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Main phase of geomagnetic storms can be sometime interrupted by extremely strong magnetospheric compression caused by very high solar wind dynamic pressure Pd of ~100 nPa. Those enormous pressures are related to fast and dense solar erupted filaments characterized by high helium abundance. A bright example of such kind of events is a magnetic storm on 21 January 2005 when Pd ~ 100 nPa is recorded on the main phase. During the beginning stage, the storm development can be well described by existing empirical models. However, after the extreme pressure enhancement, all the models have failed. This example shows that the models, developed on the base of quiet to strongly disturbed solar wind conditions, cannot predict extreme space weather disturbances. We discuss various reasons of the model failures and consider possible ways of their further improvements.