def trackOrbit(self, z0):
"""
Returns the tuple ([(position, x),...], [(position, y),...] ).
The tracking starts from the values specified as the initial parameters.
z0 fulfill: z0 = Mz0 with M as one turn matrix
"""
eps_length = 0.00001 # 10^-6 meter
pos_arr = []
orbitX_arr = []
orbitY_arr = []
orbitXP_arr = []
orbitYP_arr = []
position = 0.
pos_arr.append(position)
track_o = Matrix(6, 6)
track_ov = PhaseVector(6)
track_ov.set(0, z0[0])
track_ov.set(1, z0[1])
track_ov.set(2, z0[2])
track_ov.set(3, z0[3])
track_ov.set(4, z0[4])
track_ov.set(5, z0[5])
orbitX_arr.append(track_ov.get(0))
orbitY_arr.append(track_ov.get(2))
orbitXP_arr.append(track_ov.get(1))
orbitYP_arr.append(track_ov.get(3))
position_old = position
for matrixNode in self.getNodes():
if (isinstance(matrixNode, BaseMATRIX) == True):
if (abs(position_old - position) > eps_length):
pos_arr.append(position)
orbitX_arr.append(track_ov.get(0))
orbitY_arr.append(track_ov.get(2))
orbitXP_arr.append(track_ov.get(1))
orbitYP_arr.append(track_ov.get(3))
mt = matrixNode.getMatrix()
for i in range(6):
for j in range(6):
track_o.set(i, j, mt.get(i, j))
track_ov = track_o.mult(track_ov)
for i in range(6):
tmp = track_ov.get(i)
track_ov.set(i, tmp + mt.get(i, 6))
position_old = position
position = position + matrixNode.getLength()
pos_arr.append(position)
orbitX_arr.append(track_ov.get(0))
orbitY_arr.append(track_ov.get(2))
orbitXP_arr.append(track_ov.get(1))
orbitYP_arr.append(track_ov.get(3))
#pack the resulting tuple
graph_orbitX_arr = []
graph_orbitY_arr = []
for i in range(len(pos_arr)):
graph_orbitX_arr.append(
(pos_arr[i], orbitX_arr[i], orbitXP_arr[i]))
graph_orbitY_arr.append(
(pos_arr[i], orbitY_arr[i], orbitYP_arr[i]))
return (graph_orbitX_arr, graph_orbitY_arr)
def trackTwissData(self, alpha, beta, direction="x"):
"""
Returns the tuple ([(position, phase advance/2/pi),...], [(position, alpha),...],[(position,beta),...] ).
The tracking starts from the values specified as the initial parameters.
The possible values for direction parameter "x" or "y".
"""
if (direction.lower() != "x" and direction.lower() != "y"):
orbitFinalize(
"Class orbit.matrix_lattice.MATRIX_Lattice, method trackTwissData(...): direction should be x or y."
)
#track twiss
eps_length = 0.00001 # 10^-6 meter
dir_ind = 0
if (direction.lower() == "y"):
dir_ind = 2
gamma = (1.0 + alpha * alpha) / beta
track_m = Matrix(3, 3)
track_m.unit()
track_v = PhaseVector(3)
track_v.set(0, alpha)
track_v.set(1, beta)
track_v.set(2, gamma)
position = 0.
pos_arr = []
alpha_arr = []
beta_arr = []
#phi is for tune accumulation
phi = 0.
#phase advance
mu_arr = []
#count = 0
pos_arr.append(position)
mu_arr.append(phi)
alpha_arr.append(track_v.get(0))
beta_arr.append(track_v.get(1))
for matrixNode in self.getNodes():
mt = matrixNode.getMatrix()
ind0 = 0 + dir_ind
ind1 = 1 + dir_ind
track_m.set(
0, 0,
mt.get(ind0, ind0) * mt.get(ind1, ind1) +
mt.get(ind0, ind1) * mt.get(ind1, ind0))
track_m.set(0, 1, -mt.get(ind0, ind0) * mt.get(ind1, ind0))
track_m.set(0, 2, -mt.get(ind0, ind1) * mt.get(ind1, ind1))
track_m.set(1, 0, -2 * mt.get(ind0, ind0) * mt.get(ind0, ind1))
track_m.set(1, 1, mt.get(ind0, ind0) * mt.get(ind0, ind0))
track_m.set(1, 2, mt.get(ind0, ind1) * mt.get(ind0, ind1))
track_m.set(2, 0, -2 * mt.get(ind1, ind0) * mt.get(ind1, ind1))
track_m.set(2, 1, mt.get(ind1, ind0) * mt.get(ind1, ind0))
track_m.set(2, 2, mt.get(ind1, ind1) * mt.get(ind1, ind1))
alpha_0 = track_v.get(0)
beta_0 = track_v.get(1)
delta_phi = math.atan(
mt.get(ind0, ind1) /
(beta_0 * mt.get(ind0, ind0) - alpha_0 * mt.get(ind0, ind1)))
phi = phi + delta_phi
track_v = track_m.mult(track_v)
position = position + matrixNode.getLength()
if (isinstance(matrixNode, BaseMATRIX) == True):
#only the main nodes are used, the or-cases deal with markers with zero length
#print position, matrixNode.getParam("matrix_parent_node_active_index") == 1
#print position, matrixNode.getName(), track_v.get(1)
if matrixNode.getLength() > 0:
#print position, matrixNode.getName(), track_v.get(1)
pos_arr.append(position)
alpha_arr.append(track_v.get(0))
beta_arr.append(track_v.get(1))
mu_arr.append(phi / (2 * math.pi))
#count = count + 1
#pack the resulting tuple
tune = phi / (2 * math.pi)
graph_alpha_arr = []
graph_beta_arr = []
graph_mu_arr = []
#print count, len(pos_arr)
for i in range(len(pos_arr)):
graph_mu_arr.append((pos_arr[i], mu_arr[i]))
graph_alpha_arr.append((pos_arr[i], alpha_arr[i]))
graph_beta_arr.append((pos_arr[i], beta_arr[i]))
return (graph_mu_arr, graph_alpha_arr, graph_beta_arr)
def trackDispersionData(self, momentum, mass, disp, disp_p, direction="x"):
"""
Returns the tuple ([(position, disp),...],[(position,disp_p),...] ).
The tracking starts from the values specified as the initial parameters.
The possible values for direction parameter "x" or "y".
"""
if (direction.lower() != "x" and direction.lower() != "y"):
orbitFinalize(
"Class orbit.matrix_lattice.MATRIX_Lattice, method trackDispersionData(...): direction should be x or y."
)
#track dispersion
eps_length = 0.00001 # 10^-6 meter
dir_ind = 0
if (direction.lower() == "y"):
dir_ind = 2
track_m = Matrix(3, 3)
track_m.unit()
track_m.set(2, 0, 0.)
track_m.set(2, 1, 0.)
track_m.set(2, 2, 1.)
track_v = PhaseVector(3)
#kinematics coefficient calculation
Etotal = math.sqrt(momentum**2 + mass**2)
beta = momentum / Etotal
gamma = Etotal / mass
Ekin = Etotal - mass
m_coeff = momentum * momentum / (mass + Ekin)
track_v.set(0, disp)
track_v.set(1, disp_p)
track_v.set(2, 1.)
position = 0.
pos_arr = []
disp_arr = []
disp_p_arr = []
#put in array the initial dispersions
#count = 0
pos_arr.append(position)
disp_arr.append(track_v.get(0))
disp_p_arr.append(track_v.get(1))
for matrixNode in self.getNodes():
if (isinstance(matrixNode, BaseMATRIX) == True):
mt = matrixNode.getMatrix()
ind0 = 0 + dir_ind
ind1 = 1 + dir_ind
track_m.set(0, 0, mt.get(ind0, ind0))
track_m.set(0, 1, mt.get(ind0, ind1))
track_m.set(1, 0, mt.get(ind1, ind0))
track_m.set(1, 1, mt.get(ind1, ind1))
track_m.set(0, 2, mt.get(ind0, 5) * m_coeff)
track_m.set(1, 2, mt.get(ind1, 5) * m_coeff)
track_v = track_m.mult(track_v)
position = position + matrixNode.getLength()
#only the main nodes are used, the or-cases deal with markers with zero length
if (isinstance(matrixNode, BaseMATRIX) == True):
pos_arr.append(position)
disp_arr.append(track_v.get(0))
disp_p_arr.append(track_v.get(1))
#pack the resulting tuple
graph_disp_arr = []
graph_disp_p_arr = []
for i in range(len(pos_arr)):
graph_disp_arr.append((pos_arr[i], disp_arr[i]))
graph_disp_p_arr.append((pos_arr[i], disp_p_arr[i]))
return (graph_disp_arr, graph_disp_p_arr)
res_matrix = Matrix(6,6) res_matrix.unit() n_max = len(teapot_latt.getNodes()) #n_max = 74 length = 0. for i in range(n_max): node = teapot_latt.getNodes()[i] print "i=",i," name =",node.getName()," L=",length m = Matrix(6,6) matrixGenerator.initBunch(matrixTracker.b) node.trackBunch(matrixTracker.b) matrixGenerator.calculateMatrix(matrixTracker.b,m) #m_prt0 = m.copy() #transormToMAD(m_prt0,momentum,beta) #printM(m_prt0) res_matrix = m.mult(res_matrix) length = length + node.getLength() print "====res for TEAPOT n elements=",n_max," L=",length transormToMAD(res_matrix,momentum,beta) printM(res_matrix) m = transp_matrix det_x = m.get(0,0)*m.get(1,1) - m.get(0,1)*m.get(1,0) print "determinant det(Mx)=",det_x det_y = m.get(2,2)*m.get(3,3) - m.get(2,3)*m.get(3,2) print "determinant det(My)=",det_y cos_phi_x = (m.get(0,0)+m.get(1,1))/2.0 cos_phi_y = (m.get(2,2)+m.get(3,3))/2.0
printV(v1)
v3 = v.add(1)
printV(v3)
v3 = v.add(v1)
printV(v3)
print "v*v1 =", v.mult(v1)
print "-----------------------------------------------"
#check matrix
print "----mult ----"
m = Matrix(5, 4)
m1 = Matrix(4, 5)
setM(m)
setM(m1)
m3 = m.mult(m1)
printM(m3)
print "----add -----"
m = Matrix(4, 4)
m1 = Matrix(4, 4)
setM(m)
setM(m1)
m3 = m.add(m1)
printM(m3)
m4 = m3.invert()
if (m4 == None):
print "Cannot invert matrix:"
printM(m3)
sys.exit(1)
#print "z sigma relative[%] = ",sigma_z_rel*100.
print "==================================================================="
matrx_W = Matrix(n_cases, n_cases)
for ind0 in range(n_cases):
for ind1 in range(n_cases):
matrx_W.set(ind0, ind1, 0.)
if (ind0 == ind1):
#matrx_W.set(ind0,ind1,1./(2*z_rms_2_vctr.get(ind0)*sigma_z_rel)**2)
matrx_W.set(
ind0, ind1,
1. / (2 * math.sqrt(z_rms_2_vctr.get(ind0)) * sigma_z)**2)
#---- (MT*W*M)^(-1)
matrx_MT = Matrix(matrx_M)
matrx_MT.transpose()
MTWM_m1 = ((matrx_MT.mult(matrx_W)).mult(matrx_M)).invert()
long_corr_results_vector = MTWM_m1.mult(
matrx_MT.mult(matrx_W.mult(z_rms_2_vctr)))
phase2_rms_res = long_corr_results_vector.get(0)
phase_ekin_corr_res = long_corr_results_vector.get(1)
ekin2_rms_res = long_corr_results_vector.get(2)
phase_rms_res = math.sqrt(phase2_rms_res)
ekin_rms_res = math.sqrt(ekin2_rms_res)
#---- Error estimation
phase_rms_err = math.sqrt(MTWM_m1.get(0, 0)) / (2 * phase_rms_res)
phase_ekin_corr_err = math.sqrt(MTWM_m1.get(1, 1))
ekin_rms_err = math.sqrt(MTWM_m1.get(2, 2)) / (2 * ekin_rms_res)
print "================Zero Iteration for Long. Twiss at BNCH02 entrance================"
matrix.set(i,j, float(res_arr[j])) #printM(matrix) lattice_arr.append((name,matrix)) for it in range(stack_size-1): s_arr[it] = s_arr[it+1] s_arr[stack_size-1] = s #print "debug s=",s s = inF.readline() inF.close() mad_matrix = Matrix(6,6) mad_matrix.unit() n_max = len(lattice_arr) #n_max = 74 for i in range(n_max): (name,matrix) = lattice_arr[i] #print "i=",i," name =",name #printM(mad_matrix) mad_matrix = matrix.mult(mad_matrix) #printM(matrix) #printM(mad_matrix) print "=========One turn MAD matrix======== MAD n_elements=",n_max printM(mad_matrix) print "Stop."
res_matrix = Matrix(6, 6)
res_matrix.unit()
n_max = len(teapot_latt.getNodes())
#n_max = 74
length = 0.
for i in range(n_max):
node = teapot_latt.getNodes()[i]
print "i=", i, " name =", node.getName(), " L=", length
m = Matrix(6, 6)
matrixGenerator.initBunch(matrixTracker.b)
node.trackBunch(matrixTracker.b)
matrixGenerator.calculateMatrix(matrixTracker.b, m)
#m_prt0 = m.copy()
#transormToMAD(m_prt0,momentum,beta)
#printM(m_prt0)
res_matrix = m.mult(res_matrix)
length = length + node.getLength()
print "====res for TEAPOT n elements=", n_max, " L=", length
transormToMAD(res_matrix, momentum, beta)
printM(res_matrix)
m = transp_matrix
det_x = m.get(0, 0) * m.get(1, 1) - m.get(0, 1) * m.get(1, 0)
print "determinant det(Mx)=", det_x
det_y = m.get(2, 2) * m.get(3, 3) - m.get(2, 3) * m.get(3, 2)
print "determinant det(My)=", det_y
cos_phi_x = (m.get(0, 0) + m.get(1, 1)) / 2.0
cos_phi_y = (m.get(2, 2) + m.get(3, 3)) / 2.0
printV(v1) v3 = v.add(1) printV(v3) v3 = v.add(v1) printV(v3) print "v*v1 =", v.mult(v1) print "-----------------------------------------------" #check matrix print "----mult ----" m = Matrix(5,4) m1 = Matrix(4,5) setM(m) setM(m1) m3 = m.mult(m1) printM(m3) print "----add -----" m = Matrix(4,4) m1 = Matrix(4,4) setM(m) setM(m1) m3 = m.add(m1) printM(m3) m4 = m3.invert() if(m4 == None): print "Cannot invert matrix:"; printM(m3); sys.exit(1) printM(m4.mult(m3)) print "-----------------------------------------------"
def trackDispersionData(self,momentum,mass, disp, disp_p, direction = "x"):
"""
Returns the tuple ([(position, disp),...],[(position,disp_p),...] ).
The tracking starts from the values specified as the initial parameters.
The possible values for direction parameter "x" or "y".
"""
if(direction.lower() != "x" and direction.lower() != "y"):
orbitFinalize("Class orbit.matrix_lattice.MATRIX_Lattice, method trackDispersionData(...): direction should be x or y.")
#track dispersion
eps_length = 0.00001 # 10^-6 meter
dir_ind = 0
if(direction.lower() == "y"):
dir_ind = 2
track_m = Matrix(3,3)
track_m.unit()
track_m.set(2,0,0.)
track_m.set(2,1,0.)
track_m.set(2,2,1.)
track_v = PhaseVector(3)
#kinematics coefficient calculation
Etotal = math.sqrt(momentum**2 + mass**2)
beta = momentum/Etotal
gamma = Etotal/mass
Ekin = Etotal - mass
m_coeff = momentum*momentum/(mass + Ekin)
track_v.set(0,disp)
track_v.set(1,disp_p)
track_v.set(2,1.)
position = 0.
pos_arr = []
disp_arr = []
disp_p_arr = []
#put in array the initial dispersions
pos_arr.append(position)
disp_arr.append(track_v.get(0))
disp_p_arr.append(track_v.get(1))
position_old = position
disp_old = disp
#count = 0
for matrixNode in self.getNodes():
if(isinstance(matrixNode,BaseMATRIX) == True):
disp = track_v.get(0)
if(abs(position_old-position) > eps_length or abs(disp_old - disp) > eps_length):
pos_arr.append(position)
disp_arr.append(track_v.get(0))
disp_p_arr.append(track_v.get(1))
disp_old = disp
position_old = position
mt = matrixNode.getMatrix()
ind0 = 0+dir_ind
ind1 = 1+dir_ind
track_m.set(0,0,mt.get(ind0,ind0))
track_m.set(0,1,mt.get(ind0,ind1))
track_m.set(1,0,mt.get(ind1,ind0))
track_m.set(1,1,mt.get(ind1,ind1))
track_m.set(0,2,mt.get(ind0,5)*m_coeff)
track_m.set(1,2,mt.get(ind1,5)*m_coeff)
track_v = track_m.mult(track_v)
position = position + matrixNode.getLength()
pos_arr.append(position)
disp_arr.append(track_v.get(0))
disp_p_arr.append(track_v.get(1))
#pack the resulting tuple
graph_disp_arr = []
graph_disp_p_arr = []
for i in range(len(pos_arr)):
graph_disp_arr.append((pos_arr[i],disp_arr[i]))
graph_disp_p_arr.append((pos_arr[i],disp_p_arr[i]))
return (graph_disp_arr,graph_disp_p_arr)
def trackTwissData(self, alpha, beta, direction = "x"):
"""
Returns the tuple ([(position, phase advance/2/pi),...], [(position, alpha),...],[(position,beta),...] ).
The tracking starts from the values specified as the initial parameters.
The possible values for direction parameter "x" or "y".
"""
if(direction.lower() != "x" and direction.lower() != "y"):
orbitFinalize("Class orbit.matrix_lattice.MATRIX_Lattice, method trackTwissData(...): direction should be x or y.")
#track twiss
eps_length = 0.00001 # 10^-6 meter
dir_ind = 0
if(direction.lower() == "y"):
dir_ind = 2
gamma = (1.0+alpha*alpha)/beta
track_m = Matrix(3,3)
track_m.unit()
track_v = PhaseVector(3)
track_v.set(0,alpha)
track_v.set(1,beta)
track_v.set(2,gamma)
position = 0.
pos_arr = []
alpha_arr = []
beta_arr = []
#phi is for tune accumulation
phi = 0.
#phase advance
mu_arr = []
#put in array the initial twiss
pos_arr.append(position)
mu_arr.append(phi)
alpha_arr.append(track_v.get(0))
beta_arr.append(track_v.get(1))
position_old = position
beta_old = beta
#count = 0
for matrixNode in self.getNodes():
if(isinstance(matrixNode,BaseMATRIX) == True):
beta = track_v.get(1)
if(abs(position_old-position) > eps_length or abs(beta_old - beta) > eps_length):
pos_arr.append(position)
alpha_arr.append(track_v.get(0))
beta_arr.append(track_v.get(1))
mu_arr.append(phi/(2*math.pi))
mt = matrixNode.getMatrix()
ind0 = 0+dir_ind
ind1 = 1+dir_ind
track_m.set(0,0,mt.get(ind0,ind0)*mt.get(ind1,ind1)+mt.get(ind0,ind1)*mt.get(ind1,ind0))
track_m.set(0,1,-mt.get(ind0,ind0)*mt.get(ind1,ind0))
track_m.set(0,2,-mt.get(ind0,ind1)*mt.get(ind1,ind1))
track_m.set(1,0,-2*mt.get(ind0,ind0)*mt.get(ind0,ind1))
track_m.set(1,1,mt.get(ind0,ind0)*mt.get(ind0,ind0))
track_m.set(1,2,mt.get(ind0,ind1)*mt.get(ind0,ind1))
track_m.set(2,0,-2*mt.get(ind1,ind0)*mt.get(ind1,ind1))
track_m.set(2,1,mt.get(ind1,ind0)*mt.get(ind1,ind0))
track_m.set(2,2,mt.get(ind1,ind1)*mt.get(ind1,ind1))
alpha_0 = track_v.get(0)
beta_0 = track_v.get(1)
delta_phi = math.atan( mt.get(ind0,ind1)/( beta_0*mt.get(ind0,ind0) - alpha_0*mt.get(ind0,ind1)))
phi = phi + delta_phi
track_v = track_m.mult(track_v)
position_old = position
beta_old = beta_0
position = position + matrixNode.getLength()
#count = count + 1
pos_arr.append(position)
alpha_arr.append(track_v.get(0))
beta_arr.append(track_v.get(1))
mu_arr.append(phi/(2*math.pi))
#pack the resulting tuple
tune = phi/(2*math.pi)
graph_alpha_arr = []
graph_beta_arr = []
graph_mu_arr = []
for i in range(len(pos_arr)):
graph_mu_arr.append((pos_arr[i], mu_arr[i]))
graph_alpha_arr.append((pos_arr[i],alpha_arr[i]))
graph_beta_arr.append((pos_arr[i],beta_arr[i]))
return (graph_mu_arr,graph_alpha_arr,graph_beta_arr)
twiss_v_ini.set(4,betaY)
twiss_v_ini.set(5,gammaY)
print "==========================================="
print "Initial Twiss parameters:"
printV(twiss_v_ini)
print "==========================================="
fl_out = open("mebt_twiss_matr_distributed_quads.dat","w")
st = " ind x[m] alphaX betaX alphaY betaY "
fl_out.write(st+"\n")
v_in = twiss_v_ini
for ind in range(len(matrix_arr)):
[z_avg,trMtrx,trTwissMtrx] = matrix_arr[ind]
v_out = trTwissMtrx.mult(v_in)
alpha_x=v_out.get(0)
beta_x= v_out.get(1)
gamma_x=v_out.get(2)
alpha_y=v_out.get(3)
beta_y= v_out.get(4)
gamma_y=v_out.get(5)
v_in = v_out
st = " %4d %9.3f %12.6f %12.6f %12.6f %12.6f "%(ind,z_avg,alpha_x,beta_x,alpha_y,beta_y)
if(ind % 100 == 0): print st
fl_out.write(st+"\n")
fl_out.close()