  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.
