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.

О.М. Barkhatova et al. O»2 + e ) { ® V + e - 0 ' . J + Уш 2Ж г + К г) ] - К \ К г +-^тт)1‘» 2 + Q - r a l 2( * J + * / ) ] + AM /V х у >J s V vz 4 J J 2 ' + ( y - l ) g 2(kx2 + k y2)} = 0, H 2 where VA2 = —— - square of Alfven velocity and 4тгр0 1/ ^ V 2 - ______________________ LA ________________ - square of modified Alfven velocity in finite conductivity ш ~ c 2 1 ik 1+ i — — (k 2+k 2+k 2 ----- - t - % 4mrco * y 2 4H 2 H / 1 \ 2 conditions, Q = Vam2 —— + ik. 2H 2 Thus, the modified Alfven waves are described by the equation 0)2 + Q = 0, and MGW are described by the equation К + Q)[a>‘1- V 2 ( k 2 +— )]-®2 (V; + Vm 2) ( k 2 + ky2) + V 2Vm 2{ k 2 + - ^ ) { k 2 + ky2) + + V 2c o2( k 2 + k 2) = 0, where CO 2 = —— — - square of Brunt-Vaisaala frequency, к 2 + к 2 = к 2 — к 2 sin в , к = к C O S в , к - ® y J J х у л . Z wave number. 3 Расчет дисперсионных кривых МГВ The calculation of MGW dispersion curves according to dispersion equation (2) is made dimensionless quantities. Dimensionless frequency and wave number taken, as in [McLellan and Winterberg, 1968], in the form of 03 H og /. _ ® c W = — and К = — , where (Or = ———~— ттт and k„ 1 s Then the MGW equation in dimensionless variables takes form: W5+ AW*+BW2+CW2+DW + E = 0, (3) where J lK c o s e IK 2 1 V ^ R e / V e / R e / ’ В =?- ------ 2— K 2 - ( — + 1 )K 2 sin 2в - У- Р — К г cos2 в +i К cos в > 4 у p yP 2 p V2 с = - f 1K> a» e - ’ sn? ' K m e - , 4 ? - * i - y 'l2p R e m 4^2 Rem r ^ R e m 32Rem E = ( r ~ j ) r P K 3 s m 2 e c o s e + i ^ ^ K As \ n 2 e - i ^ ~ ^ J ^ K 2 s i n 2 e , v 2 R em ^R em 8Rem P = нг]%я ~ relation of gazokmetlc and magnetic Pressure R em = — ^2Ясг-, 0 _ angle between k and g , H 0 wave Note that the calculation of MGW dispersion curves according to equation (3) are valid only if the damping is small and propagating modes are considered. These conditions are satisfied for the height of 25o"km where we have accept the following ionospheric terms: 7’ = 103 K , / = 1 .4 , /? = 0 02 H = 3 •106cm 122