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dedx.py
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dedx.py
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import numpy as np
import matplotlib.pyplot as plt
Q = 1.602E-19
PI = 3.14159
AMU = 1.66E-27
ANGSTROM = 1E-10
MICRON = 1E-6
CM = 1E-2
EPS0 = 8.85E-12
A0 = 0.52918E-10
K = 1.11265E-10
ME = 9.11E-31
SQRTPI = 1.77245385
SQRT2PI = 2.506628274631
C = 299792000.
BETHE_BLOCH_PREFACTOR = 4.*PI*(Q*Q/(4.*PI*EPS0))*(Q*Q/(4.*PI*EPS0))/ME/C/C
LINDHARD_SCHARFF_PREFACTOR = 1.212*ANGSTROM*ANGSTROM*Q
def W(E0, E, Ma):
K = E + 2*Ma*C**2
B = E0**2 - 2*ME*C**2*E0 - 2*E*K
A = E + 2*ME*C**2 + K - 2*E0
G = A**2 - 4*E*K
D = A*B + 2*E*K*(E + K)
F = B**2 - 4*E**2*K**2
W_plus = (-D + np.sqrt(D**2 - F*G))/G
W_minus = (-D - np.sqrt(D**2 - F*G))/G
return W_plus, W_minus
def S_BV(Za, Zb, Ma, n, E, CK=1.):
#breakpoint()
#Biersack-Varelas stopping
beta = np.sqrt(1. - (1. + E/Ma/C**2)**(-2.))
v = beta*C
if Zb < 13:
I0 = 12 + 7/Zb
else:
I0 = 9.76 + 58.5*Zb**(-1.19)
I = Zb*I0*Q
if Zb < 3:
B = 100.*Za/Zb
else:
B = 5.
prefactor = BETHE_BLOCH_PREFACTOR*Zb*Za*Za/beta/beta
eb = 2.*ME*v*v/I
#Bethe stopping modified by Biersack and Varelas
S_BB_BV = prefactor*np.log(eb + 1. + B/eb)*n
#Pure Bethe stopping
S_BB = prefactor*np.log(eb)*n
#Lindhard-Scharff
S_LS = CK*LINDHARD_SCHARFF_PREFACTOR*(Za**(7./6.)*Zb)/(Za**(2./3.) + Zb**(2./3.))**(3./2.)*(E/Q)**0.5*np.sqrt(1./Ma*AMU)*n
#Biersack-Varelas Interpolation
S = 1./(1./S_LS + 1./S_BB_BV)
return S_BB, S_LS, S
def S_MV(Za, Ma, n, E, E0s, alpha0s):
#Medvedev-Volkov stopping (2020)
beta = np.sqrt(1. - (1. + E/Ma/C**2)**(-2.))
prefactor = Za**2/(PI*A0*ME*C**2*beta**2)
sum = 0.
E_min = 0.
for E0, alpha0 in zip(E0s, alpha0s):
E0 *= Q
alpha0 *= Q**2
W_plus, W_minus = W(E0, E, Ma)
if np.isnan(W_minus) or np.isnan(W_plus):
continue
#print(W_plus, W_minus)
#print((2.*Ma*C**2 + W_plus - E0)/(2.*Ma*C**2 + W_minus - E0))
term_1 = (2.*Ma*C**2 - ME*C**2)*np.log((2.*Ma*C**2 + W_plus - E0)/(2.*Ma*C**2 + W_minus - E0))
#print((W_plus - E0)/(W_minus - E0))
if (W_plus - E0)/(W_minus - E0) > 0:
term_2 = ME*C**2*np.log((W_plus - E0)/(W_minus - E0))
else:
term_2 = 0.
sum += alpha0/(ME*C**2)*(term_1 + term_2)
#breakpoint()
return prefactor*sum
def main():
Ma = 1*AMU
Za = 1
Zb = 13
n = 6.026E28
energies = np.logspace(-3, 5, 500)*1E6*Q
lw = 3
S_MV_list = []
S_BV_list = []
S_LS_list = []
S_BB_list = []
for energy in energies:
S_MV_ = S_MV(Za, Ma, n, energy, [1520, 150.7, 111, 110, 15.1], [158, 164, 260, 517, 385])
S_MV_list .append(S_MV_/Q*1E-10)
S_BB_, S_LS_, S_BV_ = S_BV(Za, Zb, Ma, n, energy, CK=2.5/2.)
S_BV_list.append(S_BV_/Q*1E-10)
S_LS_list.append(S_LS_/Q*1E-10)
S_BB_list.append(S_BB_/Q*1E-10)
plt.semilogx(energies/1E6/Q, S_MV_list, '-.', linewidth=lw)
data = np.genfromtxt('H_Al.dat')
E_PSTAR = data[:,0]
S_PSTAR = data[:,1]*270.*1E6*1E-10
S_BV_list = np.array(S_BV_list)
S_LS_list = np.array(S_LS_list)
S_BB_list = np.array(S_BB_list)
S_MV_list = np.array(S_MV_list)
plt.semilogx(E_PSTAR, S_PSTAR, linewidth=lw)
plt.semilogx(energies/1E6/Q, S_BV_list, '--', linewidth=lw)
plt.semilogx(energies/1E6/Q, S_LS_list, ':', linewidth=lw)
plt.semilogx(energies/1E6/Q, S_BB_list, '.', linewidth=lw)
dat = np.genfromtxt('dat')
e = dat[:,0]/1E6/Q
s1 = dat[:,1]/Q*1E-10
s2 = dat[:,2]/Q*1E-10
s3 = dat[:,3]/Q*1E-10
plt.semilogx(e, s1, '-*', color='red')
plt.semilogx(e, s2, '-*', color='blue')
plt.semilogx(e, s3, '-*', color='green')
plt.semilogx(np.ones(100)*24.97E3/1E6, np.linspace(0, 20, 100), '--', linewidth=1, color='black')
#plt.semilogx(energies/1E6/Q, 1./(1./S_LS_list + 1./S_MV_list), '*')
plt.axis([0., 1E5, 0., 1.3*np.max(S_BV_list)])
plt.ylabel('Stopping Power [eV/A]')
plt.xlabel('Incident Energy [MeV]')
plt.legend(['Medvedev-Volkov', 'PSTAR', 'Biersack-Varelas', 'Lindhard-Scharff', 'Pure Bethe', 'L-S Validity'])
plt.show()
if __name__ == '__main__':
main()