def sigma_weak_seaton(x, ion, line, T):
''' Compute collision cross-section for weak coupling in the IPM formula (Seaton 1962)
x: energy of colliding electron before collision [without dimension]
ion: Ionization instance of State of Level class
line: radiative transtion instance of Line class
T: temperature [K]
'''
global cst
r_i = orbital_radius(ion, line.lower)
r_j = orbital_radius(ion, line.upper)
#print(r_i, r_j)
if r_i <= r_j:
r = r_i
else:
r = r_j
de = cst / line.lbd
x0 = de * Cst.Q / Cst.K / T
#print(r, de, x0)
b0 = beta0(x, x0, r, T)
if x < x0:
return 0.
else:
#return 8 * (13.6057*Cst.Q/Cst.K/T)**2 * line.f * (1/x0) * (1/(x+x0)) * phi(b0)
return 8 * (13.6057*Cst.Q/Cst.K/T)**2 * line.f * (1/x0) * (1/(x)) * phi(b0)
def plot_ex(ion, line):
''' Plot the collisions cross-section with electrons
'''
global cst, iplot
iplot += 1
ofname = format(iplot, '0>4')+'_ex.pdf'
T = 5000.
x0 = cst / line.lbd * Cst.Q / Cst.K / T
x_vec_log = pl.linspace(-3, 4, 100)
x_vec = 10**x_vec_log
q0 = [sigma_weak_seaton(i, ion, line, T) for i in x_vec]
q1 = [sigma_strong_seaton(i, ion, line, T) for i in x_vec]
q = [sigma_seaton(i, ion, line, T) for i in x_vec]
ll = line.lower
ul = line.upper
#title='Na I: '+str(ll.cfg)+' '+str(ll.term)+' [g='+str(ll.g)+'] <=> '+str(ul.cfg)+' '+str(ul.term)+' [g='+str(ul.g)+'], Ro = '+format(orbital_radius(ion, line.lower), '4.2f')+' a$_0$, f = '+str(line.f)
title = SPE+' '+DEG+': '+str(ll.cfg)+' '+str(ll.term)+' [g='+str(ll.g)+'] '+str(ul.cfg)+' '+str(ul.term)+' [g='+str(ul.g)+'] Ro = '+str(orbital_radius(ion, line.lower))+' f = '+str(line.f)
pl.figure(figsize=(12, 6), dpi=100, facecolor='w', edgecolor='k')
pl.plot(x_vec*Cst.K*T/Cst.Q, q0, 'k', lw=1, label='Weak coupling')
pl.plot(x_vec*Cst.K*T/Cst.Q, q1, 'k', lw=2, label='Strong coupling')
pl.plot(x_vec*Cst.K*T/Cst.Q, q, 'r+', label='IPM (Seaton 1962)')
pl.semilogx()
#pl.semilogy()
pl.xlim([1e-2, 1e4])
pl.xlabel('E [eV]')
pl.ylabel('Cross-section [$\pi a_0^2$]')
pl.legend(frameon=False, loc=0)
pl.title(title)
#bbox_inches='tight'
pl.savefig(ofname, dpi=100, format='pdf', orientation='landscape', papertype='a4')
pl.close()
