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longitudinal.py
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longitudinal.py
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import numpy as np
import math
def longitudinal_evolve_delta(turns, phi_list_ini, delta_list_ini, sin_phi_s=0, E0_ini=100e9, mass=938e6, e_volt=5e6, alphac=0.002, harm=360.0, E_change=False, update_eta=True):
gamma0 = E0_ini / mass
P0_old = math.sqrt(E0_ini * E0_ini - mass * mass)
beta0 = math.sqrt(1 - 1.0 / gamma0 / gamma0)
phi_list=[]
phi_list.append(phi_list_ini)
delta_list=[]
delta_list.append(delta_list_ini)
E0=E0_ini
#nus = math.sqrt(harm * abs(ita) * e_volt / 2 / np.pi / E0_ini / beta / beta)
for _ in range(turns):
#yield (phi_list, delta_list)
pl=phi_list[-1]*1.0
dl=delta_list[-1]*1.0
dl += e_volt * (np.sin(pl) - sin_phi_s ) / beta0 /beta0 / E0
if update_eta:
delta_gamma = dl * beta0 * beta0 * E0 / mass
else:
delta_gamma =0
eta = alphac - 1.0/(gamma0+delta_gamma)/(gamma0+delta_gamma)
pl += 2.0*np.pi*harm*eta*dl
if E_change:
E0 += e_volt*sin_phi_s
P0 = math.sqrt(E0 * E0 - mass * mass)
gamma0 = E0 / mass
beta0 = math.sqrt(1 - 1.0 / gamma0 / gamma0)
dl*=(P0_old/P0)
P0_old=P0
phi_list.append(pl)
delta_list.append(dl)
return np.vstack(phi_list), np.vstack(delta_list)
def longitudinal_evolve(turns, phi_list_ini, dE_list_ini, sin_phi_s=0, E0_ini=100e9, mass=938e6, e_volt=5e6, alphac=0.002, harm=360.0, update_eta=True, energy_change=False,
damping_turn=0, excitation=False, sr_power=0):
E0 = E0_ini
p0 = np.sqrt(E0 * E0 - mass * mass)
p0_ini=np.sqrt(E0_ini*E0_ini-mass*mass)
gamma0 = E0 / mass
beta0 = math.sqrt(1 - 1.0 / gamma0 / gamma0)
phi_list=[]
phi_list.append(phi_list_ini)
dE_list=[]
dE_list.append(dE_list_ini)
delta_list=[]
e_temp=np.array(dE_list_ini)+E0
dl_ini= np.sqrt(e_temp*e_temp-mass*mass)/p0_ini-1.0
delta_list.append(dl_ini)
#nus = math.sqrt(harm * abs(ita) * e_volt / 2 / np.pi / E0_ini / beta / beta)
for _ in range(turns):
#yield (phi_list, delta_list)
pl=phi_list[-1]*1.0
dEl=dE_list[-1]*1.0
dEl += e_volt * (np.sin(pl) - sin_phi_s )
if excitation:
alpha=0.0072973525664
nph=5*np.pi*alpha*gamma0
srp=sr_power/np.power(E0, 4.0)*np.power(E0+dEl, 4.0)
ave_u=srp/nph
ave_u0=sr_power/nph
if damping_turn>0:
dEl *= (1-1.0/damping_turn)
if energy_change:
E0 += e_volt * sin_phi_s
p0 = np.sqrt(E0 * E0 - mass * mass)
dl = np.sqrt((E0 + dEl) * (E0 + dEl) - mass * mass) / p0 - 1
gamma0 = E0 / mass
beta0 = math.sqrt(1 - 1.0 / gamma0 / gamma0)
if update_eta:
delta_gamma = dEl / mass
else:
delta_gamma =0
eta = alphac - 1.0/(gamma0+delta_gamma)/(gamma0+delta_gamma)
pl += 2.0 * np.pi * harm * eta * dl
phi_list.append(pl)
dE_list.append(dEl)
delta_list.append(dl)
return np.vstack(phi_list), np.vstack(dE_list), np.vstack(delta_list)
'''
E00=100e9
mass=938e6
gamma=E00/mass
beta=pylab.sqrt(1-1.0/gamma/gamma)
eV=5e6
alphac=0.002
gammat=pylab.sqrt(1/alphac)
h=360
ita=alphac-1/(E00*E00/mass/mass)
ita0=ita
print(ita)
nus=pylab.sqrt(h*abs(ita)*eV/2/pylab.pi/E00/beta/beta)
print(nus)
turns=5000
#inideltas=[0.001, 0.003, 0.008, 0.013, 0.017, 0.0175]
#iniphis=[phi_s, phi_s, phi_s, phi_s, phi_s, phi_s]
inideltas=[0.003]
iniphis=[phi_s, phi_s, phi_s,-pylab.pi*0.5,pylab.pi-phi_s]
#iniphis=[phi_s, phi_s, phi_s,pylab.pi*1.5,pylab.pi-phi_s]
for id in range(len(inideltas)):
ini_delta=inideltas[id]
ini_phi=iniphis[id]
deltalist=[ini_delta,]
philist=[ini_phi,]
plotlist=[0,]
E0=E00
mass=938e6
gamma=E0/mass
beta=pylab.sqrt(1-1.0/gamma/gamma)
beta0=beta
eV=5e6
relative_omega=1
alphac=0.002
gammat=pylab.sqrt(1/alphac)
h=360
ita=alphac-1/(E0*E0/mass/mass)
for i in range(turns):
dE0=deltalist[-1]*E0*beta*beta
#dE0=deltalist[-1]
phi0=philist[-1]
dE1=dE0+eV*(pylab.sin(phi0)-pylab.sin(phi_s))
oldE0=E0
E0+=eV*pylab.sin(phi_s)
delta_omega=-ita*relative_omega*(E0-oldE0)/oldE0/beta/beta
relative_omega+=delta_omega
gamma=E0/mass
beta=pylab.sqrt(1-1.0/gamma/gamma)
delta1=dE1/(E0*beta*beta)
ita=alphac-1/gamma/gamma
phi1=phi0+2*pylab.pi*h*ita*delta1
plotlist.append(dE1/relative_omega)
deltalist.append(delta1)
philist.append(phi1)
pylab.plot(philist[1:],plotlist[1:])
pylab.plot(philist[0:1],deltalist[0:1],'r+')
pylab.xlabel("phase")
pylab.ylabel("energy deviation")
pylab.title('Turn {}'.format(turns))
#pylab.xlim([-pylab.pi/2,1.5*pylab.pi])
#pylab.ylim([-0.02,0.02])
pylab.show()
'''