Non-Markovian Pitch-Angle Scattering as the Origin of Particle Superdiffusive Transport Parallel to the Average Magnetic Field
Abstract
Understanding energetic particle transport in the presence of magnetic turbulence is crucial for both particle acceleration models and for energetic particle propagation in the heliosphere. Several transport regimes can be envisaged, from essentially diffusive to nearly scatterfree. Here, we develop a theoretical model for particle superdiffusive transport parallel to the average magnetic field, due to pitch-angle scattering times having a non-Markovian, power-law probability distribution. We show that a non-Markovian Fokker-Planck equation can be derived, where the traditional time derivative is changed for a fractional time derivative. By solving the fractional Fokker-Planck equation, with the time-depending part having solutions which are expressed by the Mittag-Leffler functions, it is found that an initial pitch-angle distribution slowly decays towards isotropy. This leads to a parallel velocity autocorrelation function that also has a slow power-law decay in time, thus implying superdiffusive transport in the direction parallel to the background magnetic field. In this framework, we derive for the first time the anomalous diffusion coefficient as a function of physical parameters like the background magnetic field, the resonant turbulence level, and the particle speed. Possible applications to the pitch-angle distributions of pick-up ions observed by Solar Orbiter will be discussed.
- Publication:
-
AGU Fall Meeting Abstracts
- Pub Date:
- December 2020
- Bibcode:
- 2020AGUFMSH012..06Z
- Keywords:
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- 7514 Energetic particles;
- SOLAR PHYSICS;
- ASTROPHYSICS;
- AND ASTRONOMY;
- 7807 Charged particle motion and acceleration;
- SPACE PLASMA PHYSICS;
- 7845 Particle acceleration;
- SPACE PLASMA PHYSICS;
- 7859 Transport processes;
- SPACE PLASMA PHYSICS