Effective Potential Theory for Transport Coefficients across Coupling Regimes

Abstract

A plasma transport theory that spans weak to strong coupling is developed from a binary collision picture, but where the interaction potential is taken to be an effective potential that includes correlation effects and screening self-consistently. This physically motivated approach provides a practical model for evaluating transport coefficients across coupling regimes. The theory is shown to compare well with classical molecular dynamics simulations of temperature relaxation in electronion plasmas, as well as simulations and experiments of self-diffusion in one component plasmas. The approach is versatile and can be applied to other transport coefficients as well.PACS numbers: 52.25. Fi,52.27.Gr,52.65.Yy The microscopic dynamics of Coulomb collisions determines macroscopic transport properties of plasmas such as diffusivity, resistivity, viscosity, etc. [1,2]. Usually plasmas are so hot and dilute that the average particle kinetic energy greatly exceeds the potential energy of interaction. In this weakly coupled regime, Coulomb collisions consist of a series of many small angle binary scattering events [3][4][5][6]. Strongly coupled plasmas are fundamentally different. In this regime, the interaction potential energy exceeds the particle kinetic energies, so scattering angles are large and correlation effects are important. Plasmas in several modern experiments, including inertial confinement fusion (ICF) [7,8], antimatter plasmas [9], ultra cold plasmas [10] and dusty plasmas [11], exhibit strong coupling effects; as do some naturally occurring objects including neutron star crusts [12], white dwarf stars [13,14] and giant planet interiors [15][16][17].Understanding how transport properties are modified in strongly coupled plasmas is interesting both from a fundamental physics standpoint and as a practical matter. Accounting for correlation effects remains a challenge for theory, even though accurate transport coefficients are critical input to the macroscopic (fluid) equations used to model these systems. Transport calculations typically rely on computationally expensive particle simulations, such as molecular dynamics (MD) [18][19][20]. Analytic theory is desirable because it can both elucidate the physical processes that influence transport at strong coupling, and provide an efficient means for estimating the transport coefficients that fluid equations require as input [21][22][23]. In this Letter, we describe a physically motivated method of extending conventional transport calculations, which is efficient enough to be practically implemented in fluid simulation codes. The theory provides coefficients that agree with experimental [24] and classical MD simulation data [25,26] across coupling regimes.Like weakly coupled theories, our theory is based on a binary collision picture, but where particles interact via an effective potential that includes average effects of the intervening medium; including both correlations and screening. This effective potential is used to derive a scattering cross section, wh...

Influence of coupling on thermal forces and dynamic friction in plasmas with multiple ion species

“…In turn, this frequency involves the generalized Coulomb logarithm Ξ 12 . As shown in our earlier work [52], Ξ 12 obtained from the effective potential theory [30] give better agreement with the molecular dynamics simulations than that from the Debye-Hückel [50] and Paquette [51] formalisms. Hence, when evaluating physical observables, such as the momentum exchange or diffusive flux, the effective potential theory used in the present paper is preferable.…”

“…For the DT case it is therefore given by the same function as in the onecomponent plasma model for hydrogen considered in our earlier work [30].…”

“…[30]. Equation (2) reduces to the familiar expression in the weakly coupled limit, in which Ξ αβ becomes the conventional Coulomb logarithm ln Λ [38].…”

“…Generalized Coulomb logarithms are evaluated through gas-kinetic cross-sections as described in Ref. [30] and the transport coefficients are computed with formulas of the Appendix A. Also shown is the weakly coupled limit Γ → 0 considered in our earlier work [7].…”

“…We utilize the recently proposed effective potential theory (EPT) [30,31], which models many-body correlation effects by treating binary interactions as occurring via the potential of mean force in place of the screened, Debye-Hückel potential. Our study indicates that with substantial coupling the thermal force, and therefore thermo-diffusion, rapidly diminishes, making it similar to the conventional case of a neutral gas mixture [22].…”