Molecular dynamics simulations and generalized Lenard-Balescu calculations of electron-ion temperature equilibration in plasmas

Abstract

We study the problem of electron-ion temperature equilibration in plasmas. We consider pure H at various densities and temperatures, and Ar-doped H at temperatures high enough so that the Ar is fully ionized. Two theoretical approaches are used: classical molecular dynamics (MD) with statistical 2-body potentials, and a generalized Lenard-Balescu (GLB) theory capable of treating multi-component weakly-coupled plasmas. The GLB is used in two modes: 1) with the quantum dielectric response in the random-phase approximation (RPA) together with the pure Coulomb interaction, and 2) with the classical (h −→ 0) dielectric response (both with and without local-field corrections) together with the statistical potentials. We find that the MD results are described very well by classical GLB including the statistical potentials and without local-field corrections (RPA only); worse agreement is found when static local-field effects are included, in contradiction to the classical pure-Coulomb case with like charges. The results of the various approaches are all in excellent agreement with pure-Coulomb quantum GLB when the temperature is high enough.In addition, we show that classical calculations with statistical potentials derived from the exact quantum 2-body density matrix produce results in far better agreement with pure-Coulomb quantum GLB than classical calculations performed with older existing statistical potentials.

Molecular dynamics studies of electron-ion temperature equilibration in hydrogen plasmas within the coupled-mode regime

“…Recent work on T -equilibration has involved both kinetic theory of various types [4][5][6][7][8], and MD simulations with like-charges and the pure Coulomb interaction [8,9] as well as opposite-charge simulations with quantum statistical potentials (QSPs) to mock up the effects of quantum diffraction [10][11][12][13][14]. All but a few of these studies [7,11,14] confined themselves to pure hydrogen (or the proton-positron system [8,9]).…”

“…All but a few of these studies [7,11,14] confined themselves to pure hydrogen (or the proton-positron system [8,9]). Even for H, the demonstration of agreement between MD results and kinetic theory took some time [10][11][12][13], in part because the effect of using the QSPs changes the result slightly even in weak coupling [11].…”

“…All but a few of these studies [7,11,14] confined themselves to pure hydrogen (or the proton-positron system [8,9]). Even for H, the demonstration of agreement between MD results and kinetic theory took some time [10][11][12][13], in part because the effect of using the QSPs changes the result slightly even in weak coupling [11]. For the classical like-charge proton-positron system, demonstration of agreement was somewhat more straightforward, motivating a clear connection between the classic LandauSpitzer equilibration rate [15] derived from the Fokker-Planck equation, and a generalized Lenard-Balescu [16] scheme in which both dynamical screening and 2-body static correlations (in the form of local field corrections) are included [8].…”

“…Since we invoke an approximate description of these hydrogen plasmas in which the electrons are classical particles that interact via effective T -dependent interactions, we take care to apply the CM-LB and FGR theories to the classical QSP system rather than to the quantum-Coulomb system as done in Ref. [20], to ensure that effects arising from the assumption of classical electrons and altered effective interactions are included appropriately [11].…”

“…To this end, Vorberger and Gericke searched through the existing MD results [8,9,[11][12][13][14]25] to assess if simulations within the regime of interest for…”