Current conserving theory of collisional relativistic plasmas

May 17, 2022, 9:40 AM


Martin Formanek (ELI Beamlines )


There is a renewed interest in extending relativistic description of plasma response in external electromagnetic fields from Vlasov equation to a form including Boltzmann collision term [1–4]. In this work we incorporate the relaxation rate approximation of collisions [2] in a manifestly covariant way assuring explicitly current and energy-momentum conservation for two-component electron-positron plasma. We demonstrate that the resulting equation for the perturbation of the Fermi-Dirac equilibrium distribution function can be solved analytically to the linear order in external fields [5]. The ultra-relativistic and non-relativistic limits of the resulting covariant, gauge invariant, and current-conserving polarization tensor can be taken. We evaluate the plasma susceptibility and conductivity in the ultra-relativistic case and study their dependence on the collision rate. Finally, we explore the dispersion relations for the longitudinal and transverse poles of the propagator.

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[3] D. Satow, Phys. Rev. D 90, 034018 (2014).
[4] G. S. Rocha, G. S. Denicol and J. Noronha, Phys. Rev. Lett. 127, no.4, 042301 (2021).
[5] M. Formanek, C. Grayson, J. Rafelski and B. M ̈uller, Annals Phys. 434, 168605 (2021

Primary author

Martin Formanek (ELI Beamlines )

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