Shock acceleration of solar cosmic rays

The solar cosmic ray (SCR) acceleration by the shocks driven by coronal mass ejections is studied by taking into account the generation of Alfvén waves by accelerated particles. Detailed numerical calculations of the SCR spectra produced during the shock propagation through the solar corona have been performed within a quasi-linear approach with a realistic set of coronal parameters. The resultant SCR energy spectrum is shown to include a power-law part N ∝ ɛ-γ with an index γ = 1.7–3.5 that ends with an exponential tail. The maximum SCR energy lies within the range ɛ max = 0.01–10 GeV, depending on the shock velocity V S = 750–2500 km s−1. The decrease of the shock Alfvénic Mach number due to the increase Alfvén velocity with heliocentric distance r leads to the end of the efficient SCR acceleration when the shock size reaches R S ≈ 4R ⊙. In this case, the diffusive SCR propagation begins to exceed the shock velocity; as a result, SCRs escape intensively from the shock vicinity. The self-consistent generation of Alfvén waves by accelerated particles is accompanied by a steepening of the particle spectrum and an increase of their maximum energy. Comparison of the calculated SCR fluxes expected near the Earth’s orbit with the available experimental data shows that the theory explains the main observed features.

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