A new analytic solution for 2nd-order Fermi acceleration

TL;DR

This paper introduces a comprehensive analytic solution for 2nd-order Fermi acceleration that incorporates variable rates and turbulence spectra, enhancing modeling accuracy in astrophysical contexts.

Contribution

It provides the first flexible analytic solution accounting for arbitrary turbulence spectra and time-dependent rates in 2nd-order Fermi acceleration.

Findings

Supports Kolmogorov and Kraichnan turbulence spectra

Includes Bohm diffusion and hard-sphere approximation

Enables realistic astrophysical modeling

Abstract

A new analytic solution for 2nd-order Fermi acceleration is presented. In particular, we consider time-dependent rates for stochastic acceleration, diffusive and convective escape as well as adiabatic losses. The power law index q of the turbulence spectrum is unconstrained and can therefore account for Kolmogorov (q = 5/3) and Kraichnan (q = 3/2) turbulence, Bohm diffusion (q = 1) as well as the hard-sphere approximation (q = 2). This considerably improves beyond solutions known to date and will prove a useful tool for more realistic modelling of 2nd-order Fermi acceleration in a variety of astrophysical environments.