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'''
renamed variables not to have a variable with the same name as the fuction the variable is used within
-- ME. 2018-07-23
Mamad Eshraqi
committed
added geometrical and normalized emittance calculations
-- ME. 2019-02-19
'''
from scipy import constants
# Proton mass in MeV/c
proton_mass_in_MeV=constants.physical_constants['proton mass energy equivalent in MeV'][0]
# Speed of light in m/s
c=constants.c
def beta(energy: float, mass=proton_mass_in_MeV):
'''
Parameters
----------
energy: float
kinetic energy of the particle in MeV/c2
mass: float
mass of the moving particle, optional, if not given mass of proton is used
Returns
-------
relaivistic beta of the particle
'''
b=(1-gamma(energy, mass)**-2)**0.5
return b
def beta_c(energy, mass=proton_mass_in_MeV):
'''
Parameters
----------
energy: float
kinetic energy of the particle in MeV/c2
mass: float
mass of the moving particle, optional, if not given mass of proton is used
Returns
-------
relaivistic c*beta of the particle
'''
bc=c*(1-gamma(energy, mass)**-2)**0.5
return bc
def beta_from_gamma(gamma):
'''
Parameters
----------
gamma: float
relaivistic gamma of the particle
Returns
-------
relaivistic beta of the particle
raises
------
if given gamma is smaller than one raises a warning
'''
if gamma < 1:
print('gamma cannot be less than one')
beta = 0
else:
beta=(1-gamma**-2)**0.5
return beta
def gamma(energy, mass=proton_mass_in_MeV):
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'''
Parameters
----------
energy: float
kinetic energy of the particle in MeV/c2
mass: float
mass of the moving particle, optional, if not given mass of proton is used
Returns
-------
relaivistic gamma of the particle
'''
#if mass>0:
g=1+(energy/mass)
return g
def gamma_from_beta(beta):
'''
Parameters
----------
beta: float
relaivistic beta of the particle
Returns
-------
relaivistic gamma of the particle
'''
if beta == 1:
from math import inf as math_inf
gamma = math_inf
else:
gamma = (1-beta**2)**-0.5
return gamma
def energy(gamma_beta, mass=proton_mass_in_MeV):
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'''
Parameters
----------
gamma_beta: float
gamma or beta of the particle; if gamma_beta >= 1 the value is gamma, if gamma_beta < 1 the value is beta
mass: float
mass of the moving particle, optional, if not given mass of proton is used
Returns
-------
returns kinetic energy of the particle in MeV.
example:
sprel.energy(2.55, 938)
> 1453.8999999999999
if gamma_beta < 1 the value is beta
example:
sprel.energy(.55, 938)
> 185.13182200743233
'''
if gamma_beta >= 1: #assuming the value given is gamma
e = (gamma_beta - 1) * mass
elif gamma_beta < 1: #adduming the value given is beta
e = mass * (-1 + 1 / (1 - gamma_beta ** 2) ** 0.5)
return e
Mamad Eshraqi
committed
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def emit_geo(u_up_array):
'''
parameters
----------
u_up_array: array like
a 2D array containing that has u_up_array[:,:2] as coordinates in u and u'
returns
-------
geometrical emittance of the distribution/array in units of pi.mm.mrad
'''
u_shift = u_up_array[:,0] # x
up_shift = u_up_array[:,1] # x'
u = u_shift - np.average(u_shift)
up = up_shift - np.average(up_shift)
u2 = np.square(u) # x2
u2ave = np.average(u2) # <x2>
print(u2ave)
up2 = np.square(up) # x'2
up2ave = np.average(up2) # <x'2>
print(up2ave)
uup = np.multiply(u, up) # x.x'
uupave = np.average(uup) # <x.x'>
uupave2 = uupave**2 # <x.x'>2
print(uupave2)
emit2 = (u2ave * up2ave) - uupave2
emit = np.sqrt(emit2)
return emit
def emit_norm(u_up_array, gamma):
'''
parameters
----------
u_up_array: array like
a 2D array containing that has u_up_array[:,:2] as coordinates in u and u'
gamma: float
relativistic gamma of the particles in the beam
returns
-------
normalized emittance of the distribution/array in units of pi.mm.mrad
'''
#from ess import SP_Relativity as spr
bt = spr.beta_from_gamma(gamma)
geo_emit = emit_geo(u_up_array)
emit = bt * gamma * geo_emit
return emit