Physics of auroral phenomena : proceedings of the 33rd Annual seminar, Apatity, 02 - 05 March, 2010 / [ed.: A.G. Yahnin, A. A. Mochalov]. - Апатиты : Издательство Кольского научного центра РАН, 2011. - 206 с. : ил.

Study of gamma-radiation connected to atmospheric precipitation d N ( h v , E ) = d a i h v ’E) d ( h v ) - N — dE d ( h v ) dE ( 2 ) where “gjft y>E) is differential bremsstrahlung cross section; N is density o f atoms of matter. d(hv) The total number of photons with energy hv in interval d(hv), produced by electrons with initial energy E0 are equal to (when E > hv): <#V(hv,E°) _ tda(hv,E) N ^ > d(hv) ■> d!U,A ( HF.\ (3) { h v ) dE] dx J For all electrons with energies 20keV < E < lOOkeV the value of ( - d E /d x ) in formula (3) will be dominated by ionization losses. The expression for them is [5]: _dE Л dx)„ 2ne N In E I V 2 -/ + 2 (4) Where / is ionization potential; z is average charge of the nucleus. For the air, 1 = 80.5 eV, z = 7.22. Integrating expression (3) over the electron spectrum, we have: dN( hv ) %dN(hv,E°) dNt d ( hv) - f d{hv) dE' f dE°= f ^jL dE °- f- 0 J HF° J \ d o ( h v , E ) N d ( hv ) ( - dE/dx ) dE - (5) For the differential cross section o f bremsstrahlung X-rays it was taken the expression [6]: Q(E,hv) = dcr{hv,E) _ 8 e2h ^ ,7 / d(hv) Ъл1т1съ hv \ - - 2 4 f V f - n , (6) where v , = az me zE = az me z ( E - h v ) 137 Substituting expressions (1), (4), (6) into (5) and calculating the integral, we obtain d N ( h v ) a spectrum d ( h v ) of photons for a given electron spectrum with an exponent E0. Expression (5) had been numerically integrated previously [1] and was taken as a first approximation to our data. On the results of calculations the empirical expression for the transition from the spectrum of photons to the spectrum of electrons was found [3]: fn dN(h v) I°g2- ■P- r , у ъ/ h v V ^ o J dNe dE (7) d ( hv ) where a = 1.63 , p - 3.48 • IO-4 . This expression in the energy range 20-500 keV coincides with the results of calculations within 10%. 20 n 10 o- -10 X-Rays Precipitation*j -20 67,00 67,25 68,00 67,50 67,75 Days of Year Fig.3. X-ray increase and precipitations (rain) in the event of March 8, 2010, Apatity E, keV Fig-4. The spectra of photons and electrons in the event of March 8, 2010 With this expression the electron spectrum from the measured photon spectrum can be calculated. The profile of the increase registered on March 8, 2010, is shown in Figure 3. The measured spectrum of photons and calculated from it using (7) the electron spectrum are shown in Figure 4. It should be noted that the above consideration does not take into account effects of absorption in the air of both electrons and produced by them X-ray photons. Due to the strong absorption of electrons with energies 165