Investigations of numerical avalanches in a 3D vector field

A numerical investigation of models of self-organised criticality in a 3D vector field is presented. The experiments show that the frequency distributions of peak and total energy release depend sensitively on the redistribution formula for the instabilities and on the boundary conditions, Two criteria are found to be necessary to obtain power law distributions for the energy release; 1) the field must be systematically driven, so that large scale regions with coherent tension are obtained, and 2) only a fraction of the field quantity triggering the instability may be removed by the local redistribution procedure. If these criteria are fulfilled, the resulting energy release distribution functions closely resemble the ones observed for solar flares.