Protons accelerated to relativistic energies by transient solar and interplanetary phenomena caused a ground-level cosmic ray enhancement on 14 July 2000, Bastille Day. Near-Earth spacecraft measured the proton flux directly and ground-based observatories measured the secondary responses to higher energy protons. We have modelled the arrival of these relativistic protons at Earth using a technique which deduces the spectrum, arrival direction and anisotropy of the high-energy protons that produce increased responses in neutron monitors. To investigate the acceleration processes involved we have employed theoretical shock and stochastic acceleration spectral forms in our fits to spacecraft and neutron monitor data. During the rising phase of the event (10:45 UT and 10:50 UT) we find that the spectrum between 140 MeV and 4GeV is best fitted by a shock acceleration spectrum. In contrast, the spectrum at the peak (10:55 UT and 11:00 UT) and in the declining phase (11:40 UT) is best fitted with a stochastic acceleration spectrum. We propose that at least two acceleration processes were responsible for the production of relativistic protons during the Bastille Day solar event:(1) protons were accelerated to relativistic energies by a shock, presumably a coronal mass ejection (CME).(2) protons were also accelerated to relativistic energies by stochastic processes initiated by magnetohydrodynamic (MHD) turbulence.

This paper presents results on modeling the ground-level response of the higher energy protons for the 2005 January 20 ground-level enhancement (GLE). This event, known as GLE 69, produced the highest intensity of relativistic solar particles since the famous event on 1956 February 23. The location of recent X-ray and -ray emission (N14 W61 ) was near Sun-Earth connecting magnetic field lines, thus providing the opportunity to directly observe the acceleration source from Earth. We restrict our analysis to protons of energy !450 MeV to avoid complications arising from transport processes that can affect the propagation of low-energy protons.

Extreme solar processes at the Sun on 2001 April 15 accelerated protons to relativistic energies, resulting in a groundlevel enhancement in cosmic rays observed at Earth. The GOES 10 spacecraft measured the proton flux directly, and ground-based observatories measured the secondary responses to higher energy protons. We have modeled the groundlevel response to this event using a technique that deduces the spectrum, arrival direction, and anisotropy of the highenergy protons. To investigate the acceleration process(es), we have employed theoretical shock and stochastic acceleration spectral forms in our fits to spacecraft and neutron-monitor data. In the case of stochastic acceleration, we use two different spectral forms. The first (model A) incorporates an idealized preacceleration step through monoenergetic injection. The second (model B) incorporates a more realistic injection function using preacceleration by DC electric fields in a reconnecting neutral current sheet. We find that at the rise, peak, and decline phases of the event