Interacting and Interplanetary Protons Accelerated on Diverging Magnetic Field Lines: Stochastic Acceleration
L. Kocharov, G. A. Kovaltsov, T. Laitinen, P. M\"akel\"a, J. Torsti
We study the ratio of the numbers of interplanetary to interacting protons, \ensuremath\Gamma, using a model of stochastic acceleration on open magnetic field lines in solar corona. The impact of diverging coronal magnetic field lines is incorporated into the particle transport operator and shown to be unavoidable, no matter how small the mean free path may be. We calculate the energy spectra of protons precipitating into the subcoronal regions (interacting protons) and the spectra of protons escaping into the interplanetary medium (interplanetary protons). In the case in which both injection and the magnetic field exponentially decrease with altitude, the proton spectra for interacting particles are steeper than the corresponding spectra in interplanetary space. The deduced high-energy ratio \ensuremath\Gamma varies from 1 to \raisebox-0.5ex\textasciitilde5, being almost independent on a magnetic mirror ratio beneath the acceleration region if the latter ratio does not exceed typically \raisebox-0.5ex\textasciitilde10. A quantitative relation between the interplanetary to interacting proton ratio and the magnetic field change from the top of the interaction region to the top of the acceleration region is established. The model results are qualitatively consistent with patterns of energetic protons, \ensuremath\gamma-rays, and neutrons produced during the approximately 40 minutes after the impulsive phase of the 1990 May 24 solar flare.
ApJ, 521, 898-905, 1999