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No.	： 18
Title	： SAD Update V1.0.10.9k64 CHARGE, R-matrix, etc.
Date	： 2016/01/31(Sun) 18:39:28
Name	： K. Oide
URL	：

Dear Users,

1. Now the variable CHARGE has been validated. Please try it.

2. The way to store R-matrix for x-y coupling is changed when det R is large. If det R >= 1, The transformation matrix from the physical coordinate {x,px,y,py} to
the x-y decoupled coordinate {X,Px,Y,Py} is written as

R = {{mu I, J . Transpose[r] . J}, {r, mu I}},

with the submatrix r={{R1, R2},{R3, R4}}, where mu^2 + Det[r] = 1,
I = {{1,0},{0,1}}, and J={{0, 1}, {-1, 0}}. The value of function DETR is equal
to Det[r] in this case.

Let T stand for the physical transfer matrix from location 1 to location 2, then the transformation in the decoupled coordinate is diagonalized as

R_2 . T . Inverse[R_1] = {{T_X ,0}, {0, T_Y}} .

The Twiss parameters are defined for the matrices T_X and T_Y.

If Det[r] >= 1, the above condition for mu is violated. In such a case, an
an alternative form of m is used:

R = {{J . Transpose[r] . J, mu I}, {mu I, r}},

where mu^2 + Det[r] = 1. The function DETR shows a number a-Det[r], where a = 1.375,
thus the alternative form is used when Det[r] >= 0.625.",

Now the function DETR can be used for the matching.

3. ElementValues is treated as a simple symbol, readable or changeable.

4. ElementValues, FitFunction, and FitValue are cleared at USE and BYE. In the case of VISIT, they are restored by BYE.

5. A bug in FindRoot was fixed when there is one equation.

7. Physical constants are updated using PDG 2014:
https://www.google.co.jp/url?sa=t&rct=j&q=&esrc=s&source=web&cd=2&ved=0ahUKEwjHw4unsKLKAhUEoJQKHaiPCLgQFggjMAE&url=http%3A%2F%2Fpdg.lbl.gov%2F2014%2Freviews%2Frpp2014-rev-phys-constants.pdf&usg=AFQjCNGXw6APvgkpoTdIRLeC-XV651ZbJg&sig2=-wjwSn5pfl6Juvok0hFqow

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SAD Update V1.0.10.9k64 CHARGE, R-matrix, etc.

K. Oide

No.18

Re: SAD Update V1.0.10.9.0.1k64 A bug related to CHARGE. - K. Oide 16/02/02-20:29 No.19
SAD Update V1.0.10.9.0.1k64 TouschekLifetime (Package only) - K. Oide 16/02/08-15:07 No.29
SAD Update V1.0.10.9.0.1k64 DRAW (Package only) - K. Oide 16/02/10-12:34 No.30

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> Dear Users, > > 1. Now the variable CHARGE has been validated. Please try it. > > 2. The way to store R-matrix for x-y coupling is changed when det R is large. If det R >= 1, The transformation matrix from the physical coordinate {x,px,y,py} to > the x-y decoupled coordinate {X,Px,Y,Py} is written as > > R = {{mu I, J . Transpose[r] . J}, {r, mu I}}, > > with the submatrix r={{R1, R2},{R3, R4}}, where mu^2 + Det[r] = 1, > I = {{1,0},{0,1}}, and J={{0, 1}, {-1, 0}}. The value of function DETR is equal > to Det[r] in this case. > > Let T stand for the physical transfer matrix from location 1 to location 2, then the transformation in the decoupled coordinate is diagonalized as > > R_2 . T . Inverse[R_1] = {{T_X ,0}, {0, T_Y}} . > > The Twiss parameters are defined for the matrices T_X and T_Y. > > If Det[r] >= 1, the above condition for mu is violated. In such a case, an > an alternative form of m is used: > > R = {{J . Transpose[r] . J, mu I}, {mu I, r}}, > > where mu^2 + Det[r] = 1. The function DETR shows a number a-Det[r], where a = 1.375, > thus the alternative form is used when Det[r] >= 0.625.", > > Now the function DETR can be used for the matching. > > 3. ElementValues is treated as a simple symbol, readable or changeable. > > 4. ElementValues, FitFunction, and FitValue are cleared at USE and BYE. In the case of VISIT, they are restored by BYE. > > 5. A bug in FindRoot was fixed when there is one equation. > > 7. Physical constants are updated using PDG 2014: > https://www.google.co.jp/url?sa=t&rct=j&q=&esrc=s&source=web&cd=2&ved=0ahUKEwjHw4unsKLKAhUEoJQKHaiPCLgQFggjMAE&url=http%3A%2F%2Fpdg.lbl.gov%2F2014%2Freviews%2Frpp2014-rev-phys-constants.pdf&usg=AFQjCNGXw6APvgkpoTdIRLeC-XV651ZbJg&sig2=-wjwSn5pfl6Juvok0hFqow
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Message > Dear Users, > > 1. Now the variable CHARGE has been validated. Please try it. > > 2. The way to store R-matrix for x-y coupling is changed when det R is large. If det R >= 1, The transformation matrix from the physical coordinate {x,px,y,py} to > the x-y decoupled coordinate {X,Px,Y,Py} is written as > > R = {{mu I, J . Transpose[r] . J}, {r, mu I}}, > > with the submatrix r={{R1, R2},{R3, R4}}, where mu^2 + Det[r] = 1, > I = {{1,0},{0,1}}, and J={{0, 1}, {-1, 0}}. The value of function DETR is equal > to Det[r] in this case. > > Let T stand for the physical transfer matrix from location 1 to location 2, then the transformation in the decoupled coordinate is diagonalized as > > R_2 . T . Inverse[R_1] = {{T_X ,0}, {0, T_Y}} . > > The Twiss parameters are defined for the matrices T_X and T_Y. > > If Det[r] >= 1, the above condition for mu is violated. In such a case, an > an alternative form of m is used: > > R = {{J . Transpose[r] . J, mu I}, {mu I, r}}, > > where mu^2 + Det[r] = 1. The function DETR shows a number a-Det[r], where a = 1.375, > thus the alternative form is used when Det[r] >= 0.625.", > > Now the function DETR can be used for the matching. > > 3. ElementValues is treated as a simple symbol, readable or changeable. > > 4. ElementValues, FitFunction, and FitValue are cleared at USE and BYE. In the case of VISIT, they are restored by BYE. > > 5. A bug in FindRoot was fixed when there is one equation. > > 7. Physical constants are updated using PDG 2014: > https://www.google.co.jp/url?sa=t&rct=j&q=&esrc=s&source=web&cd=2&ved=0ahUKEwjHw4unsKLKAhUEoJQKHaiPCLgQFggjMAE&url=http%3A%2F%2Fpdg.lbl.gov%2F2014%2Freviews%2Frpp2014-rev-phys-constants.pdf&usg=AFQjCNGXw6APvgkpoTdIRLeC-XV651ZbJg&sig2=-wjwSn5pfl6Juvok0hFqow
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