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- from pytpsa import *
- from numpy import sign
- quad=polmap(x='x',px='px+kn1l*x',y='y',py='py-kn1l*y')
- bend=polmap(x='x+l*px+l*angle*dpp/2.',px='px+angle*dpp',y='y+l*py',py='py')
- drift=bend(a=0)
- def tmatrix(m):
- return m.matrix(vars='x px y py dpp'.split())
- def pbeta(r11,r12,r21,r22):
- cmu=(r11+r22)/2.
- try:
- smu=sign(r12.zero()) * sqrt(-r12*r21 - (r11-r22)**2 / 4.)
- mu=.5/pi * atan(smu/cmu)
- ismu=1/smu
- except ZeroDivisionError:
- mu=pol('mu')
- smu=pol('smu')
- ismu=pol('ismu')
- bet=r12*ismu
- alf=.5*(r11-r22)*ismu
- return bet,alf,cmu,mu
- def pdisp(r11,r12,r21,r22,r16,r26):
- det==r11*r22-r12*r21
- d=(-r16*r22+r26*r12) / det
- dp=(-r26*r11+r16*r21) / det
- return d,dp
- def twiss(m):
- r=tmatrix(m)
- betx,alfx,cmux,mux=pbeta(r[0][0],r[0][1],r[1][0],r[1][1])
- bety,alfy,cmuy,muy=pbeta(r[2][2],r[2][3],r[3][2],r[3][3])
- return betx,alfx,cmux,mux,bety,alfy,cmuy,muy
- def tfquad(l,kn0l,ks0l,kn1l):
- kx=(+kn1l/l+(kn0l/l)**2)
- skx=sqrt(kx)
- cx=cos(skx*l)
- sx=sin(skx*l)/skx
- dx =(1-cx)/kx
- fx =(l-sx)/kx
- ky=(-kn1l/l+(ks0l/l)**2)
- sky=sqrt(ky)
- cy=cos(sky*l)
- sy=sin(sky*l)/sky
- dy =(1-cy)/ky
- m=polmap()
- m.x =pol('x+cx*x+sx*px+dx*kn0l/l*dpp')
- m.px=pol('px-kx*sx*x+cx*px+sx*kn0l/l*dpp')
- m.y =pol('y+cy*y+sy*py')
- m.px=pol('py-ky*sy*y+cy*px')
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