Superdiffusive stochastic Fermi acceleration in space and energy

Abstract

ABSTRACT We analyse the transport properties of charged particles (ions and electrons) interacting with randomly formed magnetic scatterers (e.g. large-scale local ‘magnetic fluctuations’ or ‘coherent magnetic irregularities’ usually present in strongly turbulent plasmas), using the energization processes proposed initially by Fermi in 1949. The scatterers are formed by large-scale local fluctuations (δB/B ≈ 1) and are randomly distributed inside the unstable magnetic topology. We construct a 3D grid on which a small fraction of randomly chosen grid points are acting as scatterers. In particular, we study how a large number of test particles are accelerated and transported inside a collection of scatterers in a finite volume. Our main results are: (1) The spatial mean-square displacement <(Δr)2 > inside the stochastic Fermi accelerator is superdiffusive, $\lt (\Delta r)^2\gt \sim t^{a_{r}},$ with ar ∼ 1.2–1.6, for the high-energy electrons with kinetic energy (W) larger than 1 MeV, and it is normal (ar = 1) for the heated low-energy (W < 10 keV) electrons. (2) The transport properties of the high-energy particles are closely related with the mean-free path that the particles travel in-between the scatterers (λsc). The smaller λsc is, the faster the electrons and ions escape from the acceleration volume. (3) The mean displacement in energy $\lt \Delta W\gt \sim t^{a_{W}}$ is strongly enhanced inside the acceleration volume (aW = 1.5–2.5) for the high-energy particles compared to the thermal low-energy particles (aW = 0.4), i.e. high-energy particles undergo an enhanced systematic gain in energy. (4) The mean-square displacement in energy <W2 > is superdiffusive for the high-energy particles and normal for the low-energy, heated particles.