A reduced coupled-mode description for the electron-ion energy relaxation in dense matter

Abstract

Abstract. -We present a simplified model for the electron-ion energy relaxation in dense twotemperature systems that includes the effects of coupled collective modes. It also extends the standard Spitzer result to both degenerate and strongly coupled systems. Starting from the general coupled mode description, we are able to solve analytically for the temperature relaxation time in warm dense matter and strongly coupled plasmas. This was achieve by decoupling the electron-ion dynamics and by representing the ion response in terms of the mode frequencies. The presented reduced model allows for a fast description of temperature equilibration within hydrodynamic simulations and an easy comparison for experimental investigations. For warm dense matter, both fluid and solid, the model gives a slower electron-ion equilibration than predicted by the classical Spitzer result. Published: Europhysics Letters 83, 15002 (2008) Introduction. -The energy equilibration in systems out of local thermodynamic equilibrium is of critical importance for the understanding of the quasi-equation of state, opacity, and optical response of astrophysical and laboratory plasmas. Transport properties such as heat conduction can be also very sensitive to the effectiveness of the energy transfer between electrons and ions. Nevertheless, the energy relaxation is often described by a simple Spitzer-like formula [1,2] or its equivalent for systems with degenerate electrons derived by Brysk [3]. Such treatment neglects many important effects, in particular, collective modes. In denser systems, close collisions and the existence of a short range structure supported by the strong Coulomb forces must be also taken into account.The effect of collective modes on the energy relaxation have been studied with different approaches. However, the magnitude of such effects is still under debate for solids (see, e.g., Refs. [4,5]) as well as for strongly coupled fluids [6][7][8][9][10]. Experimental verification of the relaxation times in dense matter is complicated by the fact that the relevant parameters are difficult to be measured directly. In fact, they are often just inferred from radiation-hydrodynamics simulations. Only a few experimental data points for the temperature relaxation times exist [11][12][13] and they indeed suggest much slower relaxation to

Electron-phonon equilibration in laser-heated gold films

“…Such deviations are typical for strongly heated, fluid systems [14][15][16][17][18] where the energy transfer does not evolve through electron-phonon coupling but through direct two-particle scattering or ion acoustic * thomas.white@imperial.ac.uk modes. Although theoretical models considering the collective behavior of these coupled system show similar effects [19][20][21], the predictions do not agree with the small amount of experimental data available.…”

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

“…Vorberger and coworkers (in various combinations) [19][20][21] used the Lenard-Balescu kinetic equation to study both the nature of the effect of coupled modes on T -equilibration, and the precise regime where they are expected to be important for weakly-coupled systems.…”

“…The potential importance for ICF simulations, however, has prompted researchers to search for approximate expressions which capture the salient features of the reduction in the rate due to ion-acoustic waves [19,23]. The work of Chapman et al in…”

“…This observation, together with the fact that experimental measurements of T -equilibration in plasmas are practically nonexistent, emphasizes the need for dedicated MD simulations specifically tailored to measure the effect of CMs on the relaxation rates. This would in turn aid in the development of more accurate in-line models for use in ICF codes, by buttressing our confidence in the theories used to construct such models [19,23], and/or critiquing their assumptions if their predictions are shown to be inaccurate.…”

Coupled mode effects on energy transfer in weakly coupled, two-temperature plasmas

“…[20,21,22,23,24]). In the beginning, we therefore consider weakly coupled plasmas, where the classical coupling parameter, Γ j = Z 2 j e 2 /a j k B T j with a j = (3/4πn j ) 1/3 is small for all species.…”