Physics of auroral phenomena : proceedings of the 33rd Annual seminar, Apatity, 02 - 05 March, 2010 / [ed.: A.G. Yahnin, A. A. Mochalov]. - Апатиты : Издательство Кольского научного центра РАН, 2011. - 206 с. : ил.

A.E. Levitin at al. However, the various models have different ranges o f validity (both spatially and in control parameters) because, among other things, the data sets used for their development were different. Moreover, the data sets used for the development o f models usually contained a rather small number o f high-latitude magnetopause crossings. Sotirelis and Meng in 1999 presented a calculation where the shape of the magnetopause is computed from the requirement that the pressure in the magnetosheath is balanced by magnetic pressure inside the magnetosphere. The authors found changes in the shape of the magnetopause with varying dipole tilt angle. The magnetotail and standoff location shifted vertically, in opposite directions, for nonzero dipole tilt. The vertical offset of the standoff location from the Earth-Sun line varies linearly with dipole tilt angle, reaching 3 Re for maximum of the tilt. Today for magnetopause crossings, most people have computed the predicted magnetopause positions according to following models: Shue et al. [1997]: R0 = 11.4 + 0.013Bz)(Dp>-,/66 , for Bz > 0 ; R0= 11.4 + 0,14Bz)(Dp>'l/6'6 , for Bz < 0\ Shue etal. [1998]: R„ = {10.22 + 1.29tanh[0.1849Bz + 8.14)]}(Dph'/66-, Kuznetsov and Suvorova [1998]: R0 = 8.6(1 + 0.407exp(-(\Bz\ - Bz)2/(200*p°'5))D p 0'9). Here Bz (nT) is interplanetary magnetic field z-component is GSM coordinates and Dp (nPa) is the solar wind dynamic pressure. We propose to estimate R0 by basing on the dynamic balance o f the solar wind plasma pressure Dp and magnetic pressure B~/2/u0, that is calculated according to some magnetospheric magnetic field model. We have used Paraboloid Model (PM) [Feldstein et al., 2005] and show that our model (PM-used procedure) results practically coincide with R0 predicted according to different analytical models. But our procedure o f R0 estimation is preferable during magnetic storms when the southern IMF component Bz becomes rather strong. The PM model has been named as paraboloid since the magnetopause, representing the paraboloid of revolution geometrically, is the essential element o f the model. PM reflects both the physical and analytical description of the geomagnetic field within the whole magnetosphere. On the basis of physical ideas of the character o f large-scale magnetospheric current systems and their magnetic fields, analytical relationships were obtained, which make it possible to calculate the geomagnetic field vector at any point in the magnetosphere as a function of input parameters of the model for magnetic storms of any intensity. The representation o f the magnetic field in the modeling region is based on the modular principle, according to which the total magnetic field B(t) is represented as the sum o f contributions from major magnetospheric field sources (modules). Every module is an independent current system and each current system has its own intrinsic relaxation and inertia.time scales. The magnetic field o f each current system depending on its own input parameters is calculated separately. During the magnetic storm intervals the large-scale current systems are influenced not only by the current state of the interplanetary medium, but also its time history during the previous hours. These effects, as well as the non-linear character of the magnetospheric response to the extreme condition in the solar wind are taken into account in PM using model input parameters that specify the magnitude and evolution of important magnetospheric quantities. These input parameters are based on observed conditions in the magnetosphere during the entire course of the magnetospheric disturbances from magneto-quiet conditions to intense magnetic storms. Until recently only a handful of empirical models o f the large-scale magnetospheric magnetic field were available. These models were built on the basis of fitting satellite magnetic field measurements in the magnetosphere to various sets of approximating mathematical functions. PM uses physical notions of the possible character of the magnetospheric currents to select basis functions for these systems. For example, in contrast to the empirical models, the coefficients in the expansion o f the potential for the magnetospheric magnetic field (BT) due to the tail current system are determined on the basis conditions that Bm = 0 ( Bm is the component o f the magnetic field BT normal to the magnetopause). As a result the tail plasma sheet current closes along the whole magnetopause, including its day sector. This is a key feature distinguishing PM from other magnetic field models, which has important consequences for the location o f the magnetopause (since the inner part of the magnetotail current closes through the subsolar magnetopause) and for the contribution of magnetopause currents to Dst. For every magnetic field source, PM assumes a zero value of the normal component o f the magnetic field on the magnetopause. The continuity equations for the magnetic field and electric current density, div В = 0 and d iv j = 0 in the magnetosphere outside the region of the current source location are valid as well. The total magnetic field vector В (t) for any point (x, y, z ) in the magnetosphere in the solar-magnetospheric coordinate system and for the time t is: B(t) =B d (y/) + BCF(у/, R l) + Вт(у/, R l, R2, Ф) + BR (у/, br) + BSR (у/, bn R l) + BFAC(у/, R l, J q ), where: Bd (y/) is the Earth's dipole field; 64