We use numerical solutions of the focused transport equation to study the evolution of the pitchangle dependent distribution function of protons in the vicinity of shock waves and compare the results with basic predictions of diffusive shock acceleration theory. We then consider the case that a seed population of protons is injected close to the Sun simultaneously with a traveling interplanetary shock for which we assume a simplified geometry. We investigate the effects of adiabatic focusing, pitch-angle dependent spatial diffusion, first-order Fermi acceleration at the shock and adiabatic energy losses in the expanding solar wind behind the shock. We analyze the resulting intensities, anisotropies, and energy spectra as a function of time and find that our simulations can reproduce the intensity-time profiles typically observed by the Helios, ACE and Wind spacecraft in interplanetary shock-associated particle events. The acceleration efficiency does not seem to be high enough to explain the energy spectra observed at the shock as being accelerated out of a thermal seed population during the time of ∼ 2 days it takes the shock to reach the Earth, and an injection spectrum of particles pre-accelerated by solar flares or coronal shocks would be required.
|Proceedings of Science
|Published - 1 Jan 2015
|34th International Cosmic Ray Conference, ICRC 2015 - The Hague, Netherlands
Duration: 30 Jul 2015 → 6 Aug 2015
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