Fractional Boltzmann equation for resonance radiation transport in plasma

TL;DR

This paper introduces a fractional Boltzmann equation to model resonance radiation transport in plasma, capturing non-local and hereditary effects through fractional derivatives, supported by numerical solutions.

Contribution

It formulates a novel fractional Boltzmann equation incorporating fractional derivatives to better describe photon transport in plasma.

Findings

The fractional Boltzmann equation aligns with heavy-tailed photon path distributions.

Numerical solutions demonstrate the equation's applicability in simple cases.

The approach captures non-local and hereditary dynamics in plasma radiation transport.

Abstract

The fractional Boltzmann equation for resonance radiation transport in plasma is proposed. We start from the standard Boltzmann equation, averaging over frequencies leads to appearance of fractional derivative. This fact is in accordance with the conception of latent variables leading to hereditary and non-local dynamics (in particular, fractional dynamics). The presence of the fractional material derivative in the equation is concordant with heavy tailed distribution of photon path lengths and with spatiotemporal coupling peculiar to the process. We discuss some methods of solution of the obtained equation and demonstrate numerical results in some simple cases.