---
abstract: 'We have constructed a semi-analytical model of the energetic-ion foreshock
  of a CME-driven coronal/interplanetary shock wave responsible for the acceleration
  of large solar energetic particle (SEP) events. The model is based on the analytical
  model of diffusive shock acceleration of Bell (1978), appended with a temporal dependence
  of the cut-off momentum of the energetic particles accelerated at the shock, derived
  from the theory. Parameters of the model are re-calibrated using a fully time-dependent
  self-consistent simulation model of the coupled particle acceleration and Alfv\''en-wave
  generation upstream of the shock. Our results show that analytical estimates of
  the cut-off energy resulting from the simplified theory and frequently used in SEP
  modelling are overestimating the cut-off momentum at the shock by one order magnitude.
  We show also that the cut-off momentum observed remotely far upstream of the shock
  (e.g., at 1 AU) can be used to infer the properties of the foreshock and the resulting
  energetic storm particle (ESP) event, when the shock is still at small distances
  from the Sun, unaccessible to the in-situ observations. Our results can be used
  in ESP event modelling for future missions to the inner heliosphere, like the Solar
  Orbiter and Solar Probe Plus as well as in developing acceleration models for SEP
  events in the solar corona.'
adsnote: Provided by the SAO/NASA Astrophysics Data System
adsurl: https://ui.adsabs.harvard.edu/abs/2014JSWSC...4A..08V
authors:
- Rami Vainio
- Arttu P\"onni
- Markus Battarbee
- Hannu E. J. Koskinen
- Alexandr Afanasiev
- Timo Laitinen
category: publications
date: '2014-02-01'
doi: 10.1051/swsc/2014005
draft: false
eid: A08
featured: false
journal: Journal of Space Weather and Space Climate
month: February
pages: A08
projects: []
publication: Journal of Space Weather and Space Climate
publication_types:
- '2'
tags:
- Energetic particle
- Sep
- Shocks
- Heliosphere
- Interplanetary medium
title: 'A semi-analytical foreshock model for energetic storm particle events inside
  1 AU'
type: ARTICLE
volume: '4'
year: '2014'
---