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.

magnetic moment acta aa an approximate i n t e g r a l o f m o t i o n ( - t o the firat order). If3£ » 1 another adiabatic invariant a r i s e s , b e c a u s e in thia caae the z-directed oscillations are the fastest i n the s y s t e m / 1 0 / . However, as we have shown in the previous paper, the p h a s e spa ce v o l ume , covered by regular, integrable trajectories, decreases r a p i d l y i f the -jfc -parameter becomes closer to unity: more and more parts o f the p h a s e s p a c e fill with stochastic trajectories /11/. If one considers the b e -parameter, which c h a r a c t e r i z e s t h e typical plas ma-sheet electrona, one may find that it is just a b o v e 1 d u r i n g the pre-storm development, when the tail starts to a c c u m u l a t e a d d i t i o n a l m a g n e t i c f l u x and energy with a tendency to decrease. That is why we tried to include into consideration the chaotisation (in sense of "deterministic chaos" see, e.g /12/) or stocnaatisation of electron motion, arising with Э€е— *■ < in the context of a kinetic stability analysis. The problem was how to consider stochastic trajectories in the framework of the Vlasov's kinetic theory. As it is well known, the usual solution of the perturbed Vlasov-differential equation is closely connected with the charact eristics of the unperturbed equation. But how to be if the characteristics, i.e. the integral curves cannot be found as regular aolutions because the particle trajectories in the external field are chaotic? Our approach to a kinetic theory of plasma in a magnetic field reveraal is based on the previous finding that at эеe > 1 the solutions are chaotic as the whole, but the particle motion follows adiabatic trajectories during most of the time. The motion is intercepted only for very short periods of neutral plane crossings, during which the magnetic moment jumps by a small, but practically unpredictable, amount. Because of the practically uncorrelated relation between the jumpa during two subsequent neutral plane encounters, the values of the jump in magnetic moment will be distributed with a zero average. Thia idea leads to the conclusion that the distribution function of weakly stochastic particles should obbey the diffusion equation in magnetic moment and in equatorial pitch angles. The diffusion coefficient may be found after some straightforward calculations as: i Or 2 % j Щ ) * / e x p ( - 2 x e F ( f i ) j (1) ) is a function rather const. (S 1 ) until jjl -~ v 2 / ( 2 m B Q j where it diverges. The expotential factor in (1) confirms that for эее larger than unity the pitch-angle scattering vanishes. There is an additional dependence on j j . in equation (1), viz. that which enters through the bounce period T b . The bounce period in fields given by equation (1) may be determined uaing the approximate conservation of the magnetic moment outside the equatorial region. The main role in determination of the system's stability play particles with distant mirror points (m/2*v2 which leads to the expression % S R ’ J i ~l (2) for the bounce-time where R ia a numerical conatant R=l6-L/(3 •Г2)-т '/г- *E3/2/B0 *Bn . Finally, one gets for the diffusion coefficient the following result: where DQ is a numerical constant. ( 3 ) 72