def thermCond_norm(z, rho, kT):
''' Traslational thermal conductivity (for hydrogen gas) as in Devoto, "Transport properties of ionized
monatomic gases"(1966) (see eq. (17))
'''
ne = iz.elec_dens(rho, z)
Q = makeQ(kT, ne)
# Total number density of free particles in gas (ne + nH+ + nH), assuming
# complete dissociation:
n_p = rho / (gau.me + gau.mp)
n = np.array([ne, ne, n_p - ne])
m = np.array([gau.me, gau.mp, gau.me + gau.mp])
lprime = lambdaPrime(kT, n, m, Q)
D = diffu(kT, rho, n, m, Q)
E = Eij(D, m)
DT = thermDiffu(kT, n, m, Q)
addend = 0
idx = np.arange(len(n))
for ii, jj in it.product(idx, idx):
addend += E[ii, jj] * DT[ii] * DT[jj] / (n[ii] * m[ii] * m[jj])
addend *= rho * gau.kB / n.sum()
return addend + lprime
def thermCond_h_norm(z, rho, kT, corr=True, B=0.0):
''' Translational thermal conductivity (for H,H+ mixture gas (equilibrium hydrogen,
but forgetting the free electrons)) as in Devoto,
"Transport properties of ionized monatomic gases"(1966) (see eq. (17))
'''
ne = iz.elec_dens(rho, z)
# I cannot keep all the collision integrals, as I have no e-
Q = makeQ(kT, ne)[:, :, 1:, 1:]
# Total number density of free particles in gas (ne + nH+ + nH), assuming
# complete dissociation:
n_p = rho / (gau.me + gau.mp)
# number densities of gas components (H, H+)
n = np.array([ne, n_p - ne])
# masses of gas components (H, H+)
m = np.array([gau.mp, gau.me + gau.mp])
lprime = lambdaPrime(kT, n, m, Q)
D = diffu(kT, rho, n, m, Q)
E = Eij(D, m)
DT = thermDiffu(kT, n, m, Q)
addend = 0
idx = np.arange(len(n))
for ii, jj in it.product(idx, idx):
addend += E[ii, jj] * DT[ii] * DT[jj] / (n[ii] * m[ii] * m[jj])
addend *= rho * gau.kB / n.sum()
return addend + lprime
def thermCond_r_norm(z, rho, kT):
''' Reactive thermal conductivity (for hydrogen gas) as in Jesper Janssen's PhD Thesis, pag 97,98.
For now I assume complete dissociation (not accurate at low T, around 3000,4000K)
'''
T = kT / gau.kB
ne = iz.elec_dens(rho, z)
Q = makeQ(kT, ne)
# Total number density of free particles in gas (ne + nH+ + nH), assuming
# complete dissociation:
n_p = rho / (gau.me + gau.mp)
n = np.array([ne, ne, n_p - ne])
m = np.array([gau.me, gau.mp, gau.me + gau.mp])
# Omega_i,j^(l,s)
Om, mu = Q2Om(Q, kT, m, ret_redmass=True)
p = n.sum() * kT
Dkl = 3 / 16 * (kT**2) / (p * mu * Om[0, 0, :, :])
# Stochiometric coefficients
R = np.array([+1, +1, -1])
# I build the A quantity (it's just one real number, instead, if I had considered
# also the dissociation reaction, it would have been a 2x2 matrix)
A = 0
# Molar fractions
x = n / n.sum()
for kk in range(0,
len(R) - 1): # species are 3, so 3-1=2 (last kk will be 1)
for ll in range(kk + 1, len(R)): # Species are 3 (last ll will be 2)
A += kT / (Dkl[kk, ll] * p) * x[kk] * x[ll] * (R[kk] / x[kk] -
R[ll] / x[ll])**2
# Entalpy difference (in reaction e- + H+ <-> H) per particle, in erg
# Original
DH = 13.6 * 1.6e-12
# Test, I am not sure it is ok!
DH += 5 / 2 * kT # See the reason for this at page 50 of Ema's INFN book (Q3)
# print("WARNING: I did a test, I computed DH using ionization energy + 5/2*kB*T")
# test, multiply by factor (delete later)
# DH = DH * 1.25
lambda_r = 1 / (kT * T) * DH**2 / A
return lambda_r
def elRes_norm_2(z, rho, kT):
''' El. resistivity of hydrogen as in paper "Transport coeff...",Devoto(1966),
excluding ion current contribution.
See eq. (29)
'''
ne = iz.elec_dens(rho, z)
Q = makeQ(kT, ne)
# Total number density of free particles in gas (ne + nH+ + nH), assuming
# complete dissociation:
n_p = rho / (gau.me + gau.mp)
n = np.array([ne, ne, n_p - ne])
m = np.array([gau.me, gau.mp, gau.mp + gau.me])
D = diffu(kT, rho, n, m, Q)
Zi = np.array([-1.0, 1.0, 0.0])
sigma = gau.qe**2 * n.sum() / (rho * kT) * np.sum(
n[1:] * m[1:] * Zi[1:] * D[0, 1:])
return 1 / sigma
def thermCond_e_norm(z, rho, kT, corr=True, B=0.0):
''' Translational thermal conductivity of electrons, as computed by Devoto in "Simplified expressions
for the transport properties of ionized monatomic gases"(1967).
See eq. 21.
'''
ne = iz.elec_dens(rho, z)
Q = makeQ(kT, ne)
# Total number density of free particles in gas (ne + nH+ + nH), assuming
# complete dissociation:
n_p = rho / (gau.me + gau.mp)
n = np.array([ne, ne, n_p - ne])
q11 = q_mp_simple(1, 1, n, Q)
q12 = q_mp_simple(1, 2, n, Q)
q22 = q_mp_simple(2, 2, n, Q)
k = 75 * ne**2 * gau.kB / 8 * np.sqrt(
2 * np.pi * kT / gau.me) * (q11 - (q12**2) / q22)**-1
return k
def elRes_norm(z, rho, kT, ne=0):
''' Electrical resistivity of hydrogen as computed by Devoto in "Simplified expressions
for the transport properties of ionized monatomic gases"(1967).
See eq. 16, and take the 3rd approximation for D11.
'''
# This should be fixed later!
if ne == 0:
ne = iz.elec_dens(rho, z)
else: # Just a reminder
print("Fix this crap!")
n_p = rho / (gau.me + gau.mp)
n = np.array([ne, ne, n_p - ne])
Q = makeQ(kT, ne)
# Total number density of free particles in gas (ne + nH+ + nH), assuming
# complete dissociation:
# Ordinary diff coefficient, 3rd approx.
D = diffu_ee(kT, rho, n, Q)
eta = rho * kT / (gau.qe**2 * ne * n.sum() * gau.me * D)
return eta
return Sigma2OmegaStar * np.pi
# <codecell>
# For testing purposes
if __name__ == "__main__":
# rho = 3.16116e-7
kT = 20000 * gau.kB
rho = 3.16116e-7
# rho = 3.28e-5
# kT = 24000*gau.kB
z = iz.ionizationSaha(rho, kT)
prs = (1 + z) * rho / (gau.mp + gau.me) * kT
ne = iz.elec_dens(rho, z)
n_i = np.array([ne, ne, rho / (gau.mp + gau.me) - ne])
m_i = np.array([gau.me, gau.mp, gau.mp + gau.me])
Q = makeQ(kT, ne)
# q00_h = q_mp_complete(0, 0, n_i[1:], m_i[1:], Qh[:,:,1:,1:])
# q01_h = q_mp_complete(0, 1, n_i[1:], m_i[1:], Qh[:,:,1:,1:])
# q10_h = q_mp_complete(1, 0, n_i[1:], m_i[1:], Qh[:,:,1:,1:])
# q11_h = q_mp_complete(1, 1, n_i[1:], m_i[1:], Qh[:,:,1:,1:])
# q12_h = q_mp_complete(1, 2, n_i[1:], m_i[1:], Qh[:,:,1:,1:])
# q21_h = q_mp_complete(2, 1, n_i[1:], m_i[1:], Qh[:,:,1:,1:])
# q22_h = q_mp_complete(2, 2, n_i[1:], m_i[1:], Qh[:,:,1:,1:])
# q20_h = q_mp_complete(2, 0, n_i[1:], m_i[1:], Qh[:,:,1:,1:])
# q02_h = q_mp_complete(0, 2, n_i[1:], m_i[1:], Qh[:,:,1:,1:])
#
q00 = q_mp_simple(0, 0, n_i, Q)