Analysis o fdispersion equationsfor magnetogravity waves in realistic ionosphere Calculations of dispersion curves are executed for such H0= 0.5 G , cr = 1010 c'1 and Re = 3 1 0 2 u tn parameters, which are close to reality. In the weak absorption and executing limitation on the TID scales (the vertical wavelength Я, is much smaller 1 ) the dispersion MGW equation (2) becomes than 4яН к, D 2 H (4) (*? + П )(*?+*?)+ V W k \ (*? + k \ )+ - 0. Figure 1 (a) presents a complete solution of the dispersion equation (3), and Fig. 1 (b) shows the dispersion curves for the short-cut equation (4) in dimensionless variables for MGW propagating fa st"+" mode and slow mode. Here solid line corresponds to longitudinal propagation (0 = 0 °), small dotted line - propagation at an angle (0 = 45 °), large dotted line - transverse propagation (0 = 90 °) of MGW. Dispersion curves are not shown in Fig. 1 (a) are outside the considered frequency range. Dependent (Figure 1 (b)) on the propagation angle for a fast "+" mode is absent, a) Fast"+" mode Slow mode Fast "+■• mode Slow mode Fig. 1. The dispersion curves for MGW propagating fa s t"+" mode and slow mode in dimensionless variables obtained for (a) of the complete dispersion equation (3) and (b) the short-cut equation (4): solid line corresponds to the longitudinal propagation (0 = 0 °), fine dotted line - the propagation at an angle (0 = 45 °), large dotted line - the transverse propagation (0 = 90 °) of MGW 4 Experimental data analysis In our study it suggested that MGW excited during substorms by auroral source namely the eastward electrojet and propagate along the geomagnetic meridian to the mid-latitudes. Search of such MGW based on comparative spectral analysis o f index AU fluctuations, variations of ionospheric layer F2 critical frequencies at vertical sounding stations and variations of geomagnetic field horizontal component on daily intervals in March-April 2006 was carried. Ionospheric and magnetic stations whose data selected for analysis are presented in Table 1. Table 1. Ionospheric and magnetic stations Stations abbreviation Geogr. latitude Geogr. longitude Geom. latitude Geom. longitude L (Mcllwain parameter) L Aquila AQU 42.38 13.32 58.7 1.9 1.5 Furstenfeldbruck FUR 48.17 11.28 64.2 1.6 1.9 HEL HLP 54.61 18.82 69.5 4.0 2.5 Lvov L W 49.9 23.75 66.3 4.7 2.05 Juliusruh/Rugen JR055 54.6 13.4 69.3 2.2 2.5 San Vito VT139 40.6 17.8 57.0 2.7 1.47 Figure 2 shows examples o f agreed dynamic spectra of index AU, ionospheric and magnetic disturbances for 4 and 5 April 2006. The coincidence of spectral features in dynamic spectra indicates the propagation of density and magnetic field disturbances from auroral source to middle latitudes. Analysis of these spectra dynamics (Fig. 4) shows the practically absence of the time shift between them. This indicates the higher MGW velocities compared with classical internal gravity waves. The characteristic MGW frequencies estimated from the spectrograms are in the range 10 —4 • 10 Hz. Such frequencies correspond to the values of the phase velocity "+" mode about 4000 m/s, mode - about 3000 m/s. Figure 3 shows the calculated phase velocities of the MGW fa st"+" mode and slow mode in this wavelength range. 123

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