Resonant scattering of particles and second phase acceleration in the solar corona

Abstract

Effective acceleration of particles by hydromagnetic turbulence requires that the particles be scattered at a rate ν comparable with the frequency ω of the turbulence. The only effective scattering process is due to resonant wave-particle interactions. The resonant waves are HM waves for ions with β≫βA(βc = particle speed, βAc = Alfven speed) and for electrons with γβ ⩾ 43β0(β0 ≈ 43βA), and are whistlers for electrons with β0 ≪ γβ≲ 43β0. The resonant waves can be generated by an anisotropic distribution of particles provided that the anisotropy factor A exceeds a threshold anisotropy A0 ≈ βA/β for HM waves and A0 ≈ β02/β2γ for whistlers. Turbulence with relative magnetic amplitude ɛ causes acceleration at a rate {ie0353-02} provided the following conditions are satisfied: (a) β ≫ βA for ions, β ≫ β0 for electrons; (b) ɛ ≫ A0; (c) n1/ne≲ω/gWi or n1/ne ≫(ω/Ωi) (γβ/43β0)2 for scattering by HM waves or whistlers respectively (n1 = number density of accelerated particles, Ωi = ion gyrofrequency).