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.

where Div is the two-dimensional divergencei v is the two-dimensional grad- A A ientj Z is the height-integrated conductivity tensor (the rank of Z is two); С is the velocity of light, V is the unit vector of an external normal to the ionosphere; W- / dS/B ia a halved volume of the magnetic force tube with unit flux ( В is the magnetic field strength, dS is the field line length element); p is the hot magnetospheric plasma pressure| ie the ionospheric potential. The right and the left parts of (1) coincide with each other only in the quasi-steady conditions, whereas in the unsteady case they are differ ent -because of the delay of the disturbances of current and potential in the ionosphere and in the magnetosphere which are transferred by the Alfven waves. The solution of the magnetospheric convection problem requires calculations of the hot plasma pressure dependence on the potential in the magnetosphere Um , the relationship of the potential in the magnetosphere to the potential in the ionosphere, finding the dependence of the volume of the magnetic force tube corresponding to given latitude and longitude in the ionosphere on the hot plasma pressure in the tube and on the conditions of the streaming of magnet ized solar wind about the magnetospherio trap (the distribution of the currents on the magnetopause). In /1,2/ the problem was solved for a low plasma pressure and for the magnetic field line equipotentiality and the main harmonics of the magnetospherio turbulence spectrum were found. The field-aligned current densities which were calculated theoretically and measured experimentally are often much in excess of the current J = e n e Te'^ / (2 (where ne , Tg are the density and the temperature of electrons at high altitudes, me , e are the electron mass and charge) accompanying the free gas-dynamic outflow of the magnetospheric electrons to the ionosphere. As shown in /5,6/ for the observed outflowing currents (j(|> 0) to be generated there should exist the potential difference between the iono sphere and the sufficiently remote magnetospheric regions. In the case of minimum energy release in the ionosphere when the current is fixed this potential difference is и,— um = Te (JM - J„ ) / « j # (2) The field-aligned potential drop is of a laminar character /6-8/ and is local ized in the magnetospheric cavity /9/» As a result, the shell-type electron distribution functions occur and ion beams appear. In the adiabatic approxim ation we get /н_ и/ ехр(-теУг/2Те) ae(V-v0 (s>)jy(s> +\>0 ) (3) Je~ n<? \2Ta l y t ( i ^ e ) r [ 3 / 2 , ( е л и / Т е )Уг] where ^ = cos 0 ; 0 is the pitch-angle; = | cos Q 0I ; Q is the apex angle of the cone inverse to the loss cone; ■$£ potential difference between the regions where the magnetic field equals to B c and B; V is the electron velocity; V 0 (>)) = ( 2 e A U / m t )1/* [1 - (1 - -О2) B c / B ] ~ ^ 2 П р , Т е i re the parameters of the initially Maxwellian distribution in the region with magnetic field B c ; ъ е is the Heaviside function. As a result of the quasi- linear relaxation and the trapping of secondary electrons between the magnetic and electrostatic mirrors, the electron distribution function is deformed up to generation of a plateau (I'ig.1). As a result of two-dimensional Fermi acceleration mechanism /10/, the development of a low-frequency nonlinear turbulence with К (where , K|, are the distortions wave vectors) gives rise to transverse acceleration mainly of heavy ions and to formation of "conic"-type distribution functions (Fig.2) the approximation of which is 39