The model of electrons dynamics in a discharge chamber of a high-frequency ion thruster

Thermal engines, electric propulsion and power plants for flying vehicles


Belousov A. P.*, Mel'nikov A. V.*, Khartov S. A.**

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



Fundamental research of the properties of high-frequency discharge is needed to improve the energy characteristics of high-frequency ion thrusters. And the development for this purpose a simplified physical model of the dynamics of electrons will allow us to quickly numerically estimate the most favorable conditions that ensure the efficient transfer of high-frequency field energy to electrons in the plasma.

Analysis of the characteristics of an inductive discharge in the gas-discharge chamber of a high-frequency ion thruster has allowed to determine the main dependences for finding the distribution of concentration and temperature of electrons along the radius of the ionizer.

The distribution of the concentration of electrons along the radius of the ionization chamber is determined by the distribution of the potential of plasma arising because more movable electrons leave the plasma volume faster than ions. Using the Harrison and Thompson solution for the flat approximation can be obtained the distribution of the potential of plasma. And, substituting this solution into the Boltzmann equation which connect the potential of plasma and the concentration of electrons, possible to calculate the distribution of concentration of electrons along the radius of the gas-discharge chamber.

The distribution of temperature of electrons, depends on the intensity of the vortex electric field in the volume of the discharge chamber. The induced electric fields are determined by the system of Maxwell’s equations. These fields can be calculated by the finite element method in the COMSOL Multiphysics program.

The comparison of the obtained numerical results with the experimental data is showed the possibility of using the proposed dependencies for a preliminary assessment of the local plasma parameters in a gas chamber of a high-frequency ion thruster.


high-frequency ion thruster, inductive discharge, distribution of electrons


  1. Hans J. Leiter, Horst W. Loeb, Karl-Heinz Schartner The RIT15 Ion Engines — A survey of the present state of Radio-Frequency Ion Thruster technology and its future potentiality // Spacecraft Propulsion, Third International Conference held 10-13 October, 2000 at Cannes, France. Edited by R.A. Harris. European Space Agency ESASP-465, 2001, pp. 423.

  2. Godyak V.A., Piejak R.B., Alexandrovich B.M. // Plasma Sources Sci.Technol. 2002. V. 11. P. 525.

  3. Godyak V.A., Alexandrovich B.M., Kolobov V.I. Lorentz force effects on the electron energy distribution in inductively coupled plasmas // Physical Review E 64, 026404 — Published 18 July 2001. URL:

  4. Valery Godyak Hot plasma effects in gas discharge plasma // Physics of Plasmas 12. 055501 — 2005. URL:

  5. Kudryavtsev A.A., Smirnov A.S., Tsendin L.D. Fizika tleyushchego razryada. (Physics of Glow Discharge), Saint Petersburg, Lan’, 2010, 512 p.

  6. Reed T.B. Induction-Coupled plasma torch. // Journal of Applied Physics; vol.32, No. 5, pp. 821-824, May 1961.

  7. Aleksandrov A.F., Vavilin K.V., Kral’kina E.A., Neklyudova P.A., Pavlov V.B. Prikladnaya fizika, 2013, no. 5, pp. 34-37.

  8. Aleksandrov A.F., Vavilin K.V., Kral’kina E.A., Neklyudova P.A., Pavlov V.B. Prikladnaya fizika, 2014, no. 1, pp. 9-11.

  9. Groh K.H. and Loeb H.W. State-of-the-Art of Radio-Frequency Ion Thrusters // Journal of Propulsion and Power, 1991, vol. 7, no. 4, pp. 573-579.

  10. Chabert C.P., Braithwaite N.St.J. Physics of Radio-Frequency Plasmas. Cambridge University Press, England, 2011, 385 p.

  11. Reed T.B. Induction-Coupled plasma torch // Journal of Applied Physics; vol.32, No. 5, May 1961. pp. 821-824.

  12. Gabovich M.D. Fizika i tekhnika plazmennykh istochnikov ionov (The Physics and Technology of Ion Sources), Moscow, Atomizdat, 1972, 304 p.

  13. Aleksandrov A.F., Vavilin K.V., Kral’kina E.A., Neklyudova P.A., Pavlov V.B., Tarakanov V.P. Prikladnaya fizika, 2013, no. 5, pp. 38-41/

  14. Forester A.T. Intensivnye ionnye puchki (Large Ion Beams), Moscow, Mir, 1991, 358 p.

  15. Kozhevnikov V.V., Khartov S.A.. XLI Akademicheskie chteniya po kosmonavtike. Tezisy dokladov, Moscow, 24–27 yanvarya 2017, pp. 76.

  16. Kanev S.V., Latyshev L.A., Nigmatzyanov V.V., Khartov S.A. Trudy MAI, 2012, no 52, available at:

  17. Kanev S.V. 15-ya Mezhdunarodnaya konferentsiya «Aviatsiya i kosmonavtika — 2016». Tezisy dokladov, Moscow, 14–18 noyabrya 2016, 2016, pp. 279-281.

  18. Aldonin F.I., Akhmetzhanov R.V. Trudy MAI, 2015, no 81, available at:

  19. Leb Kh.V., Popov G.A., Obukhov V.A., Feili D., Kollingvud Sh., Mogulkin A.I. Trudy MAI, 2012, no 60, available at:

Download — informational site MAI

Copyright © 2000-2024 by MAI