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Noise-induced resonant acceleration of a charge in an intermittent magnetic field: an exact solution for ergodic and non-ergodic fluctuations

We study the diffusion of a charged particle in a magnetic field subject to stochastic dichotomous fluctuations. The associated induced electric field gives rise to non-trivial dynamical regimes. In particular, when the mean magnetic field vanishes, the particle remains confined within a finite radius, regardless of the fluctuation statistics. For a non-zero mean field, we show, using a density approach for Poissonian fluctuations, that the particle undergoes an exponential regime of accelerated diffusion. Crucially and more generally, adopting a trajectory-based formalism, we derive an exact analytical solution valid for arbitrary waiting-time distributions, including non-Poissonian and non-ergodic cases. Even rare, abrupt field reversal are shown to trigger exponential acceleration of the particle's diffusion. We demonstrate that this behaviour stems from noise exciting resonance bands present for periodic fluctuations, and we propose noise-induced resonant acceleration as a robust and efficient charge acceleration mechanism, potentially more effective than Fermi's classic model for cosmic acceleration.