SAD\/FFS Examples<\/h2>\n
<\/center> <\/a> <\/a><\/p>\n SAD\/FFS Examples Back to SAD Home Page Back to SAD\/FFS Commands Results ! ! This is an example of SAD\/FFS to design a positron ring ! with unit cells and dispersion suppressors. Chromaticity correction...<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[6],"tags":[],"class_list":["post-84","post","type-post","status-publish","format-standard","hentry","category-how-to-use-sad"],"jetpack_featured_media_url":"","jetpack_sharing_enabled":true,"_links":{"self":[{"href":"https:\/\/acc-physics.kek.jp\/SAD\/wp-json\/wp\/v2\/posts\/84","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/acc-physics.kek.jp\/SAD\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/acc-physics.kek.jp\/SAD\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/acc-physics.kek.jp\/SAD\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/acc-physics.kek.jp\/SAD\/wp-json\/wp\/v2\/comments?post=84"}],"version-history":[{"count":10,"href":"https:\/\/acc-physics.kek.jp\/SAD\/wp-json\/wp\/v2\/posts\/84\/revisions"}],"predecessor-version":[{"id":527,"href":"https:\/\/acc-physics.kek.jp\/SAD\/wp-json\/wp\/v2\/posts\/84\/revisions\/527"}],"wp:attachment":[{"href":"https:\/\/acc-physics.kek.jp\/SAD\/wp-json\/wp\/v2\/media?parent=84"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/acc-physics.kek.jp\/SAD\/wp-json\/wp\/v2\/categories?post=84"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/acc-physics.kek.jp\/SAD\/wp-json\/wp\/v2\/tags?post=84"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}
\n<\/p>\n![\"SAD\"](\"\/SAD\/wp-content\/uploads\/2020\/05\/SAD.png\"){kind=small}
Back to SAD Home Page<\/h4>\n
\n<\/p>\nBack to SAD\/FFS Commands<\/h4>\n
Results<\/a><\/h3>\n
\n\r\n!\r\n! This is an example of SAD\/FFS to design a positron ring \r\n! with unit cells and dispersion suppressors. Chromaticity correction\r\n! and also a survey of dynamic aperture are also done.\r\n! The result of execution of this example is available in\r\n! \/SAD\/doc\/design_example.sad.result\r\n!\r\nMOMENTUM= 1 GEV;\r\nON ECHO;OFF CTIME;\r\n!\r\n! ***** DEFINITION OF ELEMENTS IN MAIN LEVEL *****\r\n! \r\n ;\r\n DRIFT L1 = (L = 1)\r\n ;\r\n BEND B = (L = 2)\r\n ;\r\n QUAD QF = (L = 1 K1 = 0.1 )\r\n QD = (L = 1 K1 = -0.1 )\r\n QSF = (L = 1 K1 = 0.1 )\r\n QSD = (L = 1 K1 = -0.1 )\r\n QRF = (L = 1 K1 = 0.1 )\r\n QRD = (L = 1 K1 = -0.1 )\r\n ; \r\n SEXT SF =(L = 1 K2 = 0.1)\r\n SD =(L = 1 K2 = -0.1)\r\n ;\r\n MARK IP1 =(BETAX = 10 BETAY =10 EMIX = 4.0E-7\r\n EMIY = 4.0E-7 DP = 0.01 )\r\n ;\r\n CAVI CA1 = (L = 1 VOLT=1 MV HARM=100)\r\n ;\r\n!\r\n! ***** DEFINITION OF UNIT CELL IN MAIN LEVEL *****\r\n!\r\n! You need at least one LINE to start FFS, but\r\n! other lines can be created in FFS.\r\n!\r\n ;\r\n LINE CELL = (IP1 QF L1 SF L1 B 3*L1 QD L1 SD L1 B 3*L1)\r\n ;\r\n FFS USE=CELL;\r\n Print[TimeUsed[]];! CPU Time used so far.\r\n!\r\n! Defining parameters:\r\n!\r\n nbends=24; ! number of bends per ring\r\n nxcell=0.25; ! horizontal tune\/cell\r\n nycell=0.25; ! vertical tune\/cell\r\n Print[TimeUsed[]];! CPU Time used so far.\r\n!\r\n! ***** UNIT CELL MATCHING *****\r\n!\r\n CELL; ! peridic condition\r\n B 2*Pi\/nbends; ! settin bending angle to the BEND B\r\n FIT; ! set fit point at end of line\r\n NX nxcell; ! set fit condition NX\r\n NY nycell; ! set fit condition NY\r\n FREE Q*; ! set Q* (in this case QF and QD) as the matching\r\n ! variable\r\n GO; ! start matching\r\n! define dr as the drawing command (needs X-Window)\r\n dr:=FFS[\"OUT 'a' DRAW BX BY & EX EY {BQ}*; TERM OUT; TDR 'a';\"];\r\n dr; ! draw optics of unit cell\r\n SAVE; ! save the matching result (values of QF, QD) to\r\n ! keep them after swtch the beam line.\r\n Print[TimeUsed[]];! CPU Time used so far.\r\n!\r\n! ***** DISPERSION SUPPRESSOR *****\r\n!\r\n unitcell=ExtractBeamLine[]; ! get the current BeamLine\r\n! define a dispersion suppressor to insert rf\r\n supp=BeamLine[QSF, 8*L1, QSD, 3*L1, B, 3*L1, QRF, 3*L1, CA1, 3*L1, QRD];\r\n USE Join[unitcell, supp]; ! switch the beam line with suppressor\r\n INS; ! now nonperiodic (a transport line)\r\n QRD L 0.5; ! set the thickness of QD\r\n FIT; \r\n AX 0; ! set the end of line to be a symmetry point\r\n AY 0; \r\n EX 0; ! and dispersion-free\r\n EPX 0;\r\n Q*F MIN 0; ! set the lower limit of K1 of QRF, QSF\r\n Q*D MAX 0; ! set the upper limit of K1 of QRD, QSD \r\n FREE QS* QR*;\r\n GO; \r\n dr; ! draw suppressor\r\n SAVE;\r\n Print[TimeUsed[]];! CPU Time used so far.\r\n!\r\n! ***** TOTAL RING *****\r\n!\r\n ncell=(nbends\/2-2)\/2; ! number of unitcells per half ring.\r\n! Defining a half ring, removing the\r\n! first QF and IP1 markers in unitcell\r\n hring=BeamLine[IP1,-supp,Rest[ncell*Rest[unitcell]],supp];\r\n USE Join[hring,-hring]; ! switch to full ring\r\n CELL; ! now periodic condition again\r\n CAL NX NY; ! set to display NX and NY after CAL\r\n CAL ! calculate the optics of ring\r\n dr; ! draw ring\r\n Print[TimeUsed[]];! CPU Time used so far.\r\n!\r\n! ***** CHROMATICITY CORRECTION *****\r\n! \r\n! get the current tunes\r\n {nx0, ny0}=Twiss[{\"NX\",\"NY\"},\"***\"]\/2\/Pi;\r\n FIT;\r\n NX nx0 5; ! set the offmomentum tunes for 5 points\r\n NY ny0 5; ! in -DP < dp\/p0 < DP\r\n DP=0.01; ! set the bandwidth |dp\/p0|max = DP = 0.01\r\n FREE S*; ! set S* (SF and SD) sextupoles as variable\r\n GO;\r\n FITP 1; ! set the off-momentum points to 1 (on-momentum only).\r\n !\r\n ! Define Functions to display tunes as functions of dp\/p0\r\n nx[dp_]:=(DP0=dp;FFS[\"CALC\"];Twiss[\"NX\",\"***\"]\/2\/Pi);\r\n ny[dp_]:=(DP0=dp;FFS[\"CALC\"];Twiss[\"NY\",\"***\"]\/2\/Pi);\r\n !\r\n ! Plot tunes -3% < dp\/p0 < 3%.\r\n Plot[{nx[dp],ny[dp]}, {dp, -0.03, 0.03},\r\n PlotLabel->\"Tune Chromaticity\",\r\n FrameLabel->{{\"`fD`np\/p`d0`n\",\"F X X\"},{\"`fn`n`dx`n, `fn`n`dy`n\",\"GX X GX X\"}}];\r\n ! draw chromaticity\r\n If[$DisplayFunction === CanvasDrawer, Update[]];\r\n TYPE; ! print out all elements\r\n PrintBeamLine[ExtractBeamLine[]]; ! print out all beam line\r\n Print[TimeUsed[]];! CPU Time used so far.\r\n!\r\n! ***** EMITTANCE CALCULATION *****\r\n!\r\n EMIOUT; ! turn on the output of matrices by EMIT.\r\n EMIT; ! This (or Emittance[]) is necessary before tracking\r\n Print[TimeUsed[]];! CPU Time used so far.\r\n!\r\n! ***** DYNAMIC APERTURE *****\r\n!\r\n! Dynamic aperture for 1000 turns,\r\n DynamicApertureSurvey[{{0,100},{0,100},Range[-30,30,4]},\r\n 1000,Output->6];\r\n!\r\n Print[TimeUsed[]];! CPU Time used so far.\r\n ABORT ! stop SAD.\r\n<\/pre>\n
\nResults:<\/a><\/h3>\n
\r\n *** Welcome to SAD Ver.1.1.0.7k64 built at 2017-06-19 14:13:42 +0900 ***\r\n *** Today: 03:24:38 Thursday 06\/22\/2017 ***\r\n OFF LOG ECHO;READ 77 ; 23\r\n!\r\n! ***** DEFINITION OF ELEMENTS IN MAIN LEVEL *****\r\n!\r\n ;\r\n DRIFT L1 = (L = 1)\r\n ;\r\n BEND B = (L = 2)\r\n ;\r\n QUAD QF = (L = 1 K1 = 0.1 )\r\n QD = (L = 1 K1 = -0.1 )\r\n QSF = (L = 1 K1 = 0.1 )\r\n QSD = (L = 1 K1 = -0.1 )\r\n QRF = (L = 1 K1 = 0.1 )\r\n QRD = (L = 1 K1 = -0.1 )\r\n ;\r\n SEXT SF =(L = 1 K2 = 0.1)\r\n SD =(L = 1 K2 = -0.1)\r\n ;\r\n MARK IP1 =(BETAX = 10 BETAY =10 EMIX = 4.0E-7\r\n EMIY = 4.0E-7 DP = 0.01 )\r\n ;\r\n CAVI CA1 = (L = 1 VOLT=1 MV HARM=100)\r\n ;\r\n!\r\n! ***** DEFINITION OF UNIT CELL IN MAIN LEVEL *****\r\n!\r\n! You need at least one LINE to start FFS, but\r\n! other lines can be created in FFS.\r\n!\r\n ;\r\n LINE CELL = (IP1 QF L1 SF L1 B 3*L1 QD L1 SD L1 B 3*L1)\r\n ;\r\n FFS USE=CELL;\r\n *** SADScript Initialization: \/Users\/oide\/SAD\/oldsad\/Packages\/init.n ***\r\n *** Run time Environment: \/Users\/oide\/SAD\/oldsad\/Packages\/init.local.n ***\r\n RFSW RADCOD RAD FLUC INTRA POL COD DAPER EMIOU CMPLO FOURI SMEAR\r\n F F F T F F T F F F F T\r\n Print[TimeUsed[]];! CPU Time used so far.\r\n.013938000425696373\r\n !\r\n ! Defining parameters:\r\n !\r\n nbends=24; ! number of bends per ring\r\n nxcell=0.25; ! horizontal tune\/cell\r\n nycell=0.25; ! vertical tune\/cell\r\n Print[TimeUsed[]];! CPU Time used so far.\r\n.013987000100314617\r\n !\r\n ! ***** UNIT CELL MATCHING *****\r\n !\r\n CELL; ! peridic condition\r\n B 2*Pi\/nbends; ! settin bending angle to the BEND B\r\n FIT; ! set fit point at end of line\r\n NX nxcell; ! set fit condition NX\r\n NY nycell; ! set fit condition NY\r\n FREE Q*; ! set Q* (in this case QF and QD) as the matching\r\n ! variable\r\n GO; ! start matching\r\n Iterations Residual Method Reduction Variables\r\n 2 4.3472E-03 (NEWTON) 1.000 2\r\n 3 1.6466E-07 (NEWTON) 1.000 2\r\n Matched. ( 1.6175E-15) DP = 0.01000 DP0 = 0.00000 ExponentOfResidual = 2.0 OffMomentumWeight = 1.000\r\n$$$ f AX ####### # -1.496566 $$$ f BX ####### # 23.647704 $$$ f NX .25 1 .250000\r\n$$$ f AY ####### # .467389 $$$ f BY ####### # 6.097759 $$$ f NY .25 1 .250000\r\n$$$ f LENG ####### # 18.000000\r\n ! define dr as the drawing command (needs X-Window)\r\n dr:=FFS[\"OUT 'a' DRAW BX BY & EX EY {BQ}*; TERM OUT; TDR 'a';\"];\r\n dr; ! draw optics of unit cell\r\n<\/pre>\n![](\"\/SAD\/example\/cell.png\")
<\/p>\n\r\nsh: tdr: command not found\r\n SAVE; ! save the matching result (values of QF, QD) to\r\n ! keep them after swtch the beam line.\r\n Print[TimeUsed[]];! CPU Time used so far.\r\n.4507949948310852\r\n !\r\n ! ***** DISPERSION SUPPRESSOR *****\r\n !\r\n unitcell=ExtractBeamLine[]; ! get the current BeamLine\r\n ! define a dispersion suppressor to insert rf\r\n supp=BeamLine[QSF, 8*L1, QSD, 3*L1, B, 3*L1, QRF, 3*L1, CA1, 3*L1, QRD];\r\n USE Join[unitcell, supp]; ! switch the beam line with suppressor\r\n INS; ! now nonperiodic (a transport line)\r\n QRD L 0.5; ! set the thickness of QD\r\n FIT;\r\n AX 0; ! set the end of line to be a symmetry point\r\n AY 0;\r\n EX 0; ! and dispersion-free\r\n EPX 0;\r\n Q*F MIN 0; ! set the lower limit of K1 of QRF, QSF\r\n Q*D MAX 0; ! set the upper limit of K1 of QRD, QSD\r\n FREE QS* QR*;\r\n GO;\r\n Iterations Residual Method Reduction Variables\r\n 3 258.4 (NEWTON) 6.2500E-02 4\r\n 4 118.5 (NEWTON) 0.2500 4\r\n 5 36.05 (NEWTON) 1.000 3\r\n 7 22.82 (NEWTON) 0.2044 3\r\n 8 4.008 (NEWTON) 0.8176 2\r\n 9 2.705 (NEWTON) 1.000 4\r\n 13 2.465 (NEWTON) 1.5625E-02 4\r\n 14 2.096 (NEWTON) 6.2500E-02 4\r\n 15 0.4112 (NEWTON) 0.2500 4\r\n 17 0.2073 (NEWTON) 0.2077 4\r\n 18 1.5378E-03 (NEWTON) 0.8306 4\r\n 19 1.4651E-06 (NEWTON) 1.000 4\r\n Matched. ( 2.7823E-13) DP = 0.01000 DP0 = 0.00000 ExponentOfResidual = 2.0 OffMomentumWeight = 1.000\r\n$$$ f AX 0 1 1.9485E-9 $$$ f BX ####### # 1.784152 $$$ f NX ####### # .716798\r\n$$$ f AY 0 1 -5.273E-7 $$$ f BY ####### # 110.11073 $$$ f NY ####### # .792207\r\n$$$ f EX 0 1 -2.011E-9 $$$ f EPX 0 1 -1.89E-10 $$$ f LENG ####### # 44.500000\r\n dr; ! draw suppressor\r\n<\/pre>\n
![](\"\/SAD\/example\/suppressor.png\")
<\/p>\n\r\nsh: tdr: command not found\r\n SAVE;\r\n Print[TimeUsed[]];! CPU Time used so far.\r\n.6118450164794922\r\n !\r\n ! ***** TOTAL RING *****\r\n !\r\n ncell=(nbends\/2-2)\/2; ! number of unitcells per half ring.\r\n ! Defining a half ring, removing the\r\n ! first QF and IP1 markers in unitcell\r\n hring=BeamLine[IP1,-supp,Rest[ncell*Rest[unitcell]],supp];\r\n USE Join[hring,-hring]; ! switch to full ring\r\n CELL; ! now periodic condition again\r\n CAL NX NY; ! set to display NX and NY after CAL\r\n CAL ! calculate the optics of ring\r\n Matched. ( 0.000 ) DP = 0.01000 DP0 = 0.00000 ExponentOfResidual = 2.0 OffMomentumWeight = 1.000\r\n$$$ f AX ####### # 4.496E-15 $$$ f BX ####### # 1.784152 $$$ f NX ####### # 4.354010\r\n$$$ f AY ####### # .000000 $$$ f BY ####### # 110.11071 $$$ f NY ####### # 4.615261\r\n$$$ f LENG ####### # 284.00000\r\n dr; ! draw ring\r\n<\/pre>\n
![](\"\/SAD\/example\/ring.png\")
<\/p>\n\r\nsh: tdr: command not found\r\n Print[TimeUsed[]];! CPU Time used so far.\r\n.7871990203857422\r\n !\r\n ! ***** CHROMATICITY CORRECTION *****\r\n !\r\n ! get the current tunes\r\n {nx0, ny0}=Twiss[{\"NX\",\"NY\"},\"***\"]\/2\/Pi;\r\n FIT;\r\n NX nx0 5; ! set the offmomentum tunes for 5 points\r\n NY ny0 5; ! in -DP < dp\/p0 < DP\r\n DP=0.01; ! set the bandwidth |dp\/p0|max = DP = 0.01\r\n FREE S*; ! set S* (SF and SD) sextupoles as variable\r\n GO;\r\n Iterations Residual Method Reduction Variables\r\n 2 3.8125E-04 (NEWTON) 1.000 2\r\n *****qcod---> Overflow & closed orbit not found\r\n ***qmdiag---> Sum resonance: (TrA-TrB)^2 = NaN\r\n *****qcod---> Overflow & closed orbit not found\r\n ***qmdiag---> Sum resonance: (TrA-TrB)^2 = NaN\r\n 19 3.8110E-04 (NEWTON) 1.000 2\r\n *****qcod---> Overflow & closed orbit not found\r\n ***qmdiag---> Sum resonance: (TrA-TrB)^2 = NaN\r\n *****qcod---> Overflow & closed orbit not found\r\n ***qmdiag---> Sum resonance: (TrA-TrB)^2 = NaN\r\n Residual = 3.8110E-04 DP = 0.01000 DP0 = 0.00000 ExponentOfResidual = 2.0 OffMomentumWeight = 1.000\r\n DP -.010000 -.005000 .000000 .005000 .010000\r\n Res. 2.1016E-4 1.4048E-5 1.262E-29 8.4830E-6 1.4841E-4\r\n$$$ f AX ####### # 1.801E-13 8.910E-15 4.496E-15 -7.77E-16 -5.68E-14\r\n$$$ f BX ####### # 1.441761 1.605653 1.784152 1.987500 2.229826\r\n$$$ f NX 4.35401 5 4.362037 4.356146 4.354010 4.355570 4.360806\r\n$$$ f AY ####### # -1.76E-13 -1.07E-14 .000000 -3.55E-15 2.842E-14\r\n$$$ f BY ####### # 120.28086 114.82778 110.11071 105.30067 99.771915\r\n$$$ f NY 4.61526 5 4.623219 4.617256 4.615261 4.616912 4.621898 $$$ f LENG ####### # 284.00000\r\n FITP 1; ! set the off-momentum points to 1 (on-momentum only).\r\n !\r\n ! Define Functions to display tunes as functions of dp\/p0\r\n nx[dp_]:=(DP0=dp;FFS[\"CALC\"];Twiss[\"NX\",\"***\"]\/2\/Pi);\r\n ny[dp_]:=(DP0=dp;FFS[\"CALC\"];Twiss[\"NY\",\"***\"]\/2\/Pi);\r\n !\r\n ! Plot tunes -3% < dp\/p0 < 3%.\r\n Plot[{nx[dp],ny[dp]}, {dp, -0.03, 0.03},\r\n PlotLabel->\"Tune Chromaticity\",\r\n FrameLabel->{{\"`fD`np\/p`d0`n\",\"F X X\"},{\"`fn`n`dx`n, `fn`n`dy`n\",\"GX X GX X\"}}];\r\n ! draw chromaticity\r\n<\/pre>\n![](\"\/SAD\/example\/chromaticity.png\")
<\/p>\n\r\n If[$DisplayFunction === CanvasDrawer, Update[]];\r\n TYPE; ! print out all elements\r\n ;\r\n DRIFT L1 =(L =1 )\r\n ;\r\n BEND B =(L =2 ANGLE =.2617993877991494 )\r\n ;\r\n QUAD QRD =(L =.5 K1 =-.10786211799536628 )\r\n QRF =(L =1 K1 =.19457865291109588 )\r\n QSD =(L =1 K1 =-.21812755206494133 )\r\n QSF =(L =1 K1 =.15519425429347913 )\r\n QD =(L =1 K1 =-.1560624058480439 )\r\n QF =(L =1 K1 =.12696257666020427 )\r\n ;\r\n SEXT SF =(L =1 K2 =.12077485876546518 )\r\n SD =(L =1 K2 =-.20111895529987897 )\r\n ;\r\n CAVI CA1 =(L =1 VOLT =1e+06 HARM =100 )\r\n ;\r\n MARK IP1 =(AX =7.860360223627436e-16 BX =2.133211472511629 AY =-8.940641242780481e-16 BY =101.954887820973\r\n EX =-.14915073411690172 EPX =-1.0665720120238569e-15 DX =-.0006171254879809269 DPX =-3.331075846934373e-16\r\n DDP =.008125 BZ =1 DP =.01 EMITX =4e-07 EMITY =4e-07 )\r\n ;\r\n PrintBeamLine[ExtractBeamLine[]]; ! print out all beam line\r\nBeamLine[\r\n IP1, -QRD, -L1, -L1, -L1, -CA1, \r\n -L1, -L1, -L1, -QRF, -L1, -L1, \r\n -L1, -B, -L1, -L1, -L1, -QSD, \r\n -L1, -L1, -L1, -L1, -L1, -L1, \r\n -L1, -L1, -QSF, L1, SF, L1, \r\n B, L1, L1, L1, QD, L1, \r\n SD, L1, B, L1, L1, L1, \r\n QF, L1, SF, L1, B, L1, \r\n L1, L1, QD, L1, SD, L1, \r\n B, L1, L1, L1, QF, L1, \r\n SF, L1, B, L1, L1, L1, \r\n QD, L1, SD, L1, B, L1, \r\n L1, L1, QF, L1, SF, L1, \r\n B, L1, L1, L1, QD, L1, \r\n SD, L1, B, L1, L1, L1, \r\n QF, L1, SF, L1, B, L1, \r\n L1, L1, QD, L1, SD, L1, \r\n B, L1, L1, L1, QSF, L1, \r\n L1, L1, L1, L1, L1, L1, \r\n L1, QSD, L1, L1, L1, B, \r\n L1, L1, L1, QRF, L1, L1, \r\n L1, CA1, L1, L1, L1, QRD, \r\n -QRD, -L1, -L1, -L1, -CA1, -L1, \r\n -L1, -L1, -QRF, -L1, -L1, -L1, \r\n -B, -L1, -L1, -L1, -QSD, -L1, \r\n -L1, -L1, -L1, -L1, -L1, -L1, \r\n -L1, -QSF, -L1, -L1, -L1, -B, \r\n -L1, -SD, -L1, -QD, -L1, -L1, \r\n -L1, -B, -L1, -SF, -L1, -QF, \r\n -L1, -L1, -L1, -B, -L1, -SD, \r\n -L1, -QD, -L1, -L1, -L1, -B, \r\n -L1, -SF, -L1, -QF, -L1, -L1, \r\n -L1, -B, -L1, -SD, -L1, -QD, \r\n -L1, -L1, -L1, -B, -L1, -SF, \r\n -L1, -QF, -L1, -L1, -L1, -B, \r\n -L1, -SD, -L1, -QD, -L1, -L1, \r\n -L1, -B, -L1, -SF, -L1, -QF, \r\n -L1, -L1, -L1, -B, -L1, -SD, \r\n -L1, -QD, -L1, -L1, -L1, -B, \r\n -L1, -SF, -L1, QSF, L1, L1, \r\n L1, L1, L1, L1, L1, L1, \r\n QSD, L1, L1, L1, B, L1, \r\n L1, L1, QRF, L1, L1, L1, \r\n CA1, L1, L1, L1, QRD, -IP1 \r\n];\r\n Print[TimeUsed[]];! CPU Time used so far.\r\n1.1492799520492554\r\n !\r\n ! ***** EMITTANCE CALCULATION *****\r\n !\r\n EMIOUT; ! turn on the output of matrices by EMIT.\r\n EMIT; ! This (or Emittance[]) is necessary before tracking\r\n\r\n Closed orbit:\r\n x px\/p0 y py\/p0 z dp\/p0 \r\n Entrance : .000000 .000000 .000000 .000000 .000000 .000000\r\n Exit : .000000 .000000 .000000 .000000 .000000 .000000\r\n\r\n Symplectic part of the transfer matrix:\r\n x px\/p0 y py\/p0 z dp\/p0 \r\n x : -.607983 1.416528 .000000 .000000 -1.5E-11 -4.04E-9\r\n px\/p0 : -.445001 -.607983 .000000 .000000 -8.1E-12 -1.07E-9\r\n y : .000000 .000000 -.749024 -72.9530 .000000 .000000\r\n py\/p0 : .000000 .000000 .006017 -.749024 .000000 .000000\r\n z : 1.073E-9 4.037E-9 .000000 .000000 .902210 -21.8235\r\n dp\/p0 : 8.06E-12 1.52E-11 .000000 .000000 .008524 .902210\r\n\r\n x px\/p0 y py\/p0 z dp\/p0 \r\n x : 1.000000 .000000 .000000 .000000 1.02E-15 -2.5E-13\r\n px\/p0 : .000000 1.000000 .000000 .000000 3.49E-18 2.31E-15\r\n y : .000000 .000000 1.000000 .000000 .000000 .000000\r\n py\/p0 : .000000 .000000 .000000 1.000000 .000000 .000000\r\n z : 2.31E-15 2.53E-13 .000000 .000000 1.000000 .000000\r\n dp\/p0 : -3.5E-18 1.02E-15 .000000 .000000 .000000 1.000000\r\n\r\n X Px Y Py Z Pz \r\n X : -.607983 .793950 .000000 .000000 -3.3E-15 -1.3E-14\r\n Px : -.793950 -.607983 .000000 .000000 1.09E-16 1.89E-16\r\n Y : .000000 .000000 -.749024 -.662542 .000000 .000000\r\n Py : .000000 .000000 .662542 -.749024 .000000 .000000\r\n Z : -1.1E-14 -7.9E-15 .000000 .000000 .902210 -.431296\r\n Pz : -2.1E-15 -1.7E-15 .000000 .000000 .431296 .902210\r\n\r\n Extended Twiss Parameters:\r\nAX: 2.22E-16 BX: 1.784152 ZX: 1.23E-16 EX: -2.67E-9\r\n PSIX: -1.5E-25 ZPX: -5.3E-12 EPX: 3.18E-16\r\nR1: .000000 R2: .000000 AY: -7.1E-14 BY: 110.1107 ZY: .000000 EY: .000000\r\nR3: .000000 R4: .000000 PSIY: .000000 ZPY: .000000 EPY: .000000\r\n AZ: 7.03E-14 BZ: 50.59996\r\n PSIZ: -6.2E-17\r\n Units: B(X,Y,Z), E(X,Y), R2: m | PSI(X,Y,Z): radian | ZP(X,Y), R3: 1\/m\r\n\r\nDesign momentum P0 = 1.0000000 GeV Revolution freq. f0 = 1055607.1 Hz \r\nEnergy loss per turn U0 = .0115797 MV Effective voltage Vc = 4.0000000 MV \r\nEquilibrium position dz = 1.3085120 mm Momentum compact. alpha = .0791212\r\nOrbit dilation dl = .0000000 mm Effective harmonic # h = 100.00000\r\nBucket height dV\/P0 = .0178992\r\n\r\n Eigen values and eigen vectors:\r\n\r\n Real:-0.6079827-0.6079827-0.7490243-0.7490243 0.9022104 0.9022104\r\n Imaginary: 0.7939503-0.7939503-0.6625425 0.6625425-0.4312961 0.4312961\r\n Imag.tune:-0.0000000 0.0000000 -0.0000000\r\n Real tune: 0.3540105 -0.3847387 -0.0709718\r\n\r\n X Px Y Py Z Pz \r\n x : 1.335722 -2.1E-25 .000000 .000000 8.76E-16 -3.8E-10\r\n px\/p0 : -1.7E-16 .748659 .000000 .000000 -3.8E-11 4.47E-17\r\n y : .000000 .000000 10.49336 .000000 .000000 .000000\r\n py\/p0 : .000000 .000000 6.74E-15 .095298 .000000 .000000\r\n z : -4.2E-16 -2.00E-9 .000000 .000000 7.113365 -4.4E-16\r\n dp\/p0 : -7.1E-12 -9.2E-17 .000000 .000000 -9.9E-15 .140580\r\n\r\n x px\/p0 y py\/p0 z dp\/p0 \r\n X : .748659 2.05E-25 .000000 .000000 -9.2E-17 2.001E-9\r\n Px : 1.67E-16 1.335722 .000000 .000000 7.12E-12 -4.2E-16\r\n Y : .000000 .000000 .095298 .000000 .000000 .000000\r\n Py : .000000 .000000 -6.7E-15 10.49336 .000000 .000000\r\n Z : 4.47E-17 3.76E-10 .000000 .000000 .140580 4.44E-16\r\n Pz : 3.79E-11 8.76E-16 .000000 .000000 9.87E-15 7.113365\r\n\r\n x px\/p0 y py\/p0 z dp\/p0 \r\n x : 1.000000 .000000 .000000 .000000 4.26E-31 -5.2E-26\r\n px\/p0 : .000000 1.000000 .000000 .000000 4.19E-30 -2.1E-30\r\n y : .000000 .000000 1.000000 .000000 .000000 .000000\r\n py\/p0 : .000000 .000000 .000000 1.000000 .000000 .000000\r\n z : -2.1E-30 5.17E-26 .000000 .000000 1.000000 .000000\r\n dp\/p0 : .000000 3.94E-31 .000000 .000000 .000000 1.000000\r\n\r\n Radiation part of the transfer matrix:\r\n x px\/p0 y py\/p0 z dp\/p0 \r\n x : 1.512E-6 -4.38E-6 .000000 .000000 -2.63E-8 -3.50E-6\r\n px\/p0 : 1.375E-6 2.246E-6 .000000 .000000 1.562E-8 4.142E-6\r\n y : .000000 .000000 4.261E-6 4.224E-4 .000000 .000000\r\n py\/p0 : .000000 .000000 -3.48E-8 4.413E-6 .000000 .000000\r\n z : 1.182E-6 -1.00E-6 .000000 .000000 1.043E-6 3.116E-4\r\n dp\/p0 : 4.457E-9 -7.50E-9 .000000 .000000 -1.22E-7 -2.68E-5\r\n\r\n X Px Y Py Z Pz \r\n X : 1.512E-6 -2.45E-6 .000000 .000000 -1.40E-7 -3.69E-7\r\n Px : 2.454E-6 2.246E-6 .000000 .000000 1.485E-7 7.777E-7\r\n Y : .000000 .000000 4.261E-6 3.836E-6 .000000 .000000\r\n Py : .000000 .000000 -3.84E-6 4.413E-6 .000000 .000000\r\n Z : 2.219E-7 -1.05E-7 .000000 .000000 1.043E-6 6.158E-6\r\n Pz : 4.235E-8 -4.00E-8 .000000 .000000 -6.16E-6 -2.68E-5\r\n\r\n Damping per one revolution:\r\n X : -3.090634E-06 Y : -5.789858E-06 Z : -1.427878E-05\r\n Damping time (sec):\r\n X : 0.306514 Y : 0.163618 Z : 6.634474E-02\r\n Tune shift due to radiation:\r\n X : 4.149566E-13 Y : -7.280353E-14 Z : 4.149451E-12\r\n Damping partition number:\r\n X : 0.5338 Y : 1.0000 Z : 2.4662\r\n\r\n Beam matrix by radiation fluctuation:\r\n x px\/p0 y py\/p0 z dp\/p0 \r\n x 4.887E-12\r\n px\/p0 -1.27E-13 1.645E-12\r\n y .0000000 .0000000 .0000000\r\n py\/p0 .0000000 .0000000 .0000000 .0000000\r\n z -3.91E-12 7.694E-12 .0000000 .0000000 7.342E-10\r\n dp\/p0 5.521E-13 -6.12E-13 .0000000 .0000000 -4.65E-11 4.131E-12\r\n\r\n X Px Y Py Z Pz \r\n X 2.739E-12\r\n Px -1.27E-13 2.934E-12\r\n Y .0000000 .0000000 .0000000\r\n Py .0000000 .0000000 .0000000 .0000000\r\n Z -4.12E-13 1.445E-12 .0000000 .0000000 1.451E-11\r\n Pz 2.940E-12 -5.82E-12 .0000000 .0000000 -4.65E-11 2.090E-10\r\n\r\n Equiliblium beam matrix:\r\n X Px Y Py Z Pz \r\n X 4.5893E-7\r\n Px 1.112E-13 4.5893E-7\r\n Y .0000000 .0000000 .0000000\r\n Py .0000000 .0000000 .0000000 .0000000\r\n Z 1.633E-13 5.471E-18 .0000000 .0000000 3.9141E-6\r\n Pz 2.538E-17 -1.86E-12 .0000000 .0000000 1.391E-12 3.9141E-6\r\n\r\n x px\/p0 y py\/p0 z dp\/p0 \r\n x 8.1881E-7\r\n px\/p0 1.112E-13 2.5723E-7\r\n y .0000000 .0000000 .0000000\r\n py\/p0 .0000000 .0000000 .0000000 .0000000\r\n z 1.551E-12 -1.71E-15 .0000000 .0000000 1.9805E-4\r\n dp\/p0 -2.06E-16 -1.96E-13 .0000000 .0000000 1.391E-12 7.7353E-8\r\n\r\nEmittance X = 4.58933E-7 m Emittance Y = .00000000 m\r\nEmittance Z = 3.91405E-6 m Energy spread = 2.78124E-4\r\nBunch Length = 14.0730586 mm Beam tilt = .00000000 rad\r\nBeam size xi = .90487914 mm Beam size eta = .00000000 mm\r\n\r\n Print[TimeUsed[]];! CPU Time used so far.\r\n1.1630330085754395\r\n !\r\n ! ***** DYNAMIC APERTURE *****\r\n !\r\n ! Dynamic aperture for 1000 turns,\r\n DynamicApertureSurvey[{{0,100},{0,100},Range[-30,30,4]},\r\n 1000,Output->6];\r\n Turns =1000 Maximum number of particles =224\r\n Range Xmin: 0.000 Xmax: 100.000\r\n (Ymin: 0.000 Ymax: 100.000)\r\n Zmin: -30.000 Zmax: 30.000\r\n Display: 100 turns\/character\r\n NZ 0----|----1----|----2----|----3----|----4----|----5\r\n -30.00 11 ****AAAAAAA1 113411121 1 . . .\r\n -26.00 11 ****AAAAAAA12 273332221411 1 . .\r\n -22.00 11 ****AAAAAAA 84994557337521 . . .\r\n -18.00 11 ****AAAAAAA12 236AA67494412 . . .\r\n -14.00 12 *****AAAAAAA5 127AAAA6AA442111. . .\r\n -10.00 25 ******************AAAAAAA512 . . .\r\n -6.00 13 ******AAAAAAA1AA87AAAAAA779A1112 . .\r\n -2.00 13 ******AAAAAAA78AA8AAAAAA3A421 .1 . .\r\n 2.00 12 *****AAAAAAA342AAA7AAAA54A468 . . .\r\n 6.00 12 *****AAAAAAA5223AA8AAAA4A23A6 1A . .\r\n 10.00 12 *****AAAAAAA7A16424AAA4A1 18 31 . .\r\n 14.00 12 *****AAAAAAA4493849A921A111 1A121 1 . .\r\n 18.00 11 ****AAAAAAA12 12115A231216 21 .22 . .\r\n 22.00 11 ****AAAAAAA 1 1 2 7A2211 33314113 . .\r\n 26.00 11 ****AAAAAAA1251121A3. 21432 11 1 . .\r\n 30.00 11 ****AAAAAAA 111333A24 A 16 3 5 . .\r\n NZ 0----|----1----|----2----|----3----|----4----|----5\r\n Score: 199\r\n !\r\n Print[TimeUsed[]];! CPU Time used so far.\r\n3.218843936920166\r\n ABORT ! stop SAD.\r\n<\/pre>\n
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