Magnetic Variances and Pitch-angle Scattering Times Upstream of Interplanetary Shocks

Abstract

Recent observations of power-law time profiles of energetic particles accelerated at interplanetary shocks have shown the possibility of anomalous, superdiffusive transport for energetic particles throughout the heliosphere. Those findings call for an accurate investigation of the magnetic field fluctuation properties at the resonance frequencies upstream of the shock's fronts. Normalized magnetic field variances, indeed, play a crucial role in the determination of the pitch-angle scattering times and then of the transport regime. The present analysis investigates the time behavior of the normalized variances of the magnetic field fluctuations, measured by the Ulysses spacecraft upstream of corotating interaction region (CIR) shocks, for those events which exhibit superdiffusion for energetic electrons. We find a quasi-constant value for the normalized magnetic field variances from about 10 hr to 100 hr from the shock front. This rules out the presence of a varying diffusion coefficient and confirms the possibility of superdiffusion for energetic electrons. A statistical analysis of the scattering times obtained from the magnetic fluctuations upstream of the CIR events has also been performed; the resulting power-law distributions of scattering times imply long range correlations and weak pitch-angle scattering, and the power-law slopes are in qualitative agreement with superdiffusive processes described by a Lévy random walk.