Skip to main content
SpringerLink
Log in

Hybrid Model of a Stationary Plasma Thruster Taking into Account the Finite Electron Mass

  • Published:
Mathematical Models and Computer Simulations Aims and scope

Abstract

A mathematical model is proposed for studying the processes in a stationary plasma thruster (SPT), taking into account the ionization of the working substance, xenon, based on the hybrid equations of electromagnetic hydrodynamics (EMHD) of the plasma, which fully take into account the inertia of electrons. The choice of an EMHD model for studying plasma processes is predetermined by their small scale and low concentration of plasma particles in an SPT. The 1D2V case of plane symmetry is considered in detail, for which a numerical algorithm for studying solutions of hybrid equations of EMHD equations based on the method of macroparticles is constructed. A number of fundamental questions are solved: calculation of average values, interpolation, construction of the initial distribution of macroparticles, the choice of boundary conditions for the electric field, etc. The results of calculations with and without allowance for induction fields in a plasma thruster are presented. The effect of induction fields generated by plasma currents on processes in an SPT and the role of electron inertia have not been studied before, and the results obtained are original. In particular, a new nontraditional scheme for calculating the electric field based on the generalized Ohm’s law is proposed, which in EMHD is reduced to a boundary value problem for an elliptic system of equations for the components of the electric field and, among other things, requires setting boundary conditions. The need for the spatial and temporal averaging of electromagnetic fields when calculating the acceleration of the thruster plasma, taking into account the induction field, is an important result.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1.
Fig. 2.
Fig. 3.
Fig. 4.
Fig. 5.

Similar content being viewed by others

REFERENCES

  1. K. N. Kozubskii, V. M. Murashko, Yu. P. Rylov, Yu. V. Trifonov, V. P. Khodnenko, V. Kim, G. A. Popov, and V. A. Obukhov, “Stationary plasma thrusters operate in space,” Plasma Phys. Rep. 29 (3), 251–266 (2003). https://doi.org/10.1134/1.1561120

    Article  Google Scholar 

  2. V. Kim, K. N. Kozubsky, V. M. Murashko, and A. V. Semenkin, “History of the Hall Thrusters development in USSR,” in 30th International Electric Propulsion Conference, Florence, Italy, September 17–20, 2007, Paper IEPC-2007-142.

  3. V. P. Kim, A. V. Semenkin, and S. A. Khartov, Design and Physical Features of Engines with Closed Electron Drift (Mosk. Aviats. Inst., Moscow, 2016) [in Russian].

  4. A. I. Morozov, Introduction to Plasmadynamics (Fizmatlit, Moscow, 2006) [in Russian].

    Google Scholar 

  5. O. A. Mitrofanova, R. Yu. Gnizdor, V. M. Murashko, A. I. Koryakin, and A.N. Nesterenko, “New Generation of SPT-100,” in 32nd International Electric Propulsion Conference, Wiesbaden, Germany, September 11–15, 2011, Paper IEPC-2011-041.

  6. L. Garrigues, A. Héron, J. C. Adam, and J.-P. Boeuf, “Hybrid and particle-in-cell models of a stationary plasma thruster,” Plasma Sources Sci. Technol. 9 (2), 219–226 (2000). https://doi.org/10.1088/0963-0252/9/2/316

    Article  Google Scholar 

  7. A. A. Bykov, V. Yu. Popov, A. G. Sveshnikov, and S. A. Yakunin, “Inner transitional layers for potential in a strongly magnetized plasma,” Mat. Model. 1 (6), 33–47 (1989).

    MathSciNet  MATH  Google Scholar 

  8. A. I. Morozov and V. V. Savelyev, “Fundamentals of stationary plasma thruster theory,” in Reviews of Plasma Physics, Ser. Reviews of Plasma Physics, 21 (Springer, Boston, MA, 2000), pp. 203–391. https://doi.org/10.1007/978-1-4615-4309-1_2

  9. B. I. Volkov and S. A. Yakunin, Mathematical Problems of Plasma Optics, Nov. Zhizni, Nauke, Tekh., Ser.: Mat., Kibern., No. 11 (Znanie, Moscow, 1982).

  10. G. I. Budker, Collection of Works (Nauka, Moscow, 1982) [in Russian].

    Google Scholar 

  11. A. I. Morozov and L. S. Solov’ev, “Steady-state plasma flow in a magnetic field,” in Reviews of Plasma Physics, Ed. by M. A. Leontovich, Ser. Reviews of Plasma Physics (Springer, Boston, MA, 1980), Vol. 8, pp. 1–103. https://doi.org/10.1007/978-1-4615-7814-7_1

  12. M. B. Gavrikov, Two-Fluid Electromagnetic Hydrodynamics (KRASAND, Moscow, 2018) [in Russian].

    Google Scholar 

  13. V. A. Vshivkov, G. I. Dudnikova, Yu. P. Zakharov, and A. M. Orishich, Generation of Plasma Perturbations under Collisionless Interaction of Plasma Flows (Inst. Teor. Prikl. Mekh., Sib. Otd., Akad. Nauk SSSR, Novosibirsk, 1987), preprint No. 20-87 [in Russian].

  14. L. Vshivkova, G. Dudnikova, and K. Vshivkov, “Hybrid numerical model of shock waves in collisionless plasma,” AIP Conf. Proc. 1773 (1), 110017 (2016). https://doi.org/10.1063/1.4965021

    Article  Google Scholar 

  15. L. Spitzer, Physics of Fully Ionized Gases, 2nd ed. (Interscience, New York, 1962, Mir, Moscow, 1965).

  16. V. S. Imshennik, “On the thermal conductivity of plasma,” Sov. Astron. 5 (4), 495–497 (1962).

    Google Scholar 

  17. S. Chapman and T. G. Cowling, The Mathematical Theory of Non-Uniform Gases (Cambridge University Press, Cambridge, 1952; Inostr. Lit., Moscow, 1960).

  18. L. D. Landau, “The kinetic equation in the case of Coulomb interaction,” Zh. Eksp. Teor. Fiz. 7 (2), 203–209 (1937).

    MATH  Google Scholar 

  19. J.-P. Boeuf, “Tutorial: Physics and modeling of Hall thrusters,” J. Appl. Phys. 121 (1), 011101 (2017). https://doi.org/10.1063/1.4972269

    Article  Google Scholar 

  20. A. I. Morozov, “Wall conduction in a highly magnetized plasma,” J. Appl. Mech. Tech. Phys. 9 (3), 249–251 (1968).

    Article  Google Scholar 

  21. Yu. S. Sigov, Computational Experiment: A Bridge between the Past and the Future of Plasma Physics. Selected Works, Compiled by G. I. Zmievskaia and V. D. Levchenko (Fizmatlit, Moscow, 2001 [in Russian].

  22. Yu. A. Berezin and V. A. Vshivkov, Particle Method in Rarefied Plasma Dynamics (Nauka, Novosibirsk, 1980) [in Russian].

    Google Scholar 

  23. R. W. Hockney and J. W. Eastwood, Computer Simulation Using Particles (McGraw-Hill, New York, 1981; Mir, Moscow, 1987).

  24. C. K. Birdsall and A. B. Langdon, Plasma Physics via Computer Simulation (McGraw-Hill, New York, 1985; E-nergoatomizdat, Moscow, 1989).

  25. A. A. Arsen’ev, Lectures on Kinetic Equations (Nauka, Moscow, 1992) [in Russian].

    MATH  Google Scholar 

  26. M. B. Gavrikov and A. A. Taiurskii, “Hybrid model of a stationary plasma thruster,” KIAM Preprint No. 35 (Keldysh Inst. Appl. Math. Russ. Acad. Sci., Moscow, 2021) [in Russian]. https://doi.org/10.20948/prepr-2021-35

    Book  Google Scholar 

  27. H. A. Lorentz, De Theorie van Maxwell (1900–1902) (Brill, Leiden, 1925); Electromagnetic Field Theory (ONTI, Moscow, 1933) [in Russian].

Download references

Author information

Authors and Affiliations

  1. Keldysh Institute of Applied Mathematics, Russian Academy of Sciences, Moscow, Russia

    M. B. Gavrikov & A. A. Taiurskii

Authors
  1. M. B. Gavrikov
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. A. A. Taiurskii
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding authors

Correspondence to M. B. Gavrikov or A. A. Taiurskii.

Ethics declarations

The authors declare that they have no conflicts of interest.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Gavrikov, M.B., Taiurskii, A.A. Hybrid Model of a Stationary Plasma Thruster Taking into Account the Finite Electron Mass. Math Models Comput Simul 14, 1021–1031 (2022). https://doi.org/10.1134/S2070048222060060

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S2070048222060060

Keywords:

Search

Navigation