Statistics of charged particles in external random longitudinal electric fields

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Abstract
Charged particle diffusion in a given one‐dimensional Gaussian random longitudinal electric field is investigated by three different methods; quasilinear theory, resonance broadening theory, and direct numerical integration of trajectories. Analytical predictions of both theories are expressed using a random walk approach. An analytic frequency and wavenumber spectrum of constant shape but variable amplitude, related to experimental observations, is used for comparison between the three methods. They all agree at low amplitude. At larger amplitude, resonance broadening theory shows the right tendency for the maximum diffusion coefficient to increase less rapidly than the mean square field. However, the exact value diverges from quasilinear and resonance broadening predictions as soon as the product of the quasilinear correlation time multiplied by mean bounce frequency increases above 0.4.