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

TL;DR

This paper demonstrates that Lynden-Bell's statistical-mechanical approach explains the emergence of universal power-law tails in non-thermal plasma distributions, highlighting a common high-energy tail form across diverse initial conditions.

Contribution

It shows that Lynden-Bell equilibria naturally produce universal power-law tails with an exponent of -2 in collisionless plasmas, revealing a fundamental universality in these systems.

Findings

Power-law tails with exponent -2 are common at high energies.

The core distribution depends on initial conditions, but the tail is universal.

Most energy resides in the high-energy tail, indicating a universal relaxation process.

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 (1967) 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.