Modeling the rate of occurrence of solar flares

Dimensional considerations are used to analyze the distribution of times be tween solar flares (the flare waiting-time distribution). An analytical est imate for the mean flaring rate lambda (0) is obtained, based on the idea t hat the rate reflects a balance between the processes of energy input into the corona and energy dissipation by flaring. The estimate is shown to be i n good agreement with observations of flares by Geostationary Operational E nvironmental Satellite detectors. The analytic result is confirmed using th e master equation (probability balance equation) formalism. Analysis of tim e variation leads to a differential equation describing how the free energy in the corona changes when the rates of driving of the system and of flari ng vary. This equation may be used to describe the global energy balance in the corona over the solar cycle.