__Keywords:__space vehicles plasma dynamics radio wave propagation

B.S. Borisov, F.F. Gabdullin, V.I. Garkusha, A.G. Korsun, M.Yu. Kurshakov, V.A. Strashinskiy, E.M. Tverdokhlebova, V.V. Khakhinov

Mathematical models developed at TsNIIMash describe artificial plasma formations (APF), in particular plasma plumes and the shape of the exhaust of electric propulsion engines. The models take into account how the characteristics of the APF are affected by own electric fields and currents, by the geomagnetic field, by high-energy ionospheric fluxes, and also by conductive parts of the spacecraft or the bench and gas-plasma environment. These models are based on self-similar solutions of the Braginsky equations for entirely ionized plasma. The models describe how the above factors affect the pattern of fluxes in plasma plumes and clouds existing around a spacecraft. The internal electric field enhances transversal fluxes as a plasma body expands into the space vacuum. The geomagnetic field B impedes plasma expansion in the direction normal to the induction vector B. As a result, needle- and petal-shaped APF with specific radiophysical characteristics emerge in the vicinity of the spacecraft. The computations are consistent with the data of both bench and space experiments. The mathematical models for APF and the corresponding computer programs help, first, to assess and predict the effect of gas-plasma environment of a spacecraft on sensitive onboard equipment and, second, to parry hazardous effects already when designing spacecrafts powered by electric propulsion engines.
To describe the radiophysical characteristics of APF in space the ray approximation was used. The calculation results are in good agreement with flight data of several space experiments. These results confirm that plasma plumes and clouds transformed in space under influence of the Earth magnetic field into needle- and petal-shaped APF. The radiophysical characteristics of such APF depend on the angle between the direction of incidence and the vector of geomagnetic induction.
The scattering of radio waves on relatively dense APF, the electron density in which is higher than critical for probe signal, is characterized by the anisotropy, so the values of effective echoing area are varied in a large range. Large zones of radio shadow are formed behind APF. There is the gradient of electron density in APF, so these plasma formations can be considered as plane-layered medium in solving problems of APF impact on radio waves propagation.
The carried out experiments demonstrate that the engagement of standard rather than special equipment, both onboard and earth-based, makes the experiment cheaper and quickens its preparations. Therefore, analyzing the technical capability of spacecraft standard equipment and corresponding earth-based facilities should be an obligatory stage in the planning of any space project.

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