Effective theory for stochastic particle acceleration, with application to magnetized turbulence

Abstract: The physics of particle acceleration in turbulent plasmas is a topic of broad interest, which is making rapid progress thanks to dedicated, large-scale numerical experiments. The first part of this paper presents an effective theory of stochastic Fermi acceleration, which subsumes all forms of non-resonant acceleration in ideal electric fields and is applicable in generic settings. It combines an exact equation connecting the energization rate to the statistics of the velocity field with a statistical model of particle transport through the structures (i.e., the regions of strong velocity gradients). In a second part, this formalism is applied to MHD turbulence to obtain a comprehensive assessment of the scale-by-scale contributions to the advection and diffusion coefficients. Acceleration is found to be maximal on scales where particles can be trapped inside structures for an eddy turn-around timescale, or in intense structures associated with sharp bends of the magnetic field lines in large-amplitude turbulence (as reported earlier). These fast acceleration regimes, which are inhomogeneous in space, pave the way for a rich phenomenology. We discuss the scalings obtained, their interpretation and show that the findings compare satisfactorily with existing numerical results.