Mathematical modeling turning of a plasma stream expiring from the plasma thruster, in cross magnetic field

Propulsion and Power Plants


Kotel'nikov V. A.*, Kotelnikov M. V.*, Morozov A. V.**

Moscow Aviation Institute (National Research University), 4, Volokolamskoe shosse, Moscow, А-80, GSP-3, 125993, Russia



Research of turning plasma stream, expiring from electric propulsion, by cross magnetic field is discussed. The geometrical shape of a nozzle looks like an elongated rectangle. Thus the task in a phase space is four-dimensional, nonstationary and can be solved with use of mean power desktop computers.
The mathematical model of a task corresponding to this physical model, includes the kinetic equations for ions and electrons (Vlasov equation) which are supplemented with a Poissons equation for a self-consistent electric field. The set of equations of Vlasov Poisson given to the dimensionless type was solved by method of serial iterations on time.
For the numerical solution of the Vlasov kinetic equations the explicit scheme of Yu.M. Davidov method of large particle was used combined with a method of matrix prorace for solution of a Poisson equation on each time layer. The error of the chosen method of solution does not exceed several percent.
Process model operation consisted of two stages. At the first stage it was simulated the kinetics of the stream which at the second stage got to a transversal magnetic field. The developed program code and the made numerous computing experiments allowed:
  • to reveal conditions, at which effective management direction of the electric propulsions thrust vector is possible;
  • to investigate evolution of a cumulative distribution function of ions and electrons in a plasma stream in the course of its interaction with a transversal magnetic field;
  • to investigate profiles of ions and electrons concentrations, and also potential contour lines;
The developed software allows you to get recommendations for the design of control systems with electromagnetic methods of electric propulsion thrust vector control.
As a result of modeling, the cumulative distribution functions of the charged particles, fields of speeds, concentration of self-consistent electric fields in a plasma stream, depending on the parameters of a task (such as induction of a magnetic field; plasma flow rate on a nozzle cut; concentration of the charged particles; geometrical sizes of a nozzle; relations of temperatures of ions and electrons) were received.


a stream of rarefied plasma, a stationary plasma, magnetic field, the equations of VlasovPuasson, a method of large particles, a distribution function of charged particles


  1. Kubarev Yu.V. Nauka i tekhnologii v promyshlennosti, 2006, no. 2, pp. 19-35.
  2. Kotelnikov M.V., Gidaspov V.Yu., Kotelnikov V.A. Matematicheskoe modelirovanie obtekaniya tel potokami besstolknovitelnoi i stolknovitelnoi plazmy (Mathematical modeling of a flow of bodies by streams of collisionless and stolknovitelny plasma), Moscow, Fizmatlit, 2010, 288 p.
  3. Kotelnikov V.A., Uldanov S.V., Kotelnikov M.V. Protsessy perenosa v pristenochnykh sloyakh plazmy (Transfer processes in the wall surface layer of plasma), Moscow, Nauka, 2004, 422 p.
  4. Belotserkovskii O.M., Davydov Yu.M. Metody krupnykh chastits v gazovoi dinamike (Methods of large particles in gas dynamics), Moscow, Nauka, 1982, 392 p.
  5. Kotelnikov M.V., Morozov A.V. Materialy XVII mezhdunarodnoi konferentsii po vychislitelnoi mekhanike i sovremennym prikladnym sistemam, Alushta, 2011, pp. 562-563 (830 p.).
  6. Kotelnikov M.V., Morozov A.V. Sbornik tezisov «10-ya Mezhdunarodnaya konferentsiya «Aviatsiya i kosmonavtika 2011», Moscow, pp. 167-168 (326 p.). — informational site of MAI

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