Position and velocity space diffusion of test particles in stochastic electromagnetic fields

TL;DR

This paper investigates how test particles diffuse in both position and velocity spaces within a stochastic electromagnetic field, revealing that energization occurs only during anomalous diffusion in position space, with Gaussian processes exhibiting non-standard scaling.

Contribution

It introduces a model of electromagnetic fluctuations generated by oscillating magnetized clouds and analyzes the resulting diffusion behaviors in position and velocity spaces.

Findings

Particles show Brownian, anomalous, or ballistic motion depending on frequency.

Energization occurs only during anomalous diffusion in position space.

Diffusion processes are Gaussian but have non-standard scaling exponents.

Abstract

The two--dimensional diffusive dynamics of test particles in a random electromagnetic field is studied. The synthetic electromagnetic fluctuations are generated through randomly placed magnetised ``clouds'' oscillating with a frequency $\omega$. We investigate the mean square displacements of particles in both position and velocity spaces. As $\omega$ increases the particles undergo standard (Brownian--like) motion, anomalous diffusion and ballistic motion in position space. Although in general the diffusion properties in velocity space are not trivially related to those in position space, we find that energization is present only when particles display anomalous diffusion in position space. The anomalous character of the diffusion is only in the non--standard values of the scaling exponents while the process is Gaussian.