Evaluation of the Coulomb logarithm using cutoff and screened Coulomb interaction potentials

Abstract

The Coulomb logarithm is a fundamental plasma parameter which is commonly derived within the framework of the binary collision approximation. The conventional formula for the Coulomb logarithm, λ=ln Λ, takes into account a pure Coulomb interaction potential for binary collisions and is not accurate at small values (λ<10). However, a more exact Fokker–Planck equation was recently presented by Li and Petrasso which is accurate at small Coulomb logarithm values (λ≳2) [Phys. Rev. Lett. 70, 3063 (1993)]. This theory and computer simulations which are accurate for small Coulomb logarithm values provide the motivation for a more precise evaluation of the Coulomb logarithm. In the present work, the Coulomb logarithm is evaluated more precisely by using a cutoff Coulomb interaction potential. The result is compared to an exact numerical evaluation of the Coulomb logarithm which considers a screened Coulomb interaction potential. Fits to the numerical results are also provided. The fitted formula λ=ln(0.6 Λ) is recommended for most applications providing values within 4% of the exact numerical values for λ≳2. This formula is easily implemented by using 0.6λD in place of λD (the Debye length) in the conventional formula for the Coulomb logarithm.