Ion and electron superdiffusive transport in the interplanetary space

We study the propagation of energetic particles, accelerated by interplanetary shock waves, upstream of the shock. By using the appropriate propagator, we show that in the case of superdiffusive transport, the time profile of particles accelerated at a traveling planar shock is a power-law with slope 0 < gamma < 1, at variance with the exponential profile obtained for normal diffusion. By analyzing data sets of interplanetary shocks in the solar wind observed by the Ulysses and the Voyager 2 spacecraft, we find that the time profiles of energetic electrons correspond to power-laws, with slopes gamma similar or equal to 0.30-0.98, implying a mean square displacement (Delta x(2)) proportional to t(alpha), with alpha = 2 - gamma > 1, i.e., superdiffusion. In addition, the propagation of ions is also superdiffusive, with alpha = 1.07-1.13. (C) 2009 COSPAR. Published by Elsevier Ltd. All rights reserved.