Energetic particle parallel diffusion in a cascading wave turbulence in the foreshock region

Abstract

Abstract.We study parallel (field-aligned) diffusion of energetic particles in the upstream of the bow shock with test particle simulations. We assume parallel shock geometry of the bow shock, and that MHD wave turbulence convected by the solar wind toward the shock is purely transverse in one-dimensional system with a constant background magnetic field. We use three turbulence models: a homogeneous turbulence, a regular cascade from a large scale to smaller scales, and an inverse cascade from a small scale to larger scales. For the homogeneous model the particle motions along the average field are Brownian motions due to random and isotropic scattering across 90 degree pitch angle. On the other hand, for the two cascade models particle motion is non-Brownian due to coherent and anisotropic pitch angle scattering for finite time scale. The mean free path λ calculated by the ensemble average of these particle motions exhibits dependence on the distance from the shock. It also depends on the parameters such as the thermal velocity of the particles, solar wind flow velocity, and a wave turbulence model. For the inverse cascade model, the dependence of λ at the shock on the thermal energy is consistent with the hybrid simulation done by Giacalone (2004), but the spatial dependence of λ is inconsistent with it.

The upstream‐propagating Alfvénic fluctuations with power law spectra in the upstream region of the Earth's bow shock

“…The upstream-propagating waves excited by the beam instability of energetic ions reaching far upstream (up to 1750 R E in the radial direction according to Desai et al [2008]) can undergo an inverse cascade to generate UPAFs [Giacalone, 2004;Otsuka et al, 2007]. These energetic ions keep propagating upstream, while the UPAFs are transported downstream by the solar wind and thus are separated from the source ions.…”

“…Giacalone [2004] made a large-scale hybrid simulation at a parallel shock and found that near the shock, the spectrum of self-excited waves in the frequency range of 2 × 10 −3 to 0.1 Hz is approximately a power law with an index close to −5∕3. Otsuka et al [2007] proposed that if wave-wave interactions occur as the high-frequency waves are transported by the solar wind to the bow shock, the inverse cascade will take place. However, the previous observational studies all focused on monochromatic waves.…”