An Improved Model for Relativistic Solar Proton Acceleration applied to   the 2005 January 20 and Earlier Events
  This paper presents results on modelling 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 gamma-ray emission (N14 W61) was near to 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 greater than 450 MeV to avoid complications arising from transport processes that can affect the propagation of low energy protons. In light of this revised approach we have reinvestigated two previous GLEs: those of 2000 July 14 (GLE 59) and 2001 April 15 (GLE 60). Within the limitations of the spectral forms employed, we find that from the peak (06:55 UT) to the decline (07:30 UT) phases of GLE 69, neutron monitor observations from 450 MeV to 10 GeV are best fitted by the Gallegos-Cruz & Perez-Peraza stochastic acceleration model. In contrast, the Ellison & Ramaty spectra did not fit the neutron monitor observations as well. This result suggests that for GLE 69, a stochastic process cannot be discounted as a mechanism for relativistic particle acceleration, particularly during the initial stages of this solar event. For GLE 59 we find evidence that more than one acceleration mechanism was present, consistent with both shock and stochastic acceleration processes dominating at different times of the event. For GLE 60 we find that Ellison & Ramaty spectra better represent the neutron monitor observations compared to stochastic acceleration spectra. The results for GLEs 59 and 60 are in agreement with our previous work. 
D. J. Bombardieri, M. L. Duldig, J. E. Humble and K. J. Michael