Geodesic
Numeric method for evaluation of parameters of high-intensive soft-X-ray radiation propagated in nonhomogeneous rarefied atmosphere
Matematičeskoe modelirovanie, Tome 7 (1995) no. 1, pp. 22-34.

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The physical and mathematical models of high-intensive soft-X-ray pulse propagation in high layers of atmosphere including nonlinear effects of air medium transparensation are suggested. Atoms concentration is supposed to be small and the pulse is supposed to be short enough to neglect the processes of recombination and electron impact ionization during radiation exposure at absorbing ions. Energy and time-form variations of the sufficiently high-intensive pulse may be described with simple analytic expressions. The estimations of applicability limits of these expressions are represented. The investigations of air transparensation influence on radiation propagation distance and pulse time-form for different radiation characteristics and problem geometry are carried out with the help of created mathematical apparatus. The results of these investigations allows to estimate radiation parameters, that make possible a break of atmosphere layer in result of full ionization of air atoms on the way of pulse propagation. 
@article{MM_1995_7_1_a2,
     author = {I. A. Volkov and A. V. Ostrik and S. V. Rybakov},
     title = {Numeric method for evaluation of parameters of high-intensive {soft-X-ray} radiation propagated in nonhomogeneous rarefied atmosphere},
     journal = {Matemati\v{c}eskoe modelirovanie},
     pages = {22--34},
     publisher = {mathdoc},
     volume = {7},
     number = {1},
     year = {1995},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MM_1995_7_1_a2/}
}
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I. A. Volkov; A. V. Ostrik; S. V. Rybakov. Numeric method for evaluation of parameters of high-intensive soft-X-ray radiation propagated in nonhomogeneous rarefied atmosphere. Matematičeskoe modelirovanie, Tome 7 (1995) no. 1, pp. 22-34. http://geodesic.mathdoc.fr/item/MM_1995_7_1_a2/