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 field of the current flowing over the magnetospheric surface B B= - y U can be approximated by the next formula: U = B 0 Rg /R* X. R n/R" [sin'f,a n Pn (cos9)+cosy(jbri+cos‘f'CM )Pn1(cDS0)] (4) where j=bt/40y* R^/(10 Rg)"3; an , Ьц, cn are coefficients, 2bt is the field jump across the neutral sheet. ia determined from the assumption that the total field ia tangential to the surface of the magnetosphere. 3. The outside magnetic field is determined calculating the field in the magnetoaheath in dependence on IMP direction. The UHD problem, as usual, is decoupled into gaadynamical problem (Euler's equations) and a kinematic prob lem for magnetic field determination using the velocity field and the circums tance that the magnetic field is "frosen in". rot (i7> if ) - 0 , d i i r § = 0 (5) The gaadynamical problem is solved using the code, described in the work of Kartalev and Mastikov (1982) or the code of Spreiter and Stahara (1980). The second code was especially applied in finding the below presented results. Then, using the numerical procedure of Kartalev and Mastikov (1982), the magnetic field distribution in the magnetosheath was found out. The following system in spherical coordinates is considered: + - ^ ( S i n 0 - ^ + C O S 0 B e ) + — ^ = 0, (6) dr r rsinfl as e rsine d<f ( , r - — <r ^ + — ir + -1 ) q = 0 (7) (irr a T г ^ з Г ^ Ч г + r t/r + r ae > B1 u> / COS0 / _ n \. f dB*f / q \ ^as-8e+ зё“-ue56 ~вг дет) + (urBe_ueBr)+sli^e4- - 0 A coordinate transformation is applied then (Baranov, Mastikov,1984) on the equations in such a way that the shock wave and the magnetopause are coordin ate surfaces. In order to avoid the inaccuracy near the magnetopause, as well as to make sure that the numerical procedure is stopped outside the magnetopause structure, the idea of Luhmann et al. (1984) was used. Namely, the computed model field components at a distance of 0.5 Rg from the "obstacle" are taken to represent the field at its outer side. The field on the magnetopause, derived in this way, has a nonzero component, normal to the magnetopause. NUMERICAL SEARCHING FOR OPEN FIELD LINES. A following procedure was applied for a set of points on the dayside magnetopause: beginning from such a point, a curve is derived of the magnetio field line passing through it and going inward from the magnetopause. It appeara that again (as in the mentioned works) different cases are poasible: 1) the field line is connected to the north or south polar region, 2) the field line enters the magnetosphere, but is unlinked to the Earth. Closed lines generally do not touch the magnetopause in this approach. They are somewhere inside the region, formed by the second group of lines. They are not presented here. 3) as a third group of field lines we present those of them, which cross the dawn-dusk plane. In this particular presentation we aimply are not I37