ANALYTICAL STUDY OF THE ENERGY RATE BALANCE EQUATION FOR THE MAGNETOSPHERIC STORM-RING CURRENT

We present some results of the analytical integration of the energy ra te balance equation, assuming that the input energy rate is proportion al to the azimuthal interplanetary electric field, E-y, and can be des cribed by simple rectangular or triangular functions, as approximation s to the frequently observed shapes of E-y, especially during the pass age of magnetic clouds. The input function is also parametrized by a r econnection-transfer efficiency factor alpha (which is assumed to vary between 0.1 and 1). Our aim is to solve the balance equation and deri ve values for the decay parameter tau compatible with the observed Dst peak values. To facilitate the analytical integration we assume a con stant value for tau through the main phase of the storm. The model is tested for two isolated and well-monitored intense storms. For these s torms the analytical results are compared to those obtained by the num erical integration of the balance equation, based on the interplanetar y data collected by the ISEE-3 satellite, with the tau values parametr ized close to those obtained by the analytical study. From the best fi t between this numerical integration and the observed Dst the most app ropriate values of tau are then determined. Although we specifically f ocus on the main phase of the storms, this numerical integration has b een also extended to the recovery phase by an independent adjust. The results of the best fit for the recovery phase show that the values of tau may differ drastically from those corresponding to the main phase . The values of the decay parameter for the main phase of each event, tau(m), are found to be very sensitive to the adopted efficiency facto r, alpha, decreasing as this factor increases. For the recovery phase, which is characterized by very low values of the power input, the res ponse function becomes almost independent of the value of alpha and th e resulting values for the decay time parameter, tau(r), do not vary g reatly as alpha varies. As a consequence, the relative values of tau b etween the main and the recovery phase, tau(m)/tau(r), can be greater or smaller than one as alpha varies from 0.1 to 1.