def match_tunes(lat, tw0, quads, nu_x, nu_y, ncells=1, print_proc=0):
print("matching start .... ")
end = Monitor(eid="end")
lat = MagneticLattice(lat.sequence + [end])
# tw0.E = lat.energy
tws = twiss(lat, tw0, nPoints=None)
nu_x_old = tws[-1].mux / 2 / np.pi * ncells
nu_y_old = tws[-1].muy / 2 / np.pi * ncells
# print nu_y, nu_y_old
strengths1 = [p.k1 for p in quads]
constr = {
end: {
'mux': 2 * np.pi * nu_x / ncells,
'muy': 2. * np.pi * nu_y / ncells
},
'periodic': True
}
# print constr
vars = quads
match(lat, constr, vars, tws[0])
for i, q in enumerate(quads):
print(q.id, ".k1: before: ", strengths1[i], " after: ", q.k1)
lat = MagneticLattice(lat.sequence[:-1])
tws = twiss(lat, tw0, nPoints=None)
print("nu_x: before: ", nu_x_old, "after: ",
tws[-1].mux / 2 / np.pi * ncells)
print("nu_y: before: ", nu_y_old, "after: ",
tws[-1].muy / 2 / np.pi * ncells)
print("matching end.")
return lat
def __init__(self,
lattice,
beam,
coupling=0.01,
nsuperperiod=1,
tws0=None):
if beam.E == 0:
exit("beam.E must be non zero!")
self.E = beam.E
if tws0 == None:
tws = twiss(lattice, Twiss(beam))
self.tws0 = tws[0]
else:
#tws0.E = lattice.energy
self.tws0 = tws0
tws = twiss(lattice, tws0)
self.lat = lattice
(I1, I2, I3, I4, I5) = radiation_integrals(lattice, self.tws0,
nsuperperiod)
self.I1 = I1
self.I2 = I2
self.I3 = I3
self.I4 = I4
self.I5 = I5
#print "I2 = ", I2
#print "I3 = ", I3
#print "I4 = ", I4
#print "I5 = ", I5
self.Je = 2 + I4 / I2
self.Jx = 1 - I4 / I2
self.Jy = 1
self.gamma = self.E / m_e_GeV
self.sigma_e = self.gamma * sqrt(Cq * self.I3 / (self.Je * I2))
self.emittance = Cq * self.gamma * self.gamma * self.I5 / (self.Jx *
self.I2)
self.U0 = Cgamma * (beam.E * 1000)**4 * self.I2 / (2 * pi)
#print "********* ", twiss_0.Energy
self.Tperiod = nsuperperiod * lattice.totalLen / speed_of_light
self.Length = nsuperperiod * lattice.totalLen
self.tau0 = 2 * self.E * 1000 * self.Tperiod / self.U0
self.tau_e = self.tau0 / self.Je
self.tau_x = self.tau0 / self.Jx
self.tau_y = self.tau0 / self.Jy
self.alpha = self.I1 / (speed_of_light * self.Tperiod)
self.coupl = coupling
self.emitt_x = self.emittance / (1 + self.coupl)
self.emitt_y = self.emittance * self.coupl / (1 + self.coupl)
self.sigma_x = sqrt((self.sigma_e * self.tws0.Dx)**2 +
self.emitt_x * self.tws0.beta_x)
self.sigma_y = sqrt((self.sigma_e * self.tws0.Dy)**2 +
self.emitt_y * self.tws0.beta_y)
self.sigma_xp = sqrt((self.sigma_e * self.tws0.Dxp)**2 +
self.emitt_x * self.tws0.gamma_x)
self.sigma_yp = sqrt((self.sigma_e * self.tws0.Dyp)**2 +
self.emitt_y * self.tws0.gamma_y)
def compensate_chromaticity(lattice,
ksi_x_comp=0,
ksi_y_comp=0,
nsuperperiod=1):
'''
old chromaticity compensation with 2 sextupole families
'''
tws0 = Twiss()
tws = twiss(lattice, tws0)
tws_0 = tws[0]
ksi_comp = (ksi_x_comp, ksi_y_comp)
ksi = natural_chromaticity(lattice, tws_0, nsuperperiod)
print("ksi_x = ", ksi[0])
print("ksi_y = ", ksi[1])
sex_dict_stg = calculate_sex_strength(lattice, tws_0, ksi, ksi_comp,
nsuperperiod)
print("Chromaticity compensatation: After: ", sex_dict_stg)
#print sex_dict_stg
sex_name = list(sex_dict_stg.keys())
for element in lattice.sequence:
if element.__class__ == Sextupole:
if element.id == sex_name[0]:
element.k2 = sex_dict_stg[element.id] / element.l
#if element.l != 0: element.k2 = element.ms / element.l
elif element.id == sex_name[1]:
element.k2 = sex_dict_stg[element.id] / element.l
#if element.l != 0: element.k2 = element.ms / element.l
if element.__class__ == Multipole and element.n == 3:
if element.id == sex_name[0]:
element.kn[2] = sex_dict_stg[element.id]
elif element.id == sex_name[1]:
element.kn[2] = sex_dict_stg[element.id]
lattice.update_transfer_maps()
def compensate_chromaticity(lattice, ksi_x_comp=0, ksi_y_comp=0, nsuperperiod=1):
'''
old chromaticity compensation with 2 sextupole families
'''
tws0 = Twiss()
tws = twiss(lattice, tws0)
tws_0 = tws[0]
ksi_comp = (ksi_x_comp, ksi_y_comp)
ksi = natural_chromaticity(lattice, tws_0, nsuperperiod)
print("ksi_x = ", ksi[0])
print("ksi_y = ", ksi[1])
sex_dict_stg = calculate_sex_strength(lattice, tws_0, ksi, ksi_comp, nsuperperiod)
print("Chromaticity compensatation: After: ", sex_dict_stg)
#print sex_dict_stg
sex_name = list(sex_dict_stg.keys())
for element in lattice.sequence:
if element.__class__ == Sextupole:
if element.id == sex_name[0]:
element.k2 = sex_dict_stg[element.id] / element.l
#if element.l != 0: element.k2 = element.ms / element.l
elif element.id == sex_name[1]:
element.k2 = sex_dict_stg[element.id] / element.l
#if element.l != 0: element.k2 = element.ms / element.l
if element.__class__ == Multipole and element.n == 3:
if element.id == sex_name[0]:
element.kn[2] = sex_dict_stg[element.id]
elif element.id == sex_name[1]:
element.kn[2] = sex_dict_stg[element.id]
lattice.update_transfer_maps()
def __init__(self, lattice, beam, coupling = 0.01, nsuperperiod = 1, tws0 = None):
if beam.E == 0:
exit("beam.E must be non zero!")
self.E = beam.E
if tws0 == None:
tws = twiss(lattice, Twiss(beam))
self.tws0 = tws[0]
else:
#tws0.E = lattice.energy
self.tws0 = tws0
tws = twiss(lattice, tws0)
self.lat = lattice
(I1,I2,I3, I4, I5) = radiation_integrals(lattice, self.tws0 , nsuperperiod)
self.I1 = I1
self.I2 = I2
self.I3 = I3
self.I4 = I4
self.I5 = I5
#print "I2 = ", I2
#print "I3 = ", I3
#print "I4 = ", I4
#print "I5 = ", I5
self.Je = 2 + I4/I2
self.Jx = 1 - I4/I2
self.Jy = 1
self.gamma = self.E/m_e_GeV
self.sigma_e = self.gamma*sqrt(Cq * self.I3/(self.Je*I2))
self.emittance = Cq*self.gamma*self.gamma * self.I5/(self.Jx* self.I2)
self.U0 = Cgamma*(beam.E*1000)**4*self.I2/(2*pi)
#print "********* ", twiss_0.Energy
self.Tperiod = nsuperperiod*lattice.totalLen/speed_of_light
self.Length = nsuperperiod*lattice.totalLen
self.tau0 = 2*self.E*1000*self.Tperiod/self.U0
self.tau_e = self.tau0/self.Je
self.tau_x = self.tau0/self.Jx
self.tau_y = self.tau0/self.Jy
self.alpha = self.I1/(speed_of_light*self.Tperiod)
self.coupl = coupling
self.emitt_x = self.emittance/(1 + self.coupl)
self.emitt_y = self.emittance*self.coupl/(1 + self.coupl)
self.sigma_x = sqrt((self.sigma_e*self.tws0.Dx)**2 + self.emitt_x*self.tws0.beta_x)
self.sigma_y = sqrt((self.sigma_e*self.tws0.Dy)**2 + self.emitt_y*self.tws0.beta_y)
self.sigma_xp = sqrt((self.sigma_e*self.tws0.Dxp)**2 + self.emitt_x*self.tws0.gamma_x)
self.sigma_yp = sqrt((self.sigma_e*self.tws0.Dyp)**2 + self.emitt_y*self.tws0.gamma_y)
def __init__(self, lattice, tws0, coupling=0.01, nsuperperiod=1):
if tws0.__class__ is not Twiss:
_logger.info(" EbeamParams: tws0 is not Twiss class.")
return
self.tws0 = tws0
self.E = tws0.E
if tws0.beta_x == 0 and tws0.beta_y == 0:
tws = twiss(lattice, tws0)
self.tws0 = tws[0]
if self.E == 0.0:
_logger.info("tws0.E is 0. Some parameters will be NaN")
self.lat = lattice
(I1, I2, I3, I4, I5) = radiation_integrals(lattice, self.tws0,
nsuperperiod)
self.I1 = I1
self.I2 = I2
self.I3 = I3
self.I4 = I4
self.I5 = I5
self.Je = 2.0 + I4 / I2
self.Jx = 1.0 - I4 / I2
self.Jy = 1.0
self.gamma = self.E / m_e_GeV
self.sigma_e = self.gamma * np.sqrt(Cq * self.I3 / (self.Je * I2))
self.emittance = Cq * self.gamma * self.gamma * self.I5 / (self.Jx *
self.I2)
self.U0 = Cgamma * (self.E * 1000.0)**4 * self.I2 / (2.0 * np.pi)
self.Tperiod = nsuperperiod * lattice.totalLen / speed_of_light
self.Length = nsuperperiod * lattice.totalLen
self.tau0 = 2.0 * self.E * 1000.0 * self.Tperiod / self.U0 if self.U0 != 0.0 else np.nan
self.tau_e = self.tau0 / self.Je
self.tau_x = self.tau0 / self.Jx
self.tau_y = self.tau0 / self.Jy
self.alpha = self.I1 / (speed_of_light * self.Tperiod)
self.coupl = coupling
self.emitt_x = self.emittance / (1.0 + self.coupl)
self.emitt_y = self.emittance * self.coupl / (1.0 + self.coupl)
self.sigma_x = np.sqrt((self.sigma_e * self.tws0.Dx)**2 +
self.emitt_x * self.tws0.beta_x)
self.sigma_y = np.sqrt((self.sigma_e * self.tws0.Dy)**2 +
self.emitt_y * self.tws0.beta_y)
self.sigma_xp = np.sqrt((self.sigma_e * self.tws0.Dxp)**2 +
self.emitt_x * self.tws0.gamma_x)
self.sigma_yp = np.sqrt((self.sigma_e * self.tws0.Dyp)**2 +
self.emitt_y * self.tws0.gamma_y)
def DZ(lattice, energy):
tws0 = Twiss()
tws = twiss(lattice, tws0)
R = lattice_transfer_map(lattice, energy)
#print np.array(R[:4, :4])- np.eye(4),R[:4, 5]
x = dot(R, [1, 1, 1, 1, 0, 0])
x2 = dot(R, [1, 1, 1, 1, 0, 0.001])
#print (x2 - x)/0.001
#print R
w, v = eig(R)
#print R
v1 = dot(R, v[0].real)
#print "v0 = ", v[0].real
#print "v*R = ", v1
DZ = np.dot(inv(-R[:4, :4] + np.eye(4)), R[:4, 5])
DZ = np.append(DZ, [0, 1])
print("DZ0 = ", DZ)
DR_new = np.zeros(6)
DZ0 = deepcopy(DZ)
DQ1n = 0.
DQ2n = 0.
R_lat = np.eye(6)
for elem in lattice.sequence:
R = elem.transfer_map.R(energy)
R_lat = dot(R, R_lat)
#cosmx = (R[0, 0] + R[1, 1])/2.
#cosmy = (R[2, 2] + R[3, 3])/2.
#if abs(cosmx) >= 1 or abs(cosmy) >= 1:
# logger.warn("************ periodic solution does not exist. return None ***********")
# #print("************ periodic solution does not exist. return None ***********")
# return None
# nsinmx = np.sign(R[0, 1])*sqrt(R[0,1]*R[1, 0] - (R[0, 0]*R[1,1])/4.)
# nsinmy = np.sign(R[2, 3])*sqrt(R[2,3]*R[3, 2] - (R[2, 2]*R[3,3])/4.)
DZ = dot(R_lat, DZ0)
DR = np.zeros((6, 6))
T = elem.transfer_map.t_mat_z_e(elem.l, energy)
for i in range(6):
for j in range(6):
t = 0.
for m in range(6):
t += T[i, j, m] * DZ[m]
DR[i, j] = 2 * t # np.dot(lattice.T[i, j, :], DZ)
print(elem.l)
print(DR)
DR_new = DR + DR_new
#DQ1n += (DR[0, 0] + DR[1, 1])/(2*sin(tws[-1].mux))/2/pi
#DQ2n += (DR[2, 2] + DR[3, 3])/(2*sin(tws[-1].muy))/2/pi
print("DZ = ", DZ)
#print "DZ2 = ", dot(R, DZ)
print(DQ1n * 6, DQ2n * 6)
DR = np.zeros((6, 6))
for i in range(6):
for j in range(6):
t = 0.
for m in range(6):
t += lattice.T[i, j, m] * DZ[m]
DR[i, j] = 2 * t # np.dot(lattice.T[i, j, :], DZ)
#print DR
DR = DR_new
DQ1 = (DR[0, 0] + DR[1, 1]) / (2 * sin(tws[-1].mux)) / 2 / pi
DQ2 = (DR[2, 2] + DR[3, 3]) / (2 * sin(tws[-1].muy)) / 2 / pi
print(DQ1 * 6, DQ2 * 6)
print(tws[-1].mux / 2 / pi * 6)
print(tws[-1].muy / 2 / pi * 6)
def DZ(lattice, energy):
tws0 = Twiss()
tws = twiss(lattice, tws0)
R = lattice_transfer_map(lattice, energy)
#print np.array(R[:4, :4])- np.eye(4),R[:4, 5]
x = dot(R, [1,1,1,1,0,0])
x2 = dot(R, [1,1,1,1,0,0.001])
#print (x2 - x)/0.001
#print R
w, v = eig(R)
#print R
v1 = dot(R,v[0].real)
#print "v0 = ", v[0].real
#print "v*R = ", v1
DZ = np.dot(inv(-R[:4, :4] + np.eye(4)), R[:4, 5])
DZ = np.append(DZ, [0, 1])
print("DZ0 = ", DZ)
DR_new = np.zeros(6)
DZ0 = deepcopy(DZ)
DQ1n = 0.
DQ2n = 0.
R_lat = np.eye(6)
for elem in lattice.sequence:
R = elem.transfer_map.R(energy)
R_lat = dot(R, R_lat)
#cosmx = (R[0, 0] + R[1, 1])/2.
#cosmy = (R[2, 2] + R[3, 3])/2.
#if abs(cosmx) >= 1 or abs(cosmy) >= 1:
# logger.warn("************ periodic solution does not exist. return None ***********")
# #print("************ periodic solution does not exist. return None ***********")
# return None
# nsinmx = np.sign(R[0, 1])*sqrt(R[0,1]*R[1, 0] - (R[0, 0]*R[1,1])/4.)
# nsinmy = np.sign(R[2, 3])*sqrt(R[2,3]*R[3, 2] - (R[2, 2]*R[3,3])/4.)
DZ = dot(R_lat, DZ0)
DR = np.zeros((6,6))
T = elem.transfer_map.t_mat_z_e(elem.l, energy)
for i in range(6):
for j in range(6):
t = 0.
for m in range(6):
t += T[i,j,m]*DZ[m]
DR[i,j] = 2*t # np.dot(lattice.T[i, j, :], DZ)
print(elem.l)
print(DR)
DR_new = DR + DR_new
#DQ1n += (DR[0, 0] + DR[1, 1])/(2*sin(tws[-1].mux))/2/pi
#DQ2n += (DR[2, 2] + DR[3, 3])/(2*sin(tws[-1].muy))/2/pi
print ("DZ = ", DZ)
#print "DZ2 = ", dot(R, DZ)
print(DQ1n*6, DQ2n*6)
DR = np.zeros((6,6))
for i in range(6):
for j in range(6):
t = 0.
for m in range(6):
t += lattice.T[i,j,m]*DZ[m]
DR[i,j] = 2*t # np.dot(lattice.T[i, j, :], DZ)
#print DR
DR = DR_new
DQ1 = (DR[0,0] + DR[1,1])/(2*sin(tws[-1].mux))/2/pi
DQ2 = (DR[2,2] + DR[3,3])/(2*sin(tws[-1].muy))/2/pi
print(DQ1*6, DQ2*6)
print(tws[-1].mux/2/pi*6)
print(tws[-1].muy/2/pi*6)
