Modelling cosmic ray ground level enhancements

Analyses of seven cosmic ray ground level enhancements (GLE) are presented. The first four events were part of the unprecedented sequence of relativistic solar proton events which occurred during 1989. Three of the larger events of the 21st solar cycle have also been modelled. In each case, analysis is based on data from the world-wide network of neutron monitors. Surface muon telescope data has also been used for of the 29 September 1989 event. A sophisticated model has been developed from that of Smart et al. ( 1979). Modifications include the calculation of asymptotic directions using a geomagnetic field model which accounts for distortion of the field during geomagnetic disturbances, and the use of a least squares method for determining the best fit parameters. An exponential function used to describe the pitch angle distribution has been further developed to allow bi-directional particle flow and rigidity dependence. The form of the particle spectrum used in most of the analyses was a modified power law in rigidity. An approximation of the Ellison and Ramaty (1985) shock acceleration spectrum has recently been included in the model. A rigidity dependent pitch angle distribution was required to model the GLE on 29 September 1989 and indicates that, initially, the anisotropy of the particle distribution decreased with increasing rigidity. Significant back-scattering of particles resulted in the observation of a late peak at stations viewing in the anti-sun direction and two peaks at some other stations. The three GLEs which occurred during October 1989 have been modelled with particular emphasis on the initial spikes seen at some stations for both the 19 and 22 October events. In the case of 19 October 1989, a further spike later in the event appears to have been produced by the same mechanism as the initial spike, which had a significantly different particle distribution and spectrum to that of the main event. Enhancement of the pitch angle distributions in the anti-sun direction during the 22 October event is probably due to scattering by a disturbed plasma region beyond the Earth. The 24 October 1989 event was best modelled using a modified form of the Ellison and Ramaty shock acceleration spectrum. A rigidity dependent pitch angle distribution resulted in only marginal improvement in the fit to the observed data. The 12 October 1981 GLE has been modelled with a bi-directional pitch angle distribution. This is found to be consistent with results at lower energies and is further evidence for the presence of a looped structure in the interplanetary magnetic field. Further complexity in the interplanetary medium was present during the 7-8 December 1982 GLE. Interplanetary magnetic field data are consistent with a magnetic cloud-like feature situated just beyond the Earth. Observed neutron monitor increases were satisfactorily reproduced by a model with an elliptical deficit region to account for the scattering which impeded some particles approaching the Earth. The derived particle arrival direction for the 16 February 1984 GLE was rv40° from the measured interplanetary magnetic field direction. This could not be satisfactorily explained, however it is found to be consistent with the results of previous studies