Структура и динамика полярных токовых систем : материалы международного симпозиума «Полярные геомагнитные явления», 25-31 мая, Суздаль, СССР / Акад. наук СССР, Кол. фил. им. С. М. Кирова, Поляр. геофиз. ин-т. – Апатиты : [б. и.], 1988.

The appearance of even a weak dissipation of the particle energy consid erably changes the plaaina stability conditions in a 2-dimensional field reversal and reveals a new, dissipative, unstuble mode /13/. Coroniti has found that a similar effect may arise if a particle pitch-angle scattering is taken into account /8/. The pitch-angle scattering acts like collisions, which relax the electron anisotropy, induced by the growing mode and permits an effective energy transfer from the mode to electrons. After adding of a pitch-angle diffusion operator and averaging over gyro- phase the Vlasov's equation becomes a drift kinetic equation for the tearing mode polarization /see 14/. We have solved it by expanding g in inverse powers of T b(= ) : g = S0 + g-j+... . Averaging the second order equation for g^ over a bounce period yields an equation for gQ. One solution immediately arises: If D=Do-<^ J 4/q the Green function of the diffusion equation for gQ reduces to a Dirac delta-function and у ( у ) = This case corresponds to the well analyzed in the past metastable collisionless tearing mode. No wave growth occur up to and including long wavelengthes k . L < B n/Bo . But a completely different picture arises for a strong diffusion C / j ^ . ( « T R ) / D e - In this limit the smallness of C/jx3 can be used to solve the diffusion equation by a power law expansion. Folbwing this way we found a qualitatively new, dissipative unstable mode with a growth rate (in the long wavelength limit K ’L (2Bn/B0 )** ), /14/: This mode grows if the stochastic pitch angle scattering due to deterministic chaos in the electron motion appears, i.e. if d t e tends to unity. The growth rate (4) exceeds the classical one /6/ by, at least, one order of magnitude, if one assumes parameters typical for the Earth's magnetotail. Therefore, our theory explains three principal features of the substorm behaviour: 1. If the field line curvature in the tail midplane is small (large curvature radii, thick plasma sheet, expressed by зге>1 for thermal electrons) th tail is stable against tearing mode perturbations. 2. In the course of the pre-substorm evolution, when energy storage due to solar wind inflow goes on, the tail becomes marginal stable, controlled by the decrease of the эе -parameter down to unity. Any physical parameter, which detex-mines эе , acts to diminish it: the total energy content increases (i.e. B Q increases), the curvature decreases (Вд decreases), the plasma sheet becomes thinner (L decreases) and the electron temperature increases in the course of the adiabatic pre-storm development. Hence, the energy storage process itself leads to the destabilization of the tail. , 3. After reaching a critical value эге 1.6 a tearing mode instability breaks up. Its growth is overexpotential fast, as was found by a numerical solution of equation (4) governing the increase of the perturbation field across the neutral plane. A new neutral line spontaneously arises in the near Earth tail and reconnection may transfer the magnetic and current-energy, previously stored, into plasma heating and particle acceleration. Hence, the question mark in Figure 2b can be cancelled and replaced by the growth rate (4) which explains not only the explosive character of isolated substorm onaets but also gives the instability threshold and refers directly 73