Non-thermal particle acceleration and power-law tails via relaxation to universal Lynden-Bell equilibria

Abstract

Collisionless and weakly collisional plasmas often exhibit non-thermal quasi-equilibria. Among these quasi-equilibria, distributions with power-law tails are ubiquitous. It is shown that the statistical-mechanical approach originally suggested by Lynden-Bell (Mon. Not. R. Astron. Soc., vol. 136, 1967, p. 101) can easily recover such power-law tails. Moreover, we show that, despite the apparent diversity of Lynden-Bell equilibria, a generic form of the equilibrium distribution at high energies is a ‘hard’ power-law tail $\propto \varepsilon ^{-2}$ , where $\varepsilon$ is the particle energy. The shape of the ‘core’ of the distribution, located at low energies, retains some dependence on the initial condition but it is the tail (or ‘halo’) that contains most of the energy. Thus, a degree of universality exists in collisionless plasmas.

Loss-cone stabilization in rotating mirrors: thresholds and thermodynamics

“…From a more academic standpoint, this also provides a new example of a complex plasma phenomenon that can be captured -at least in part -by relatively simple thermodynamic arguments. There has been substantial recent progress in the field adapting some of these dynamics-agnostic theoretical tools to a wider range of plasma physics applications; the hope, generally, is that this kind of argument can allow physical arguments and intuitions that apply to broad classes of systems (Helander 2017(Helander , 2020Kolmes et al 2020bMackenbach et al 2022;Zhdankin 2022;Ewart, Nastac & Schekochihin 2023;Mackenbach et al 2023a,b).…”

A Monte Carlo Method for Calculating Lynden-Bell Equilibrium in Self-Gravitating Systems

“…It is interesting to note that for continuous initial distributions, the LB equilibrium particle distribution found using MC simulations shows the presence of algebraically decaying tails [48,49]. We examined a range of diverse initial conditions for the distributions described by Equation ( 26), as illustrated in Figure 9.…”