Shock Acceleration with Focused Transport Equation: Power-Law Energy Spectrum and Injection Efficiency

Physics – Plasma Physics

Scientific paper

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[2104] Interplanetary Physics / Cosmic Rays, [2124] Interplanetary Physics / Heliopause And Solar Wind Termination, [2152] Interplanetary Physics / Pickup Ions, [7845] Space Plasma Physics / Particle Acceleration

Scientific paper

The focused transport equation (FTE) includes all the necessary physics for modeling the shock acceleration of energetic particles with a unified description of first-order Fermi acceleration, shock drift acceleration, and shock surfing acceleration. In recent years, the FTE-based theory has been proved to be an efficient tool for reproducing the observational features of the lower energy Termination Shock Particles (TSPs) by Voyagers (e. g. le Roux et al. 2007; Florinski 2009). In this study we investigate the energy spectrum of pickup ions accelerated at shocks of various obliquities with FTE by using a stochastic approach model. Here we focus our discussion on how the focused transport acceleration using FTE is transformed to diffusive shock acceleration. The shock acceleration leads to two-component energy spectra. The low-energy component of the spectrum is made of particles that interact with shock one to a few times. For a parallel shock, the high energy component of the spectrum of power law with the spectral index being the same as the prediction of DSA theory, starts just a few times injection speed. For an oblique or quasi-perpendicular shock, the high-energy component of the spectrum exhibits a double power-law distribution: a harder power-law spectrum followed by another power-law spectrum with a slope the same as the spectral index of DSA. It can be concluded that the shock acceleration will eventually go into the DSA regime at higher energies even if the particle anisotropy is not small. The intensity of the energy spectrum given by the FTE, in the high-energy range where particles get efficient acceleration in the DSA regime, is different from that given by the standard DSA theory for the same injection source. We define the injection efficiency η as the ratio between the two theoretical intensities. One of the advantages of the focused transport theory is that it allows calculation of the injection efficiency problem, something that is not easy to solve using other popular shock acceleration theories. In addition, our simulation is able to qualitatively explain the production of multiple power-law energy spectra of TSPs observed by Voyagers.

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