Rmatrix computation

Computes in chosen intervals the 6X6 transfer matrix of the beamline comprised in these intervals. The computation is done by the tracking of seven particles chosen around a given initial set of coordinates This enables to determine the first order behaviour of beamlines affected by errors and misalignements. The program also provides the entrance and exit orbit displacements. They are needed to correctly use the matrix. Using the given emittances $\epsilon_{1} \ \epsilon_{2}$ for the two eigenmodes (when they are stable) the program computes the projected emittances on the x-plane and the y-plane. Given an injected beam by its beta alpha and emittance values, the program computes the coupled envelope and then prints the projected emittances of that envelope.

Input format  


RMATrix.......................(up to 80 characters) 

$x_{0} \ x'_{0} \ y_{0} \ y'_{0} \ l_{0} \ \delta_{0}$ 


dx dx' dy dy' dl d$\delta$ 


norder mprint [nlist] 


nmopt 

$\epsilon_{1} \
\epsilon_{2}$ 

$\beta_{x} \ alpha_{x} \ \epsilon_{x} \ beta_{y} \ alph_{y} \ \epsilon_{y}$

PParameter definitions

$x_{0} \ x'_{0} \ y_{0} \ y'_{0} \ l_{0} \ \delta_{0}$

$\parbox{10cm}{ initial coordinates of reference orbit When $\delta... ...us movement analysis. The values corresponding to the first energy are used.}$ dx dx' dy dy' dl d$\delta$

$\parbox{10cm}{ increments used to generate the six particles surrounding the reference orbit.}$

norder $\parbox{10cm}{ order of the computation: 1 or 11 . The order of th... ...omputation is 1. when norder = 11 the output is in the standard input format.}$

mprint

-2 $\parbox{10cm}{ no printing of matrix.}$

-1 $\parbox{10cm}{ print matrix at end of machine only.}$

0 $\parbox{10cm}{ print matrices at all intermediary points and at final point}$

n $\parbox{10cm}{ where n$>0$, used with list and indicates the number of intervals for which the matrix is computed.}$

nlist $\parbox{10cm}{ mprint pairs of numbers defining the intervals for which the matrix will be computed.}$

nmopt $\parbox{10cm}{ option number. when 0 the following data is not needed as the coupled beam emttances are not computed}$

$\epsilon_{1} \ \epsilon_{2}$ $\parbox{10cm}{ Emittances present in each eigenmode used to compute the projected emittances on both the horizontal and the vertical planes}$

$\beta_{x} \ \alpha_{x} \ \epsilon_{x}$ $\parbox{10cm}{ Parameters defining the horizontal projection of an injected beam}$

$\beta_{y} \ \alpha_{y} \ \epsilon_{y}$ $\parbox{10cm}{ Parameters for the vertical projection of the injected beam}$

Examples

The first example comes from demo9.

The second, which illustrates its use in conjunction with a movement analysis operation, comes from demo12.

rmatrix
0 0 0 0 0 0
1.0e-06 1.0e-06 1.0e-06 1.0e-06 1.0e-06 1.0e-06
1 -1
0,

* The following is to illustrate the use of rmat and geometric
* aberrations in conjunction with movement analysis
movement analysis
1 1 1 -3 1 0 0.00001
0 0 0 0 0 0.002
0,
geometric aberration
0 0 0 0
0 0 0 0 0
1 100 1
1 -2
10 10,
print
interval
m1 m2
99,
end,
rmat
0 0 0 0 0 0
1.0e-6 1.0e-6 1.0e-6 1.0e-6 1.0e-6 1.0e-6
1 1,