Paper detail

Superdiffusion revisited in view of collisionless reconnection

The concept of diffusion in collisionless space plasmas like those near the magnetopause and in the geomagnetic tail is reexamined from a fundamental statistical point of view making use of the division of particle orbits into waiting orbits and break-out into ballistic motion lying at the bottom, for instance, of Lévy flights and the celebrated $κ$-distribution. A stringent derivation yields an anomalous diffusion coefficient increasing with time, thus describing superdiffusion. Contrary to wide belief, superdiffusion, though faster than classical, is a weak process. Absolute values of the coefficient are small due to the largeness of the anomalous collision frequency in waiting statistics compared with the infinitesimally small binary collision frequency. We provide parallel and perpendicular diffusion coefficients, determine the exponents of temporal increase, determine the power and $κ$ for two-dimensional diffusion by referring to published numerical particle-in-cell simulations, fix the range of permitted $κ$s, and construct a relation between the diffusion coefficients and the resistive scale. We furthermore find an expression for the anomalous collision frequency from the electron pseudo-viscosity in reconnection thus identifying reconnection as a localized diffusion process in satisfactory agreement with basic physical concepts.