Inward diffusion and acceleration of particles driven by turbulent fluctuations in magnetosphere

Abstract

Charged particles in a magnetosphere are spontaneously attracted to a planet while increasing their kinetic energy via inward diffusion process. A constraint on particles' micro-scale adiabatic invariants restricts the class of motions available to the system, giving rise to a proper frame on which particle diffusion occurs. We investigate the inward diffusion process by numerical simulation of particles on constrained phase space. The results reveal the emergence of inhomogeneous density gradient and anisotropic heating, which is consistent with spacecraft observations, experimental observations, and the recently formulated diffusion model on the constrained phase space.Magnetospheres are the prototypical systems that demonstrate spontaneous confinement of plasmas by magnetic force. Since magnetic force is free of mechanical work, its effect does not appear as an energy term in the Boltzmann distribution (which is in marked contrast with the gravitational confinement created by a star). Instead, the magnetic field manifests itself as topological constraints in the dynamics and equilibrium structures; for example, see Ref. 1 for a recent formulation of magnetic confinement in the perspective of phasespace foliation.The self-organization of a magnetospheric plasma confinement, both in astronomical magnetic dipoles 2,3 and laboratory ones 4-6 , requires a spontaneous mechanism that 'creates' density gradients. As a concomitant effect, particles are accelerated (heated) as they climb up the density gradients 7 ; conservation of first and second adiabatic invariants along the inward displacement increases particle's kinetic energy. The Van Allen radiation belt is believed to be the product of such process [8][9][10] (electrons in an ultra-relativistic regime are created by non-local acceleration mechanisms, such as wave particle interaction [11][12][13] ). Recently, the inward diffusion heating was observed in laboratory magnetosphere experiments 14,15 . As mentioned above, magnetic field does not produce a potential energy (unlike gravity or electrostatic force); hence the concentration and acceleration are not due to centripetal force. The driving force for such 'up-hill diffusion' 16 and acceleration may come from some fluctuations. The key element of the mechanism is, then, the symmetry breaking that selects the preferential direction for particles to penetrate. The symmetry breaking appears in the metric of the phase space; the root cause of an inhomogeneous metric is the topological constraint imposed on magnetized particles by the adiabatic invariants such as magnetic moments 1,17,18 .The early theoretical studies developed an empirical Fokker-Planck type diffusion model on a phase space spanned by adiabatic invariants 19 and explained planetary radiation belt with inhomogeneous density gradients (see Ref. 20 and references therein). This theory was later developed into a unified model according to which the number of particles contained in each magnetic flux tube tends to be homogenized, with the result tha...