parameter[lattice] = "PRSTAB 7, 2004 Toy Lattice"


betaa=1e4
betab=1e4
alphaa=0
alphab=0
 beginning[beta_a]  =    betaa
 beginning[alpha_a]=   alphaa
 beginning[beta_b] =    betab
 beginning[alpha_b] =   alphab

beginning[e_tot] = 5e9

parameter[geometry] = open


rfw: lcavity, l = 0, gradient = 0.0, lr_wake_file="prstab2004.dat", lr_freq_spread=0.0E-3, rf_frequency = 1.3e9

m1: match, beta_a1=betaa, alpha_a1=alphaa, beta_b1=betab, alpha_b1=alphab, dphi_a=1, dphi_b=1, l=1.269, match_end=.true.

p0c=5e9
!p0c=1

m12=-1.0e-6*p0c
m21=-m12/(betaa^2)
m11=sqrt(1-m12*m21)
m22=m11

xi=500

! Expand xout = x'in (beta1*beta2)^1/2 * sin(Psi+xi*delta)
! Multiply by 1/(1+delta) simeq (1-delta) to account for 
! delta dependence of x'in.
! Average over symmetric delta distribution to keep only
! even powers of delta.
! xout propto (1+(1-0.5*xi^2)*delta^2)*sin(Psi) - xi*delta^2*cos(Psi)
! M12 = (beta1*beta2)^1/2 * sin(psi)=-5e3, so sin(psi)=-0.5 for beta1=beta2=1e4 m.
! So cos(psi) = sqrt(1-sin^2) = 0.87
sinpsi=m12/betaa
cospsi=sqrt(1-sinpsi^2)
m1266=betaa*((1-0.5*(xi^2))*sinpsi-xi*cospsi)
!m1266=0
!t1: Taylor, {1:   m12,  0 1 0 0 0 0}, l=1.269

! Simple phase space rotation
!t1: Taylor, {1:   m12,  0 1 0 0 0 0}, &
!            {1:   m11,  1 0 0 0 0 0}, &
!            {2:   m21,  1 0 0 0 0 0}, &
!            {2:   m22,  0 1 0 0 0 0}, l=1.269

! Add chromatic terms
t1: Taylor, {1:   m12,  0 1 0 0 0 0}, &
!            {1:   m11,  1 0 0 0 0 0}, &
!            {2:   m21,  1 0 0 0 0 0}, &
!            {2:   m22,  0 1 0 0 0 0}, &
!            {1:    1.,  1 0 0 0 0 1}, &
!            {2:    1.,  0 1 0 0 0 1}, &
! linear dependence on delta 
!            {1: .0001,  0 1 0 0 0 1}, l=1.269
! Quadratic dependence on delta 1/2 * delta^2
!            {1: -xi/2,  0 1 0 0 0 2}, l=1.269
! With cosine term: -xi*delta^2*cos(psi), cos(psi)about unity
!            {1: -xi,  0 1 0 0 0 2}, l=1.269
            {1: m1266,  0 1 0 0 0 2}, l=1.269

simple: line[multipass] = (rfw, t1)

dual: line = (simple,simple)

use, dual