Detailed chromatic analysis

Traces particles (2 per plane, per momentum) to determine the linearized transfer matrix from the initial point to any related point in the lattice. A twiss function computation is then done at these points. The initial central particle position is assumed to be $v_{0}=(x_{0}\ x'_{0}\ y_{0}\ y'_{0})$.

NOTE: no kicks simulating synchrotron oscillation (parameter $T < 0$ ) may exist in the lattice. Results are meaningless in the presence of such kicks. For each chosen momentum, particles are generated around the point $v_{0}$ to compute the elements $R_{ij}$ of the matrix describing the linear motion around the trajectory defined by the point $v_{0}$.

Input format 


DETAiled chromatic analysis...(up to 80 characters) 


nh nv nhv 

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

$dx\ dx'\ dy\ dy'$ 

$\beta_{x} \alpha_{x} \eta_{x} {\eta '}_{x}$ 

$\beta_{y} \alpha_{y} \eta_{y} {\eta '}_{y}$ 


nener ncoef 

$\delta_{1}\ \delta_{2}\ \dots\ \delta_{nener}$ 


mlocat [list]

Parameter definitions

nh

1 $\parbox{10cm}{ only $x\ x'$\ motion is traced and computed. $\beta_{x}\ \alpha_{x}$\ and $\nu_{x}$\ are computed.}$

0 $\parbox{10cm}{ $x\ x'$\ motion alone is not analyzed.}$

nv

1 $\parbox{10cm}{ only $y\ y'$\ motion is traced and computed. $\beta_{y}\ \alpha_{y}$\ and $\nu_{y}$\ are computed.}$

0 $\parbox{10cm}{ $y\ y'$\ motion alone is not analyzed.}$

nhv

1 $\parbox{10cm}{ coupled motion $x\ x'$, $y\ y'$\ is traced. The full beam matrix is computed.}$

2 $\parbox{10cm}{ coupled motion is computed. A short print for $x\ x... ...a_{x}\ \beta_{y}\ \alpha_{y}\ \nu_{x}\ \nu_{y} $\ for all energies requested}$

3 $\parbox{10cm}{ in this case three energies have to be defined : \par... ...value is 1.0. When set to 1.0e03(say)) the printed values are in mm and mrad.}$

4 $\parbox{10cm}{ The beam matrix values (as defined in the BEAM opera... ...he scale factor SIGFAC which can be set via the constant defintion operation.}$

5 $\parbox{10cm}{ same as three with the code added in the first column to facilitate some plotting work}$

0 $\parbox{10cm}{ coupled $x\ x'$, $y\ y'$\ motion is not analyzed. When NH, NV, and NHV are all zero, the program prints the centroid positions only.}$

NOTE: the input beam must have been defined previously in a BEAM MATRIX TRACKING operation.

dx dx' dy dy'

$\parbox{10cm}{ increments at which the off orbit particles are placed to compute the sx, cx, sy, cy functions (see reference \cite{klb} ).}$

$\beta_{x}\ \alpha_{x}\ \eta_{x}\ {\eta '}_{x}\ \beta_{y}\ \alpha_{y}\ \eta_{y}\ {\eta '}_{y}$

$\parbox{10cm}{ initial values used in the twiss function computations.}$

nener

$\parbox{10cm}{ number of energies for which the analysis is done (maximum 15).}$

ncoef

$\parbox{10cm}{ number of coefficients used in the Taylor series expansion as a function of momentum (max 6).}$

$\delta_{1} \dots \delta_{nener}$

$\parbox{10cm}{momentum values }$

mlocat

$\parbox{10cm}{ indicates the number of intervals in which printing ... ...T = -1, then printing occurs at end of lattice only and no number is in list.}$

list

$\parbox{10cm}{contains the beginning and end of all intervals in wh... ...der list of machine elements) List may contain up to mxlist pairs of numbers.}$

Examples

The first example, taken from demo7, produces a multiple momentum analysis of the beam centroid and beam matrix at the end of the lattice.

The second example, taken from demo9, gives a "short" printout of the beam centroid and the twiss parameters at every point of the lattice, for the on momentum motion.

DETAILED CHROMATIC ANALYSIS
1 1 1
0 0 0 0
0.000001 0.000001 0.000001 0.000001
49.26950355 0 0 0 22.75617615 0 0 0
7 5
0.0 -.001 0.001 -.003 0.003 -.005 0.005
-1,

detailed
1 1 2
0 0 0 0
1.0e-06 1.0e-06 1.0e-06 1.0e-06
1.76806 -0.0032 0 0
15.0736 -0.0034 0 0
1 0
0.00
0;
stop