Physics of auroral phenomena : proceedings of the 34th Annual seminar, Apatity, 01 - 04 March, 2011 / [ed.: A. G. Yahnin, A. A. Mochalov]. - Апатиты : Издательство Кольского научного центра РАН, 2011. - 231 с. : ил.

M.A. Volkov the electron density is approximately equal to the ions density ne ~ ni. In this case, the precipitating electrons have to replace the other electrons, or the ions must leave the tube. The ionospheric electrons can not get to the magnetic flux tube from the ionosphere along magnetic field lines because the field-aligned electric field prevents them. The cold magnetospheric electrons move together with the tube with the speed of the magnetospheric convection. Thus the condition of charge neutrality can be provided only when the hot magnetospheric ions drift from the magnetic flux tube across the magnetic field lines. The ions are moving across the magnetic flux tube with the velocity of the gradient or diamagnetic drift. The direction of the magnetosphere current is shown in fig. 2, it coincides with the gradient drift VGo f the ions directed along the line of the equal magnetic field. Let the magnetic field be directed to us, then the electric drift of ions VEis directed to the right in fig. 2. The ions will drift under the electric field in the region of the weaker magnetic field. Since the magnetic moment of ions is saved their energy will decrease. We shall consider this mechanism in more details. For simplicity, we assume that all of the magnetospheric ions have the magnetic moment |i. The total energy o f the ion is equal to: Ei = t^ L + /лВ + е(р, (1) where цВ -the transverse ion energy, <p -the potential electric field. Let the induction inside the flux tube in the center of the arc be equal to B u the potential <p) =- <p0, outside the arc B2, q >2 = 0. The total energy of the ion (1) conserves at any point of the particle trajectory. Assuming B {> B2, the minimum value of this energy is equal to \xB2, the condition of the magnetic moment conservation is not satisfied for lower values energy. For the case B =B2 reflection points lie far from the equatorial plane of the magnitosphere and longitudinal velocities of the ions are small, this follows from the second adiabatic invariant I = v/, where v-the average speed, /-the length of the magnetic field line between the reflection points. The expression of the potential Фо can be obtained from (1): <Po= M(B]- B 2) / e +^ ( 2 ) 2e Accepting B\iB2 = 3, = mv///2 = 2.5keV, we shall receive value <p0 = 6 kV, which is close to the observed values. Let us estimate the change in concentration of the charged particles inside the magnetic flux tube above the auroral arc in this simple model. Assuming the magnetic moment of the electron being small, the relationship between the concentration and the magnetic field is given by the following expression: , , « 1 ^ , (3) MoV where nli2-the charged particle concentration inside and outside the magnetic flux tube, ^o-the magnetic permeability. For the situation described in [Runov et al., 2009], from the observations by satellite Themis (e) take the values of В i = 35 nT, B2= lOnT, \ j .B\ = 4.5 keV, the depletion of the concentration from the formula (3) will be equal (n2-nx) = 0.97 cm'3. The observed value of changes in the concentration is equal= 0.9 cm'3. This good accordance with the experiment can be explained by the fact that the velocity of the dipolarization front is much smaller than the ion thermal and Alfen velocity and that the curvature of the magnetic field line is much larger than the ion gyroradius. The evaluation of the plasma velocity at the different distances from the Earth will be made further. Thus in the magnetic flux tube with the intense current flowing from the ionosphere the density and the pressure of the magnetospheric particles decreases due to precipitation of energetic electrons. The decrease in the pressure leads to the increase in the magnetic field strength in the flux tube because the plasma is diamagnetic. The increase of the magnetic field in turn leads to compression of the magnetic flux tube and the particles in it. The pressure in the flux tube changes and a new configuration of the distribution of the pressure and the magnetic field in the magnetotail arise. Calculation results Figure 3 shows the thermal energy distributions of charged particles 3/2 pV in the magnetic flux tube vers, the colatitude 0(1) before and after dipolarization (2), it allows to track changes in these quantities in the magnetic flux tubes. The presented data have been obtained by solving the balance equation for the magnetic and plasma pressure with constant pressure along the magnetic field lines [Volkov, 2011] using the model of the magnetic field [Tsyganenko, 1995]. For the case of the preceding dipolarization the component of the IMF Bz is equal - 5 nT, after depolarization Вг = 0 nT, By = 0 in both cases. The IMF components values correspond to the observed on the satellite ACE values of the IMF given in the dipolarization time. The solar wind pressure is equal 2nPa, Dst = 0. The pressure in the plasma sheet at X= - 20RE was set equal 0.5 nPa before and 0.25 nPa after dipolarization which is close to the values observed by the satellite Themis (b) [Runov et al., 2009] 22