to give the local {x,y,s} is written
{x, y, s}_local
= rotate[s, chi3] rotate[x, chi2] rotate[y, chi1]{x, y, s}_origin,
where rotate[a, b] reads "rotate around the newa vector by b righthandedly.
geometric functions disignate the geometry of the coordinate. If the geometry of orbit is needed,
use LINE["OGEO"], etc., or DISP OG.
See also:
opticalfunctions matchingfunctioncommands DISPLAY(DISP)
GEOCAL GEOFIX ORG LINE
Usage: GO [[NO]EXPAND]
Does matching for fitting conditions given by matchingfunctioncommands with variables specified
by FREE.
If an option EXPAND is given (default), it expands the beam line before the calculation. If NOEXPAND
is given, it avoids any expansion. FFS["CAL"] and FFS["GO"] returns the result as a list, whose
format is
{dp, kind, reslist, functionvalues},
where
dp: a list contains dp/p0 .
kind: a list of kind of the orbit (usually 0, but 1 to 6 for the finite amplitude matching, see
MatchingAmplitude).
reslist: a list of {residual, xstab, ystab}, where
residual: matching residual,
xstab: True when the matrix is stable in X,
ystab: True when the matrix is stable in Y, for each orbit.
Above are lists with length nf (== number of orbits).
functionvalues: a list of length nc (== number of calculated items). Each element has the form:
{component1, component2, function, listofvalues},
where
component1, component2: fit locations (see FIT).
function: name of the function (see matchingfunctioncommands).
listofvalues: list of the value of the function for each orbit Length nf.
The central orbit comes at the Floor[(n+1)/2]th element.
See also:
FIT SHOW matchingfunctioncommands offmomentummatching
FREE FIX VARIABLES(VAR) COUPLE(COUP) ATTRIBUTE(ATTR) CALCULATE(CAL)
VARY SHOW CONV CONVERGENCE MatchingResidual MatchingAmplitude
FitFunction FFS OptimizeOptics
Usage: IF expr1 body1 [ELSEIF expr2 body2 [ELSEIF ..]] [ELSE body3] ENDIF
This is a FORTRAN77 like IFstructure. If the expression expr1 is True(==1) or nonzero, executes
commands in body1. If it is False(==0), skip commands until ELSE, ELSEIF or ENDIF appears at the
same level of the IFstructure, and executes commands after ELSE or ENDIF, or executes the ELSEIF
command. If expr1 is not a real number, an error message is printed and ignores the command line.
See also:
ELSE ELSEIF ENDIF expression commandsyntax If
IN {filename  filenumber} switches the input stream to the specified file or the filenumber. The
original stream is kept and to be returned by TERMINATE(TERM). The input file is not rewound.
See also:
TERMINATE(TERM) CLOSE(CLO) READ OUTPUT(OUT) APPEND(APP)
END
Usage: machineerrorcommand [options] amount componentpattern ..
where machineerrorcommand is one of
command keyword affected applicable types
DELX DX BEND QUAD SEXT OCT DECA DODECA SOL CAV
DELY DY BEND QUAD SEXT OCT DECA DODECA SOL CAV
DL L DRIFT SOL
DTHETA ROTATE QUAD SEXT OCT DECA DODECA CAV
DTHETA DROTATE BEND
DK defaultkeyword DRIFT BEND QUAD SEXT OCT DECA DODECA MULT SOL CAV
DDK K0 or DBZ BEND SOL
amount is the amount of the error,
componentpattern is the pattern to specify the components to be applied.
Options are
RANDOM(R) Set amount*GaussRandom[] to the keyword.
UNIFORM(U) Set the specified amount to the keyword without random number.
INCOHERENT(INC) GaussRandom[] is called for each component. Default.
COHERENT(C) GaussRandom[] is called once for each componentpattern.
PUT(P) Set the error to the keyword. Default.
ADD(A) Add the error to the keyword.
See also:
components wildcards keywords defaultkeyword DUMP SEED
Usage: (1) matchingfunction goalvalue [offmomentumpoints]
(2) matchingfunctionM goalvalue [offmomentumpoints]
(3) matchingfunctionI incomingvalue
(4) matchingfunctionSCALE scale
(1) sets the matching condition for matchingfunction at the current fitting point or region with
the goalvalue and the offmomentumpoints (see offmomentummatching).
If offmomentumpoints is omitted, the previous value for this matchingfunction at this fittingpoint
is assumed. If the previous value is not defined, 1 is assumed. If 1 is given for offmomentumpoints,
the matchingfunction is rejected from the matching (see REJECT(REJ)).
If "*" is given for goalvalue, the previous value is used if exists.
Example: BX 10 3 (beta_x to be 10 at 3 momenta)
BX 20 (now beta_x to be 20 at 3 momenta (previous setting))
BX * 5 (now beta_x to be 20 (previous setting) at 5 momenta)
(2) If the letter "M" is appended to matchingfunction, it means the maximumfitting for the function.
The maximum of either the value (for positivedefinite functions) or the absolute value (for bipolar
functions) are to be limited in the matching.
(3) If the letter "I" is appended to matchingfunction, it specifies the value of the incoming beam.
(4)
If SCALE is appended to matchingfunction, it sets the scale of the input/output of the function
to scale. This scale is used in the matchingfunction commands, DISPLAY(DISP), SHOW, etc.
(5) If the current fit location is at a MARK, @ for the goal value refers the save value at the MARK.
@ refers (save value). These are useful to match between two beam lines.
Available matchingfunctions are:
opticalfunctions (see opticalfunctions):
AX BX GMX NX AY BY GMY NY EX EPX EY EPY R1 R2 R3 R4 DETR DX DPX DY DPY DZ DDP PEX PEPX PEY PEPY TRX
TRY LENG
geometricfunctions (see geometricfunctions):
GX GY GZ CHI1 CHI2 CHI3
See also:
FIT GO SHOW MARK opticalfunctions geometricfunctions
offmomentummatching xycoupling REJECT(REJ) specialvariables
DP functions FitValue MatchingAmplitude
The multiturn tracking can be done by TrackParticles or DynamicApertureSurvey[] function in FFS.
The
multiturn tracking uses the closed orbit, normal coordinate, and the equilibrium emittances. Therefore
One of EMITTANCE(EMIT), the Emittance[] function, or the EMIT command in the MAIN level are necessary
to be done once in prior to the multiturntracking. The values of EMITX, EMITY, EMITZ, SIGE can
be changed between EMITs and the multiturntracking.
See also:
TrackParticles DynamicApertureSurvey EMITTANCE(EMIT)
RFSW RAD FLUC RADCOD SPAC WSPAC specialvariables equilibriumbeamenvelope
Usage: MATRIX [{SYMPLECTIC(S)  PHYSICAL(P)}] [from to]
prints out the 4 by 5 (w/CALC4D) or 6 by 6 (w/CALC6D) transfer matrix from fromcomponent to tocomponent.
If SYMPLECTIC(S) is specified (default), the symplectic transfer matrix on {x,px/p0,y,py/p0,dp/p0}
where p0 is the nominal momentum at the entrance, is given. Otherwise, in the case of TRPT, the transfer
matrix on {x,px/p0(s),y,py/p0(s),dp/p0(s)} is printed out.
If the from and to components are omitted, entire beam line is assumed.
If tocomponent is upstream the fromcomponent, it gives the inverse matrix (TRPT) or oneturnwrapped
matrix (RING).
See also:
DISPLAY(DISP) TRPT RING CALC4D CALC6D TransferMatrix
Usage: MEA [endcomponent] [OUT file plotspaces]
tracks particles from the entrance to endcomponent and prints out the statistics at the end. If
endcomponent is omitted, the component end used in the last MEASURE(MEA) (default: end of the beam
line) is assumed.
If OUT file plotspaces are attached, it plots phase space distribution on file. The phasespaces
are specified like as XPX,
or XY, etc., (up to any numbers).
Parameters for the tracking are specified by specialvariables and flags:
seed for the randomnumber generator:
SeedRandom[seed_Real] or SeedRandom[{seeds__Real}]
specialvariables (can be set with =):
NP number of particles
EMITX horizontal emittance
EMITY vertical emittance
DP relative momentum spread
DP0 relative momentum offset dp/p0
GCUT cutoff value of the Gaussian tail
flags:
GAUSS/UNIFORM Gaussian/uniform(default) momentum distribution
JITTER/NOJITTER off(default)/on nullifying the incoming centroid offset
RFSW/NORFSW switch on(default)/off the rfcavities
RAD/NORAD synchrotron radiation on/off
RADCOD/NORADCOD off/on compensation of energy loss due to radiation
FIXSEED/MOVESEED keep(default)/unkeep the initial randomnumber seed
The initial transverse distribution is Gaussian.
See also:
specialvariables TrackParticles SeedRandom RESULTOFTRACKING
FFS matches the optical functions for an orbit with finite momentum deviation.
Example:
DP=0.01; sets the range of momentum to DP00.01 < dp/p0 < DP0+0.01 .
BX 10 9; sets the goal of betax to 10 m, at 9 points.
in the range above, i.e.,
dp/p0 = {0.01,0.0075,0.005,0.0025,0,
0.0025,0.005,0.0075,0.01} + DP0 .
GO starts the matching.
As this example, the offmomentum points are chosen with equal separation. If the offmomentum point
n is an even number, the chosen points are same as the case of n+1, but the onmomentum point (==DP0)
is excluded.
See also:
matchingfunctioncommands DP DP0
Available optical functions for matching are:
AX alpha_X
BX beta_X
GMX gamma_X
NX psi_X, the default scale is 1/(2Pi)
AY alpha_Y
BY beta_Y
GMY gamma_Y
NY psi_Y, the default scale is 1/(2Pi)
EX eta_X (dispersion_X)
EPX eta_Px (dispersion_PX)
EY eta_Y (dispersion_Y)
EPY eta_Py (dispersion_PY)
R1 R_1 (see xycoupling)
R2 R_2 (see xycoupling)
R3 R_3 (see xycoupling)
R4 R_4 (see xycoupling)
DETR R_1*R_4  R_2*R_3 (see xycoupling)
DX dx
DPX dpx
DY dy
DPY dpy
DZ dz
DDP delta=dp/p0
AZ alpha_Z
BZ beta_Z
GMZ gamma_Z
NZ psi_Z, the default scale is 1/(2Pi)
ZX zeta_X (zdispersion_X)
ZPX zeta_Px (zdispersion_PX)
ZY zeta_Y (zdispersion_Y)
ZPY zeta_Py (zdispersion_PY)
PEX eta_x (dispersion_x)
PEPX eta_px (dispersion_px)
PEY eta_y (dispersion_y)
PEPY eta_yy (dispersion_py)
TRX trace(T_X), only defined at the end of the beam line.
TRY trace(T_Y), only defined at the end of the beam line.
LENG length of the design orbit
In the above, upper case X, Px, Y, Py represents the xy decoupled coordinate. EX, EPX, EY, EPY refer
the decoupled coordinate, while PEX, PEPX, PEY, PEPY are in the physical coordinate. On the other
hand, DX, DPX, DY, DPY refer the physical coordinate.
See also:
geometricfunctions xycoupling matchingfunctioncommands
GO CALCULATE(CAL) DISPLAY(DISP) SHOW
Usage: ORG location, dgx, dgy, dgz, dchi1, dchi2, dch3
sets the origin of the geometrical coordinate relative to the location with a relative shift (dgx,
dgy, dgz) and rotation (dchi1, dchi2, dchi3).
OUT {filename  filenumber} switches the output stream to the specified file or the filenumber.
The file is written from the beginning.
See also:
TERMINATE(TERM) CLOSE(CLO) INPUT(IN) READ APPEND(APP)
END
Pattern is a special expression for mathing arguments in function definitions and rules with several
forms:
_ matches any single argument.
__ matches a sequence of 1 or more arguments.
___ matches a sequence of 0 or more arguments.
x_ matches any single argument, which is names x.
x__ matches a sequence of 1 or more arguments, which is named x.
x___ matches a sequence of 0 or more arguments, which is named x.
x:pattern a pattern which is named x.
pattern:v a pattern which has a default value v when matching is failed.
pattern.. a nonnull sequence of arguments each of which matches pattern.
pattern... a sequence, which can be null, of arguments each of which matches pattern.
expression matches expression.
See also:
MatchQ definingfunctions rules
See also:
constants expression specialvariables
PRI expression evaluates expression and prints out the result.
See also:
expression Print
Exits FFS and return to SAD/MAIN level, without saving the values of the elements.
See also:
STOP SAVE ABORT USE VISIT BYE
RADINT prints out the radiation integrals involving the xcoupling for all components of the beam
line.
READ {filename  filenumber} switches the input stream to the specified file or the filenumber.
The original stream is kept and to be returned by TERMINATE(TERM). The input file is rewound.
See also:
TERMINATE(TERM) CLOSE(CLO) INPUT(IN) OUTPUT(OUT) APPEND(APP)
END
REC exchanges the values of FREEd elements with those when the last GO command was issued. FIXed
elements are not affected.
See also:
GO FREE FIX RESET SAVE
REFERENCE(REF) sets the current optics as the reference optics.
See also:
referenceoptics

Optics stored as a reference. Can be refered by DISP REF (mode), DRAW, Twiss, OpticsPlot. Set automatically
by the first CALC or GO after USE. Can be updated by REFERENCE(REF).
See also:
REFERENCE(REF) DISPLAY(DISP) DRAW Twiss OpticsPlot
Usage: (1) REJ matchingfunctionpattern [matchingfunctionpattern1..]
(2) REJ TOTAL
(3) REJ TOTALFIT
rejects the matchingfunctions which match matchingfunctionpattern at the current FIT location.
If TOTAL or TOTALFIT is given, the entire matching conditions in all locations are rejected, then
output parameters by CALCULATE are reset when TOTAL is given.
See also:
matchingfunctioncommands FIT wildcards
RENUM comp renumbers the component number starting from a component comp.
See also:
components
Usage: REP [n] body UNTIL [expr1]
executes commands in body n times until expr1 gives nonzero. The number n can be any expression which
gives a number. If n is omitted, infinity is assumed. If expr1 is omitted, False(==0) is assumed.
See also:
UNTIL
Usage: RESET [ALL] [elementpattern]
restores the value of the elements. What are restored are the value of the default keyword of all
elements, the values of the nondefault keywords which have been changed manually or by the matching.
If ALL is given, it resets all keywords. If elementpattern is given, reset is limited to the elements
which match the pattern.
See also:
SAVE USE VISIT wildcards RECOVER(REC)
Resumes reading from the previous input stream suspended by SUSPEND(SUSP) or END.
See also:
SUSPEND(SUSP) END
REV changes the sign of AX, AY, EPX, EPY, R2, R3, DPX, DPY at the
entrance of the beam line.
See also:
matchingfunctioncommands
Usage: elementpattern [keyword] [{MIN  MAX  MINMAX  MAXMIN}] value
sets value to the specified keyword of the elements which match elementpattern. If keyword is omitted,
the defaultkeyword is assumed. keyword can be a wildcard to apply all matching keywords.
If MIN, MAX, MINMAX, MAXMIN are specified, it sets the limit of the defaultkeyword. Both MINMAX
and MAXMIN means MIN=Abs[value] and MAX=+Abs[value].
If the keyword is not the defaultkeyword, it affects both the current and the saved value.
See also:
ATTRIBUTE(ATTR) SAVE elements defaultkeyword wildcards
Element

Available keywords are:
type keywords
DRIFT L RADIUS
BEND L ROTATE DROTATE DX DY ANGLE K0 K1 E1 E2 AE1 AE2 F1 FB1 FB2 FRINGE DISFRIN DISRAD EPS RANKICK
QUAD L ROTATE DX DY K1 F1 F2 FRINGE DISFRIN DISRAD EPS
SEXT L ROTATE DX DY K2 DISFRIN DISRAD
OCT L ROTATE DX DY K3 DISFRIN DISRAD
DECA L ROTATE DX DY K4 DISFRIN DISRAD
DODECA L ROTATE DX DY K5 DISFRIN DISRAD
MULT L DX DY DZ CHI1 CHI2 ROTATE(=CHI3) K0..K21 SK0..SK21 DISFRIN F1 F2 FRINGE DISRAD EPS VOLT
DVOLT HARM PHI DPHI FREQ RADIUS ANGLE E1 E2 AE1 AE2 DROTATE
SOL BZ DX DY DZ DPX DPY BOUND GEO CHI1 CHI2 CHI3 DBZ DISFRIN
CAVI L ROTATE DX DY VOLT DVOLT V1 V20 V11 V02 FREQ PHI HARM RANVOLT RANPHASE DISFRIN FRINGE
TCAVI L ROTATE DX DY K0 V1 FREQ PHI HARM RANKICK RANPHASE
COORD DX DY CHI1 CHI2 CHI3 DIR
MARK AX BX AY BY EX EPX EY EPY R1 R2 R3 R4 DETR DX DPX DY DPY DZ DDP AZ BZ NZ ZX ZPX ZY ZPY EMITX
EMITY DP AZ SIGZ GEO OFFSET
APERT DX1 DX2 DY1 DY2 DP AX AY DX DY
See also:
defaultkeyword setvalueofelement Element

The default and available nondefault variable keywords are:
type defaultkeyword nondefault variable keyword
DRIFT L 
BEND ANGLE K1,K0,E1,E2
QUAD K1 ROTATE
SEXT K2 ROTATE
OCT K3 ROTATE
DECA K4 ROTATE
DODECA K5 ROTATE
MULT K1 K0,K2..K21,SK0,SK1,SK2..SK21,ROTATE,ANGLE
MARK  AX,BX,EX,EPX,AY,BY,EY,EPY,R1,R2,R3,R4,DETR,
DX,DPX,DY,DPY,DZ,DDP,AZ,BZ,ZX,ZPX,ZY,ZPY
See also:
keywords
There are several variables which have special rolls in FFS. Some of them are also accessible in
the MAIN level.
See also:
constants expression flags

%Line counts the number of the results in FFS Shown with Out[]:= . Out remembers all outputs up
to Out[$Line]. $Line = 0 resets the counter and forgets the outputs.

CASE is a characterstring to be attached with TITLE to issue the CASE command of TopDrawer in DRAW
or GEO commands.
See also:
TITLE DRAW GEO

CHARGE contains the charge of the particle. The default is +1.

CONVERGENCE is the goal of the convergence(==MatchingResidual) in the matching. If MatchingResidual
becomes smaller than CONVERGENCE times the effective number of the conditions, the matching by GO
terminates. The flag CONV is set when MatchingResidual is smaller than CONVERGENCE after GO or CALCULATE(CAL).
The default value is 10^9.
See also:
GO MatchingResidual CONV

DAPWIDTH is the successive width of the xamplitudes to terminate the tracking assuming that the
aperture is enough. The default is 7.
See also:
DynamicApertureSurvey

DP represents the relative momentum spread of the beam. It is automatically set by the keyword DP
of the MARK element at the beginning of the beam line. The value of EMITY affects the default weight
of variables in the matching. In the offmomentum matching, the range DP0  DP < dp/p0 < DP0 + DP
is used for the matching. The assumed momentumdistribution in the BEAMSIZE(BEAM), MEASURE(MEA),
etc. commands, is Gaussian with the standard deviation DP and the mean DP0 if the flag GAUSS is on,
otherwise uniform (square) in the range DP0  DP < dp/p0 < DP0 + DP.
See also:
DP0 offmomentummatching GAUSS UNIFORM elements MARK

DP0 represents the central value of the relative momentum offset in the optics calculation, or the
center of the momentum distribution of the beam. The onmomentum optics has the relative momentum
deviation dp/p0 == DP0, and the offmomentum calculation is done in the range DP0  DP < dp/p0 <
DP0 + DP.
DP0 sets the momentum deviation of the closed orbit at the entrance for EMIT with RADTAPER.
See also:
DP offmomentummatching matchingfunctioncommands
EMITTANCE(EMIT) RADTAPER

DTSYNCH is the equilibrium arrival time advance (= c*delta t, in meter) where the synchrotron radiation
loss balances with the RF, calculated by EMIT/Emittance[SaveEMIT>True]. This corresponds to the
origin of the RF phase. The default is zero.
See also:
EMITX EMITY EMITZ SIGZ SIGE EMITTANCE(EMIT) Emittance PHICAV

The effective angular frequency weff (= 2 Pi EFFRFFREQ) is obtained using the second derivative
d^2Vcacc/dt^2 == weff^2 Vcacc ,
ehere Vcacc is the total acceleration voltage at the equilibrium phase PHICAV. These quantities Vcacc
and its derivatives are summed over all CAVIs and MULTs.
It is set by EMITTANCE(EMIT) or Emittance[]. Effective with RING only.
See also:
EFFVC PHICAV

Effective peak rf voltage EFFVC is given by
Abs[ weff Vcacc + I dVcacc/dt ] / weff ,
where Vcacc, weff are total acceleration voltage at the equilibrium phase PHICAV and the effective
RF angular frequency (=2 Pi EFFRFFREQ). DVcacc/dt is the time derivative of Vcacc. The quantity Vcacc
and its derivatives are summed over all CAVIs and MULTs.
It is set by EMITTANCE(EMIT) or Emittance[]. The unit is Volt. Effective with RING only.
See also:
EFFVCRATIO EFFRFFREQ PHICAV

Ratio of (effective voltage)/(Sum[VOLT_k,{k}]) (default: 1). Set by EMITTANCE(EMIT) or Emittance[].
Effective with RING only.
See also:
PHICAV EFFVC

ElementValues is a symbol to assign rules to determine values of keywords of elements or components.
This is used to give a dependence between keywords of different elements or components, or determine
then by a parametric expression.
Useage: ElementValues = { key[elem] :> expr, ...}
where
key: keyword to specify a value (string).
elem: String to specify the elements or components, wildcards are allowed.
expr: an expression which returs a real number to be set to the elements or components.
Example: ElementValues =
{ "DX"["QF1"] :> "DX"["QD1"]0.001,
"DY"["QF2.3"] :> "DY"["QD1.2"],
"ROTATE"["QF*"] :> f[x] }
Remarks:
1. Iff elem contains ".", it is recognized as components, otherwise as elements.
2. In the r.h.s. of the rule, an expression like key[elem] is evaluated as either LINE[key, elem]
or Element[key, elem], depending on elem has ".".
3. The expression expr can be any expression returning a real number.
4. Later rules overrides the former, if many rules apply on the same keyword of the same element.
5. The rule given by ElementValues overrides the relation given by COUP_LE command.
6. Use a[b] in stead of a@b.
7. ElementValues is cleared by USE. It is hidden by VISIT and restored by BYE.
See also:
COUPLE(COUP)

EMITX is a real variable for the horizontal emittance (not normalized by gamma beta). It is automatically
set by the keyword EMITX of the MARK element at the beginning of the beam line. The EMITTANCE(EMIT)
command returns its calculated value in EMITX. The value of EMITX affects the default weight of variables
in the matching. Accessible in MAIN.
See also:
EMITY EMITZ SIGZ SIGE DP elements MARK

EMITXE specifies the minimum horizontal emittance for EMITTANCE(EMIT) and Emittance[] calculations.
It is useful to give emittance determined externally, such as for proton machines.
See also:
EMITYE EMITZE

EMITY is a real variable for the vertical emittance (not normalized by gamma beta). It is automatically
set by the keyword EMITY of the MARK element at the beginning of the beam line. The EMITTANCE(EMIT)
command returns its calculated value in EMITY. The value of EMITY affects the default wei÷ht of
variables in the matching. Accessible in MAIN.
See also:
EMITX EMITZ SIGZ SIGE DP elements MARK

EMITYE specifies the minimum vertical emittance for EMITTANCE(EMIT) and Emittance[] calculations.
It is useful to give emittance determined externally, such as for proton machines.
See also:
EMITXE EMITZE

EMITZ is a real variable for the longitudinal emittance (not normalized by gamma beta). It is automatically
set by the keyword EMITZ of the MARK element at the beginning of the beam line. The EMITTANCE(EMIT)
command returns its calculated value in EMITZ. Accessible in MAIN.
See also:
EMITX EMITY SIGZ SIGE DP elements MARK

EMITZE specifies the minimum longitudinal emittance for EMITTANCE(EMIT) and Emittance[] calculations.
It is useful to give emittance determined externally, such as for proton machines.
See also:
EMITXE EMITYE

The exponent to calculate MatchinResidual. The default is 2.
See also:
MatchingResidual GO

If False (default), the calculation of response matrix for each matching variables uses analytical
expressions as much as possible. If True, performs numerical differentiation during the matching
by GO. It is useful for some variables and matching functions in some cases. It is slow, so should
be avoided for offmomentummatching for a large beam line.
See also:
GO offmomentummatching

FitFunction is a symbol to assign userdefined functions for matching with the GO command.
Usage: FitFunction := fun,
where fun is a function that returns a real number or a list of real numbers, to be matched to zero
by GO. The goal of GO is to make fun zero or a list of zeros, together with builtin matching conditions.
Thus the sum of fun^2 is added to MatchingResidual. GO also evaluates FitFunction to obtain the derivatives
numerically. The function fun can refer the value of variables by Element or LINE functions, and
the optical functions at DP0 by Twiss. The algorithm of matching is same as that for builtin conditions,
but it is slower because of the numerical differentiation, when the beam line is long and the number
of variables large.
Example: FitFunction := {Twiss["BX","$$$"]20, Twiss["BY","$$$"]20};
which puts the same goal as
FIT $$$ BX 20 BY 20 .
FitFunction is cleared by USE. It is also hidden by VISIT and restored by BYE.
See also:
GO FREE MatchingResidual DP0 Element LINE Twiss

FSHIFT is the relative shift df/f0 of the revolution (or rf) frequency in a ring. This is valid in
EMITTANCE(EMIT), the particletracking, and CAL/GO with CALC6D. For CAL/GO with CALC4D, DP0 should
be used instead.
See also:
EMITTANCE(EMIT) CALCULATE(CAL) GO CALC6D CALC4D DP0

GCUT specifies the cutoff value of Gaussian distribution in unit of the standard deviation. Accessible
in MAIN.
See also:
SEED GAUSS GaussRandom

Usage: InitialOrbits = { {x1, px1, y1, py1, z1, dp1}, ...};
or InitialOrbits = { {ax1, bx1, nx1, ay1, by1, ny1,
ex1, epx1, ey1, epy1, r11, r21, r31, r41,
x1, px1, y1, py1, z1, dp1, 0, 0, 0, 0, 0, 0, 0}, ...};
specifies initial conditions of a number of orbits for the optics calculation by CALCULATE(CAL) and
GO. Those coordinates are offset from the central orbit. If six numbers are given, only the offsets
of the orbits are affected. If 27 numbers are given, all Twiss parameters are set (values for nonorbit
params are used directly. Orbits are giving offsets.)
If InitialOrbits are given, the offmomentum matching and finiteamplitude matching is disabled.
InitialOrbits is also necessary to calculate optics with wake field.
See also:
CALCULATE(CAL) GO offmomentummatching MatchingAmplitude

LOSSAMPL is the transverse amplitude beyond which a particle is judged to have been lost. The default
is 1 m. Accessible in MAIN.
See also:
LOSSDZ APERT

LOSSDZ is the longitudinal position z beyond which a particle is judged to have been lost. The default
is 100 m. Accessible in MAIN. LOSSDZ is effective only when SPAC is ON.
See also:
LOSSAMPL APERT SPAC

MatchingAmplitude is a list of amplitudes for the finiteamplitude matching.
Usage: MatchingAmplitude := { {dp1,x1,y1}, ..};
where dp1 is the momentum deviation to be matched, x1 and y1 are the horizontal and vertical amplitudes
at the beginning of the beam line, normalized by Sqrt of the sum of the emittance, i.e., Sqrt[(EMITX+EMITY)].
Three orbits are chosen in each dimension. The initial conditions of the orbit is chosen as
{X,Px,Y,Py} =
{ {x1,0,0,0}, {x1/2,Sqrt[3]/2 x1,0,0}, {x1/2,Sqrt[3]/2 x1,0,0},
{0,0,y1,0}, {0,0,y1/2,Sqrt[3]/2 y1}, {0,0,y1/2,Sqrt[3]/2 y1} },
and when x1==0 or y1==0 corresponding orbits are excluded. The above are labeled {x1,x2,x3,y1,y2,y3}
in the output of CALCULATE(CAL) or GO, and also labeled 1 to 6 in the second element of FFS["CALC"]
and FFS["GO"].
This matching is done when dp1 is within the offmomentum range given by DP, i.e., Abs[dp1] <
DP. If dp1 is in the range, the nearest zero amplitude optics is chosen. The maching conditions
for the finite amplitude optics are same as those for the zeroamplitude one.
Th orbit with finte initial condition never close after one revolution, but FFS simply ignores
it and obtain the periodic optics around the open
orbit.
See also:
DP EMITX EMITY offmomentummatching CALCULATE(CAL) GO

MatchingResidual holds the convergence in the last GO or CALCULATE(CAL) commands. It is calculated
by
sw*(Sum[(w_i*df_i)^ExponentOfResidual,{i}]/sw)^(2/ExponentOfResidual)
+penalty
where w_i is the weight of the ith condition, df_i is the difference of the ith function from
the goal, penalty is an additional big number (typically 10), when the optics is unstable or closed
orbit is not found in the case of CELL. The parameter sw is defined as
sw=Sum[(OffMomentumWeight/2/woff)^2,{i}]
with
woff = 1 for onmomentum optics
= Sqrt[numberofmomentumpoints] for offmomentum optics.
The weight of the function is lighter in the case of offmomentummatching so that all offmomentum
deviations functions weight equal to the onmomentum one. However, the relative weight for the offmomentum
part can be changed by setting OffMomentumWeight.
The weight of each function at each point with each momentum can be specified by defining the
FitWeight function.
See also:
ExponentOfResidual CONVERGENCE OffMomentumWeight offmomentummatching
FitWeight

MASS is the rest mass of the particle in eV. The default is the electron mass.

MINCOUP is the minimum emittance ratio to be assumed in the calculation of intrabeam effects in EMITTANCE(EMIT)
and Emittance[]. Emittances Max[emit_k, MINCOUP*(emit_x+emit_y)] (k=x,y) are assumed in the intrabeam
calculation. Accessible in MAIN.
See also:
EMITTANCE(EMIT) Emittance INTRA equilibriumbeamenvelope

MOMENTUM is the nominal momentum of the beam line at the entrance in eV/c. Accessible in MAIN.

NBUNCH is the number of bunches for the calculation of WakeFunction. Accessible in MAIN.
See also:
PBUNCH

The net residual of convergence except the penalty for unstable optics.
See also:
MatchingResidual StablilityLevel

NP is the number of particles in the tracking. Accessible in MAIN.
See also:
MEASURE(MEA)

NPARA specifies the maximum number of parallel processes for various calculations such as CALC, GO,
TrackParticles, DynamicApertureSurve, etc.
See also:
CALCULATE(CAL) GO TrackParticles DynamicApertureSurvey

Relative weight of the offmomentum deviation for the offmomentum matching. The default is 1.
See also:
ExponentOfResidual CONVERGENCE MatchingResidual offmomentummatching
FitWeight

OMEGA0 is 2*Pi*SpeedOfLight/LINE["s","$$$"] . Accessible in MAIN.
See also:
SpeedOfLight LINE

OpticsEpilog is a variable to assign a userdefined function which is to be executed every time after
an optics calculation is done in CALCULATE(CAL) or GO commands. In GO, OpticsEpilog is called at
the end of each iteration. This function is useful, for instance, for setting parameters which depends
on the result of optics calculation itself.
See also:
OpticsProlog

OpticsProlog is a variable to assign a userdefined function which is to be executed every time before
an optics calculation is done in the CALCULATE(CAL) or GO commands. In GO, OpticsProlog is called
at the beginning of each iteration. This function is useful, for instance, for setting parameters
which depends on the result of optics calculation itself.
See also:
OpticsEpilog

PBUNCH is the number of particles/bunch for the calculation of the intrabeam and space charge effects
in EMITTANCE(EMIT), and WakeFunction. Accessible in MAIN.
See also:
EMITTANCE(EMIT) INTRA WSPAC WakeFunction equilibriumbeamenvelope

When PHOTONS is ON (default is OFF), with RAD and FLUC, TrackParticles generates a list of all photons
radiated through the tracking. The list is assigned to a symbol PhotonList. PhotonList is a list
of
{en, gx, gy, gz, nx, ny, nz, xi1, xi2, xi3, np, nele}
where
en: photon energy [eV]
gx: GX coordinate of the emission point [m]
gy: GY coordinate of the emission point [m]
gz: GZ coordinate of the emission point [m]
nx: GX component of the photon direction vector
ny: GY component of the photon direction vector
nz: GZ component of the photon direction vector (nx^2+ny^2+nz^2)=1.
xi1: Stokes' parameter for polarization 45 degree to the GZ=0 plane.
xi2: Stokes' parameter for righthanded polarization
xi3: Stokes' parameter for polarization in the GZ=0 plane.
np: particle number
nele: component number in the beam line
The probability of each polarization is given by each Stokes' parameter as (1+xi)/2 . TrackParticles
always updates PhotonList. The length of PhtonList is the number of emitted photons.
Remember that the {GX, GY, GZ} = {0, 0, 0} and their directions are {z, x, y} at the entrance
of the beam line by default. It is changeable by the GEO command anyway.
See also:
PHOTONS TrackParticles

The equilibrium RF phase (in radian, = 2 Pi EFFRFFREQ DTSYNCH/c) where the synchrotron radiation
loss and acceleration balances. If there are phase, voltage, frequency variations in RF cavities,
it is calculated based on "effective voltage". Effective with RING only.
See also:
EFFVC EFFRFFREQ DTSYNCH CAVI MULT

SIGE is the equilibrium momentum spread at the entrance of the beam line calculated by EMIT/Emittance[SaveEMIT>True].
See also:
EMITX EMITY EMITZ SIGZ EMITTANCE(EMIT) Emittance

SIGZ is the equilibrium bunch length at the entrance of the beam line calculated by EMIT/Emittance[SaveEMIT>True].
See also:
EMITX EMITY EMITZ SIGE EMITTANCE(EMIT) Emittance

SpeedOfLight is 299792458.

Number of unstable planes in the optics calculations. Equal to zero if all x and y optics are stable
for on/offmomentum and finite amplitude matching.
See also:
NetResidual MatchingResidual

TITLE is a characterstring to make the title of the plot in DRAW or GEO commands.
See also:
CASE DRAW GEO
Usage: SAVE [elementpattern]
saves the values of the elements. What are saved are the value of the default keyword of all elements,
the values of the nondefault keywords which have been changed manually or by the matching. If ALL
is given it resets all keywords. If elementpattern is given, it is only limited to the elements
which match the pattern, otherwise all elements are saved.
See also:
RESET USE VISIT BYE STOP QUIT wildcards
The SEED command is obsolete. Use SeedRandom[] function instead of SEED.
See also:
MEASURE(MEA) FIXSEED MOVESEED SeedRandom
SHOW prints out the current matching conditions.
FFS["SHOW"] or FFS$SHOW[] returns the current matching conditions as a list. Each element has
a form of
{component1, component2, function, goalvalue, numberofmomentums, scale},
which corresponds to the format of the printout by SHOW.
See also:
matchingfunctioncommands FIT FFS FFS$SHOW
Usage: SPLIT component length
splits the component into two pieces at the point where the distance from the entrance is length.
The new components have the same name as the original, and the strengths are proportional to the
new lengths. Only magnets and cavities can be split. You should CALCULATE(CAL) after SPLIT to get
optical parameters after SPLIT. Matching using SPLIT element as a variable may degrade the speed
of convergence.
STAT shows the current settings of flags, fit points,
specialvariables, the region for DISPLAY, seed of the random number generator, and elapsed CPU time,
etc.
See also:
specialvariables flags
Exits FFS and returns to SAD/MAIN level, with saving the values of the elements.
See also:
QUIT SAVE ABORT USE VISIT BYE
Suspend reading from the current input stream, and wait for input from the console. Resumes by RESUME(RES)
See also:
RESUME(RES) END
TERM [INPUT(IN)] suspends the current input stream and switches it to the previous input stream.
TERM OUTPUT(OUT) suspends the current output and switches it to the previous output stream.
See also:
CLOSE(CLO) INPUT(IN) READ OUTPUT(OUT) APPEND(APP) END
Usage: TYPE [elementpattern [elementpattern1..]]
prints out the values of elements which match elementpattern in the SAD MAIN input format. Keywords
which have zero values are omitted unless it is the default variable. If non elementpattern is given,
all elements are printed out.
See also:
DISPLAY(DISP) VARIABLES(VAR) elements
Usage: REP [n] body UNTIL [expr1]
executes commands in body n times until expr1 gives nonzero. The number n can be any expression which
gives a number. If n is omitted, infinity is assumed. If expr1 is omitted, False(==0) is assumed.
See also:
REPEAT(REP) expression commandsyntax functions Do
Usage: USE [[NO]EXPAND] beamline
switches the beam line used in FFS to the beam line given by beamline. beamline can be an BeamLine
object or the name of a beam line defined in MAIN. All information specific to the current beam line,
such as matching conditions is lost. If the keyword EXPAND is given (default), the new beam line
is expanded, i.e., the values of components are refreshed to the saved values.
If a BeamLine object is used by USE or VISIT, the new beam line becomes a
new LINE in the MAIN level, with a name which is created automatically.
See also:
VISIT BYE EXPAND BeamLine BeamLineName
VARIABLES displays a list of current matchingvariables and their present, previous, saved, minimum,
and maximum values together with the COUPLEd master elements and their coefficients.
When executed in the FFS function, it returns the result as a list.
Usage: FFS["VAR"]
returns a list of nvar elements, where nvar is the number of current matchingvariables given by
the FREE command. Each element has the form
{name, keyword, present, previous, saved, minimum, maximum, coupledmasterelement, couplingcoefficient}
,
which corresponds to the output of the VARIABLES(VAR) command.
See also:
FREE COUPLE(COUP) FFS
Usage: VARY keyword elementpattern
changes the defaultkeyword of the elements which match elementpattern to keyword.
See also:
FREE elements wildcards
Usage: VISIT [[NO]EXPAND] beamline
switches the beam line used in FFS to the beam line given by beamline. beamline can be an BeamLine
object or the name of a beam line defined in MAIN. All information specific to the current beam line,
such as matching conditions are reserved, and the previous beam line is restored when BYE command
is issued. If the keyword EXPAND is given (default), the new beam line is expanded, i.e., the values
of components are refreshed to the saved values.
If a BeamLine object is used by USE or VISIT, the new beam line becomes a new LINE in the MAIN
level, with a name which is created automatically.
See also:
USE BYE EXPAND BeamLine BeamLineName
Many commands and functions accept the wildcards as a specification for the name of elements or
components. The valid wildcards are:
* matches any zero or more characters.
% matches one character.
{..} matches any character enclosed.
{^..} matches any character not enclosed.
.... alternative pattern.
See also:
elements components DISPLAY(DISP) TYPE(T) SAVE RESET FREE
FIX ATTRIBUTE(ATTR) REJECT(REJ) CALCULATE(CAL) functions
Element LINE Twiss