---
abstract: '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.'
adsnote: Provided by the SAO/NASA Astrophysics Data System
adsurl: https://ui.adsabs.harvard.edu/abs/1999ApJ...521..898K
authors:
- L. Kocharov
- G. A. Kovaltsov
- T. Laitinen
- P. M\"akel\"a
- J. Torsti
category: publications
date: '1999-08-01'
doi: 10.1086/307582
draft: false
featured: false
journal: ApJ
month: August
number: '2'
pages: 898-905
projects: []
publication: ApJ
publication_types:
- '2'
tags:
- 'Sun: corona'
- 'Sun: flares'
- 'Sun: magnetic fields'
- 'Sun: particle emission'
- 'Sun: x-rays'
- Gamma rays
- 'Sun: corona'
- 'Sun: flares'
- 'Sun: magnetic fields'
- 'Sun: particle emission'
- 'Sun: x-rays'
- Gamma rays
title: 'Interacting and Interplanetary Protons Accelerated on Diverging Magnetic
  Field Lines: Stochastic Acceleration'
type: ARTICLE
volume: '521'
year: '1999'
---