Movement analysis

This operation finds closed orbits and analyses both stable and unstable motions for up to 15 different momenta.
NOTE: no kicks simulating synchrotron oscillation (gkick parameter T $<$ 0 ) may exist in the lattice. Results are meaningless in the presence of such kicks.

Input Format 


MOVEment analysis ..... (up to 80 char) 


nprint nturn nanal nit nener ncoef dist 


x x' y y' l  $\delta_{1} \dots \delta_{{\rm nener}}$ 


naplt delmin delmax dnumin dnumax dbmin dbmax ncol nline

Parameter definitions

nprint $\parbox{10cm}{ print action for the closed orbit information}$

0 $\parbox{10cm}{ action after every element}$

n $\parbox{10cm}{ action after every n turn}$

nturn $\parbox{10cm}{ number of turns over which analysis is performed. It enables user to study higher order resonances.}$

nanal

0 $\parbox{10cm}{ no stability analysis is done, only the closed orbit is computed.}$

1 $\parbox{10cm}{ stability analysis is performed (both stable and unstable).}$

2 $\parbox{10cm}{ gives information about an order two resonance. (nturn must then be equal to 2.)}$

3 $\parbox{10cm}{ gives information about an order three resonance. (nturn must then be equal to 3.)}$

NOTE: in both cases where NANAL is equal to 2 or 3 the resonance motion analyzed is supposed to occur in the horizontal phase plane. If the user wants to study resonance in the vertical plane, the machine should be set up so that its planes are exchanged. In the versions subsequent to April 1 1988, the coordinates of the particles close to the unstable fixed point of the first momentum are stored for subsequent use in a tracking operation. See the demo3 input file for its use

nit $\parbox{10cm}{ number of iterations used. ABS(nit) iterations are ... ...ormed. If nit is negative only the results of the last iteration are printed.}$

nener $\parbox{10cm}{ number of momenta for which the analysis is performed. (max 15)}$

ncoef $\parbox{10cm}{ number of coefficients to be used in the Taylor ex... ... fixed at 0.01(1momentum can be changed by the CONStant definition operation.}$

dist $\parbox{10cm}{ indicates the 'distance' (in phase space) from the ... ...e lower value depending on the size of the phase space occupied by the beam.}$

x,x',y,y',l $\parbox{10cm}{estimate of the coordinates of the closed orbit.}$

$\delta_{i}$ $\parbox{10cm}{ Momenta(dp/p) for which the analysis is performed. i = 1 to nener}$

naplt

0 $\parbox{10cm}{ no plot of the Taylor expansion is required}$

1 $\parbox{10cm}{ a plot is required}$

delmin delmax $\parbox{10cm}{ min max of dp/p for the plot.}$

dnumin dnumax $\parbox{10cm}{ min max for dnu (the first momentum serves as the reference to compute the tune difference dnu).}$

dbmin dbmax $\parbox{10cm}{ min max for relative difference in betas.}$

ncol nline $\parbox{10cm}{ number of columns and lines desired for plot.}$

Examples

The first example comes from demo2 where it is used to analyse the momentum dependence of the parameters of a stable motion.

The second, taken from demo3, illustrates the study of a third order resonance, and the use of a subsequent tracking operation to obtain the separatrices associated to the third order resonance.

MOVEMENT ANALYSIS (CHROMATIC EXPANSION) NO GRAPH
1 1 1 -4 15 6 0.00001
0 0 0 0 0
0.0 -.00001 0.00001 -.00003 0.00003
-.0001 0.0001 -.0003 0.0003 -.001 0.001
-.003 0.003 -.006 0.006
0,

MOVEMENT ANALYSIS TO FIND UNSTABLE CLOSED ORBIT NEAR .03 .002 0 0
1 3 3 -4 1 0 .00001 0.03 0.002 0.0 0.0 0.0 0.00 0,
tracking the 10 particles generated by the movemenet analysis just above
1 -2 0 1600
0
11
-.010 0.010 -.002 0.002
-.0006 0.0006 .0003 0.0003
51 51,