Speaker
Description
A linear theory of non local transport in relativistic unmagnetized plasmas is presented. The relativistic effects are due to high electron thermal energy. The relativistic Fokker-Planck equation is analytically solved for perturbed plasmas with respect to the global thermal equilibrium defined by the Maxwell–Boltzmann–Jüttner electron distribution function (EDF). The perturbed EDF is calculated for arbitrary collisionality range defined by the parameter λ_ei/L where λ_ei is the electron-ion mean free path, and L is the homogeneity scale length. and for arbitrary relativistic regime defined by the relativistic parameter z=m_e c^2/T, where m_e is the electron mass, T is the electron temperature (in energy units) and c is the speed of light. Using the Branginskii notations [1] we deduced in the Fourier space (x↔k), the nonlocal electron heat flux, δq and the transfer of momentum from ions to electrons, δR_ei:
δq=-K_T n_e c ik/k δT+α_u n_e Tδu+α_V n_e δV and δR_ei=-β_T n_e ikδT+β_u c/λ_ei n_e mδu where n_e is the electron density, δT is the perturbed temperature, δV is the perturbed fluid velocity, δu is the relative velocity of electron with respect to ions, K_T is the thermal conductivity, α_(u,V) are the relative and convective velocities respectively; β_T and β_u are the coefficients of the thermal force and the friction force respectively. Note here that these coefficients depend on both the Knudsen number kλ_ei and the relativistic parameter z. We illustrate our result in figure given below for the thermal conductivity K_T with respect of kλ_ei for two values of the relativistic parameter z:
We can see that the relativistic effects tend to increase the thermal conductivity and thus the dissipation of plasma modes. In the non relativistic limit and high collisonal regime kλ_ei<<1, the classical thermal conductivity [1], the frictional and thermal forces [1] were recovered. Furthermore, in the collisonless regime and arbitrary temperature values the result reported in Refs. 2 and 3 were also retrieved. New transport coefficients valid for arbitrary relativistic regime and collisionality were derived which can be used as reliable closure relations in fluid equations.
This work has been carried out within the framework of the PRFU 2023-2026 (Projet de Recherche et de Formation Universitaire) and under grant agreement No B00L02UN160420230002.
References:
[1] S. I. Braginskii, in Reviews of Plasma Physics, edited by M. A. Leontovich (Consultants Bureau, NewYork, 1965),Vol. 1,p. 205.
[2] K. Bendib-Kalache, A. Bendib, and K. Mohammed El Hadj, Phys. Rev. E 82, 056401 (2010).
[3] B. Touil, A. Bendib and K. Bendib-Kalache Phys. Plasmas 24, 022111 (2017).
