def map_x_twiss(self, tws0):
E = tws0.E
M = self.R(E)
zero_tol = 1.e-10
if abs(self.delta_e) > zero_tol:
Ei = tws0.E
Ef = tws0.E + self.delta_e
k = np.sqrt(Ef / Ei)
M[0, 0] = M[0, 0] * k
M[0, 1] = M[0, 1] * k
M[1, 0] = M[1, 0] * k
M[1, 1] = M[1, 1] * k
M[2, 2] = M[2, 2] * k
M[2, 3] = M[2, 3] * k
M[3, 2] = M[3, 2] * k
M[3, 3] = M[3, 3] * k
E = Ef
m = tws0
tws = Twiss(tws0)
tws.E = E
tws.p = m.p
tws.beta_x = M[0, 0] * M[0, 0] * m.beta_x - 2 * M[0, 1] * M[0, 0] * m.alpha_x + M[0, 1] * M[0, 1] * m.gamma_x
# tws.beta_x = ((M[0,0]*tws.beta_x - M[0,1]*m.alpha_x)**2 + M[0,1]*M[0,1])/m.beta_x
tws.beta_y = M[2, 2] * M[2, 2] * m.beta_y - 2 * M[2, 3] * M[2, 2] * m.alpha_y + M[2, 3] * M[2, 3] * m.gamma_y
# tws.beta_y = ((M[2,2]*tws.beta_y - M[2,3]*m.alpha_y)**2 + M[2,3]*M[2,3])/m.beta_y
tws.alpha_x = -M[0, 0] * M[1, 0] * m.beta_x + (M[0, 1] * M[1, 0] + M[1, 1] * M[0, 0]) * m.alpha_x - M[0, 1] * M[
1, 1] * m.gamma_x
tws.alpha_y = -M[2, 2] * M[3, 2] * m.beta_y + (M[2, 3] * M[3, 2] + M[3, 3] * M[2, 2]) * m.alpha_y - M[2, 3] * M[
3, 3] * m.gamma_y
tws.gamma_x = (1. + tws.alpha_x * tws.alpha_x) / tws.beta_x
tws.gamma_y = (1. + tws.alpha_y * tws.alpha_y) / tws.beta_y
tws.Dx = M[0, 0] * m.Dx + M[0, 1] * m.Dxp + M[0, 5]
tws.Dy = M[2, 2] * m.Dy + M[2, 3] * m.Dyp + M[2, 5]
tws.Dxp = M[1, 0] * m.Dx + M[1, 1] * m.Dxp + M[1, 5]
tws.Dyp = M[3, 2] * m.Dy + M[3, 3] * m.Dyp + M[3, 5]
denom_x = M[0, 0] * m.beta_x - M[0, 1] * m.alpha_x
if denom_x == 0.:
d_mux = np.pi / 2. * M[0, 1] / np.abs(M[0, 1])
else:
d_mux = np.arctan(M[0, 1] / denom_x)
if d_mux < 0:
d_mux += np.pi
tws.mux = m.mux + d_mux
denom_y = M[2, 2] * m.beta_y - M[2, 3] * m.alpha_y
if denom_y == 0.:
d_muy = np.pi / 2. * M[2, 3] / np.abs(M[2, 3])
else:
d_muy = np.arctan(M[2, 3] / denom_y)
if d_muy < 0:
d_muy += np.pi
tws.muy = m.muy + d_muy
return tws
def periodic_twiss(tws, R):
'''
initial conditions for a periodic Twiss slution
'''
tws = Twiss(tws)
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
sinmx = np.sign(R[0, 1]) * sqrt(1. - cosmx * cosmx)
sinmy = np.sign(R[2, 3]) * sqrt(1. - cosmy * cosmy)
tws.beta_x = abs(R[0, 1] / sinmx)
tws.beta_y = abs(R[2, 3] / sinmy)
tws.alpha_x = (R[0, 0] - R[1, 1]) / (2. * sinmx) # X[0,0]
tws.gamma_x = (1. + tws.alpha_x * tws.alpha_x) / tws.beta_x # X[1,0]
tws.alpha_y = (R[2, 2] - R[3, 3]) / (2 * sinmy) # Y[0,0]
tws.gamma_y = (1. + tws.alpha_y * tws.alpha_y) / tws.beta_y # Y[1,0]
Hx = array([[R[0, 0] - 1, R[0, 1]], [R[1, 0], R[1, 1] - 1]])
Hhx = array([[R[0, 5]], [R[1, 5]]])
hh = dot(inv(-Hx), Hhx)
tws.Dx = hh[0, 0]
tws.Dxp = hh[1, 0]
Hy = array([[R[2, 2] - 1, R[2, 3]], [R[3, 2], R[3, 3] - 1]])
Hhy = array([[R[2, 5]], [R[3, 5]]])
hhy = dot(inv(-Hy), Hhy)
tws.Dy = hhy[0, 0]
tws.Dyp = hhy[1, 0]
#tws.display()
return tws
def periodic_twiss(tws, R):
'''
initial conditions for a periodic Twiss slution
'''
tws = Twiss(tws)
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
sinmx = np.sign(R[0, 1]) * sqrt(1. - cosmx * cosmx)
sinmy = np.sign(R[2, 3]) * sqrt(1. - cosmy * cosmy)
tws.beta_x = abs(R[0, 1] / sinmx)
tws.beta_y = abs(R[2, 3] / sinmy)
tws.alpha_x = (R[0, 0] - R[1, 1]) / (2. * sinmx) # X[0,0]
tws.gamma_x = (1. + tws.alpha_x * tws.alpha_x) / tws.beta_x # X[1,0]
tws.alpha_y = (R[2, 2] - R[3, 3]) / (2 * sinmy) # Y[0,0]
tws.gamma_y = (1. + tws.alpha_y * tws.alpha_y) / tws.beta_y # Y[1,0]
Hx = array([[R[0, 0] - 1, R[0, 1]], [R[1, 0], R[1, 1] - 1]])
Hhx = array([[R[0, 5]], [R[1, 5]]])
hh = dot(inv(-Hx), Hhx)
tws.Dx = hh[0, 0]
tws.Dxp = hh[1, 0]
Hy = array([[R[2, 2] - 1, R[2, 3]], [R[3, 2], R[3, 3] - 1]])
Hhy = array([[R[2, 5]], [R[3, 5]]])
hhy = dot(inv(-Hy), Hhy)
tws.Dy = hhy[0, 0]
tws.Dyp = hhy[1, 0]
# tws.display()
return tws
def map_x_twiss(self, tws0):
E = tws0.E
M = self.R(E)
# print(E, self.delta_e, M)
zero_tol = 1.e-10
if abs(self.delta_e) > zero_tol:
# M = self.R(E + )
Ei = tws0.E
Ef = tws0.E + self.delta_e # * cos(self.phi)
# print "Ei = ", Ei, "Ef = ", Ef
k = np.sqrt(Ef / Ei)
M[0, 0] = M[0, 0] * k
M[0, 1] = M[0, 1] * k
M[1, 0] = M[1, 0] * k
M[1, 1] = M[1, 1] * k
M[2, 2] = M[2, 2] * k
M[2, 3] = M[2, 3] * k
M[3, 2] = M[3, 2] * k
M[3, 3] = M[3, 3] * k
# M[4, 5] = M[3, 3]*k
E = Ef
m = tws0
tws = Twiss(tws0)
tws.E = E
tws.p = m.p
tws.beta_x = M[0, 0] * M[0, 0] * m.beta_x - 2 * M[0, 1] * M[0, 0] * m.alpha_x + M[0, 1] * M[0, 1] * m.gamma_x
# tws.beta_x = ((M[0,0]*tws.beta_x - M[0,1]*m.alpha_x)**2 + M[0,1]*M[0,1])/m.beta_x
tws.beta_y = M[2, 2] * M[2, 2] * m.beta_y - 2 * M[2, 3] * M[2, 2] * m.alpha_y + M[2, 3] * M[2, 3] * m.gamma_y
# tws.beta_y = ((M[2,2]*tws.beta_y - M[2,3]*m.alpha_y)**2 + M[2,3]*M[2,3])/m.beta_y
tws.alpha_x = -M[0, 0] * M[1, 0] * m.beta_x + (M[0, 1] * M[1, 0] + M[1, 1] * M[0, 0]) * m.alpha_x - M[0, 1] * M[
1, 1] * m.gamma_x
tws.alpha_y = -M[2, 2] * M[3, 2] * m.beta_y + (M[2, 3] * M[3, 2] + M[3, 3] * M[2, 2]) * m.alpha_y - M[2, 3] * M[
3, 3] * m.gamma_y
tws.gamma_x = (1. + tws.alpha_x * tws.alpha_x) / tws.beta_x
tws.gamma_y = (1. + tws.alpha_y * tws.alpha_y) / tws.beta_y
tws.Dx = M[0, 0] * m.Dx + M[0, 1] * m.Dxp + M[0, 5]
tws.Dy = M[2, 2] * m.Dy + M[2, 3] * m.Dyp + M[2, 5]
tws.Dxp = M[1, 0] * m.Dx + M[1, 1] * m.Dxp + M[1, 5]
tws.Dyp = M[3, 2] * m.Dy + M[3, 3] * m.Dyp + M[3, 5]
denom_x = M[0, 0] * m.beta_x - M[0, 1] * m.alpha_x
if denom_x == 0.:
d_mux = np.pi / 2. * M[0, 1] / np.abs(M[0, 1])
else:
d_mux = np.arctan(M[0, 1] / denom_x)
if d_mux < 0:
d_mux += np.pi
tws.mux = m.mux + d_mux
# print M[0, 0]*m.beta_x - M[0, 1]*m.alpha_x, arctan(M[2, 3]/(M[2, 2]*m.beta_y - M[2, 3]*m.alpha_y))
denom_y = M[2, 2] * m.beta_y - M[2, 3] * m.alpha_y
if denom_y == 0.:
d_muy = np.pi / 2. * M[2, 3] / np.abs(M[2, 3])
else:
d_muy = np.arctan(M[2, 3] / denom_y)
if d_muy < 0:
d_muy += np.pi
tws.muy = m.muy + d_muy
# print("new")
# print(tws)
return tws