amu=0.00116592
gamma0= 29.3
betaz_0=0.6
betaz=betaz_0
gammaz=1./sqrt(1-betaz**2)

gammap=gamma0/gammaz
kappa = (amu+1/(1+gamma0))

beta=(1-1/gamma0**2)**.5
clight=2.99792458e2
R=7.112
omega = clight/R  # with betaz=0.5
omega0=omega*gamma0*(amu+1/gamma0)
omegaa = omega *gamma0*amu
blz = 0.2 #Bl/Bz
bomega(blz)=omegaa*blz*(1/gamma0*(1+amu))/amu
omegap(blz) = ((omega-omega0)**2+bomega(blz)**2)**.5
beta = (1-1./gamma0**2)**.5
beta_x(x)=beta*sin(omega*x)
beta_y(x)=-beta*cos(omega*x)
beta_z=0

sx(x,blz)= ((cos(omegap(blz) * x/2))**2-((omega-omega0)**2+bomega(blz)**2)/(omegap(blz)**2) *(sin(omegap(blz) * x/2))**2)*cos(omega *x)-(2/omegap(blz)*cos(omegap(blz)*x/2)*sin(omegap(blz)*x/2)*(omega-omega0))*sin(omega*x)
sy(x,blz)= ((cos(omegap(blz) * x/2))**2-((omega-omega0)**2+bomega(blz)**2)/(omegap(blz)**2) *(sin(omegap(blz) * x/2))**2)*sin(omega *x)+(2/omegap(blz)*cos(omegap(blz)*x/2)*sin(omegap(blz)*x/2)*(omega-omega0))*cos(omega*x)
sz(x,blz) =bomega*(cos(omegap(blz)*x/2))**2

sdotb(x,blz) = sx(x,blz)*beta_x(x)+ sy(x,blz)*beta_y(x)+ sz(x,blz)*beta_z