Temporal features of the refilling of a plasmaspheric flux tube

Time‐dependent hydrodynamic equations were solved in order to study the refilling of plasmaspheric flux tubes depleted during magnetic storms. Depending on the initial density profiles in the depleted flux tube, a variety of shock formations occur during the early stage (∼1 hour) of the refilling. After this early stage, an important feature of the flow is the formation of a pair of shocks, which propagate down, one in each hemisphere. The refilling occurs by the downward propagating shocks with speeds <1.5 km/s and by a simultaneous increase in the plasma density between the two shocks. The time rates of this increase in the density are given for magnetic shells L = 4 and 6.6. These rates depend on the density (N0) at the ionospheric boundaries. Depending on N0, a fair agreement is found between the refilling rates obtained from our calculations for L = 6.6 and those determined from the GEOS 2 observations. The refilling of a flux tube with different densities in the conjugate ionospheres was also considered, and it was found that after the initial stage of about one hour, the filling occurs through the propagation of only one shock from the hemisphere of the weak ionospheric source to that of the strong one. An interesting feature of the temporal evolution of the density of the shocked plasma after the early stage is the persistence of fluctuations with time periods ranging from about 2 to 10 minutes and corresponding wavelengths ranging from about one to several thousand kilometers. These fluctuations appear to be sound waves. Prior to the shock formation, counterstreaming of the ions is expected to occur in the equatorial region. The single‐fluid hydrodynamic model used in the present study is not suited to handle such multiple plasma streams. Therefore, some kinetic considerations for the formation of shocks are given. Results from the particle simulations of counterstreaming plasma expansion show that a potential hill, which eventually slows down the ion streams, leads to the formation of a shock pair in the “equatorial plane.” These shocks propagate in opposite directions in a manner analogous to that obtained with the hydrodynamic model of a geomagnetic flux tube. However, the kinetic calculations show that the shock formation occurs only when the electron temperature Te > 3Ti, where Ti is the ion temperature.