Effective Coulomb logarithms Quick evaluation of electrical and thermal conductivities of degenerate fully ionized plasmas without magnetic field Department of Theoretical Astrophysics [Conductivity Main page] [Neutron Star Group]
Description
The Fortran program supplied here uses atomic charge (Z) and mass (A) numbers, density \rho [g/cc], and temperature T (106 K) as input parameters and returns effective Coulomb logarithms - Lel for calculation of electrical conductivity, Lth for calculation of thermal conductivity, auxiliary Limp for inclusion of electron scattering off charged impurities in a Coulomb crystal - and values of electrical (sigma) and thermal (kappa) conductivities in the CGS units. For theoretical background, see Ref.[14] listed on the main page.

The MAIN routine can be commented-out for usage of subroutines COULOG and COULIMP (which produce the Coulomb logarithms) or COULAN (which simply implements the analytical calculations from Appendix A of Ref.[14]) with another program.

The conductivities are evaluated according to the formulae

sigma = ne e2 tel / me*,   kappa = \pi2 kB2 ne T tth / me*,

where ne, e, and me* are the electron number density, charge, and effective mass (the latter includes the relativistic Lorentz factor), and tel,th are effective relaxation times related to the corresponding Coulomb logarithms Lel,th as follows:

t = (137)2 . 0.75 \pi \hbar / (Z E L),

where E=me* c2 is the electron Fermi energy (cf. Eqs.(6),(7) of Ref.[14]). These relations are derived under the assumption that the electrons are strongly degenerate, the ions form a perfect lattice below the freezing temperature, and there is no magnetic field. If any of these assumptions does not apply, then you may want to use a more sophisticated program placed here.