Thermalization of electron–positron plasma with quantum degeneracy

Abstract

The non-equilibrium electron-positron-photon plasma thermalization process is studied using relativistic Boltzmann solver, taking into account quantum corrections both in non-relativistic and relativistic cases. Collision integrals are computed from exact QED matrix elements for all binary and triple interactions in the plasma. It is shown that in non-relativistic case (temperatures k B T ≤ 0.3m e c 2 ) binary interaction rates dominate over triple ones, resulting in establishment of the kinetic equilibrium prior to final relaxation towards the thermal equilibrium, in agreement with the previous studies. On the contrary, in relativistic case (final temperatures k B T ≥ 0.3m e c 2 ) triple interaction rates are fast enough to prevent the establishment of kinetic equilibrium. It is shown that thermalization process strongly depends on quantum degeneracy in initial state, but does not depend on plasma composition. (M. A. Prakapenia), siutsou@icranet.org (I. A. Siutsou), veresh@icra.it (G. V. Vereshchagin) 1 https://eli-laser.eu/ 2

Pauli blocking effects in thermalization of relativistic plasma

“…Note that pair annihilation is not subject to Pauli blocking so pair annihilation leads to disappearance of degeneracy. This result shows that thermalization process started from superdegenerate state is not influenced by quantum corrections and it is in a full agreement with the previous results obtained for the case of nondegenerate initial state [36]. Thermalization dynamics in the case of non-equilibrium and non-degenerate distribution of pairs with the same particle energy density and particle number is presented by dashed curves in Fig.…”

“…Thus, for the case of relativistic pair plasma thermalization process started from superdegenerate state is not influenced by Pauli blocking. Thermalization process goes in the same way as in the case of degenerate pairless initial state reported in [36]. Note that the faster onset of the evolution of the total particle number density of particles caused by the to Bose enhancement of two-photon annihilation rate in radiative pair production process, see Appendix, found previously is also valid for the case of superdegenerate initial conditions.…”

“…Thermalization process with quantum degeneracy both in non-relativistic and relativistic cases was investigated in [36]. There the relative role of binary and triple interactions has been studied.…”

Bose-Einstein condensation in relativistic plasma

“…The characteristic timescale of thermal equilibrium can be estimated as t th ∼ (ασ T n e c) −1 , where α is the fine structure constant. Detailed calculations show that both kinetic and thermal equilibrium timescales are functions of total energy density [24,23] and at high temperatures T th > 0.3m e c 2 /k they nearly coincide.…”

Numerical Scheme for Treatment of Uehling–Uhlenbeck Equation for Binary and Triple Interactions in Relativistic Plasma

“…This scheme was first introduced in the work 47 and then applied to the study of thermalization in relativistic plasma of Boltzmann particles 1,[48][49][50] , for the computation of relaxation timescales 51 , and description of electron-positron plasma creation in strong electric fields 52 . Thermalization process was studied taking into account plasma degeneracy in 53 . In con-arXiv:2010.14348v1 [physics.plasm-ph] 27 Oct 2020 e + e − ←→e + e − γ Pair production/annihilation Three-photon pair production/annihilation e + e − ←→ γ 1 γ 2 e + e − ←→γ 1 γ 2 γ 3 Radiative pair production/annihilation γ 1 γ 2 ←→e + e − γ e ± γ←→e ± e + e − trast with non-degenerate plasma described by Boltzmann equations, quantum statistics is taken into account by adopting the Uehling-Uhlenbeck equation, which contains additional Pauli blocking and Bose enhancement multipliers 54,55 .…”