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beam22

PURPOSE

BEAM22 computes the beam matrix from the 1-turn transfer matrix

SYNOPSIS

function [s,tune] = beam22(t)

DESCRIPTION

BEAM22 computes the beam matrix from the 1-turn transfer matrix
%
BEAM=BEAM22(T)
 T:    1-turn transfer matrix
 BEAM: envelope matrix

[BEAM,TUNE]=BEAM22(T)
 also returns the tune

CROSS-REFERENCE INFORMATION

This function calls:

This function is called by:

beam44 BEAM44 computes the coupled beam matrices

SOURCE CODE

0001 function [s,tune] = beam22(t)
0002 %BEAM22 computes the beam matrix from the 1-turn transfer matrix
0003 %%
0004 %BEAM=BEAM22(T)
0005 % T:    1-turn transfer matrix
0006 % BEAM: envelope matrix
0007 %
0008 %[BEAM,TUNE]=BEAM22(T)
0009 % also returns the tune
0010 
0011 cosmu=0.5*trace(t);
0012 sinmu=sign(t(1,2))*sqrt(1-cosmu*cosmu);
0013 alpha=0.5*(t(1,1)-t(2,2))/sinmu;
0014 beta=t(1,2)/sinmu;
0015 s=[beta -alpha; -alpha (alpha*alpha+1)/beta];
0016 tune=atan2(sinmu,cosmu)/2/pi;
0017 end
0018