Hybrid model of a stationary plasma thruster taking into account the final electron mass

M. B. Gavrikov ; A. A. Taiurskii

Matematičeskoe modelirovanie, Tome 34 (2022) no. 5, pp. 105-122.

Résumé

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 of the plasma, which fully take into account the inertia of electrons. The choice of an electromagnetic hydrodynamics model for studying plasma processes is predetermined by their small scale and low concentration of plasma particles in a stationary plasma thruster. The 1D2V case of plane symmetry is considered in detail, for which a numerical algorithm for investigating solutions of hybrid electromagnetic hydrodynamics equations is constructed, based on the method of macroparticles. The solution of a number of fundamental issues is given: the 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 taking into account the induction fields in the plasma thruster are presented. The effect of induction fields generated by plasma currents on processes in a stationary plasma thruster and the role of electron inertia have not been studied before, and the results obtained are original. In particular, a new unconventional scheme for calculating the electric field based on the generalized Ohm's law is proposed, which in electromagnetic hydrodynamics 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. An important result is the need for spatial and temporal averaging of electromagnetic fields when calculating the acceleration of the thruster plasma, taking into account the induction field.

Détail

Keywords: stationary plasma thruster (SPT), hybrid electromagnetic hydrodynamics (EMHD), macroparticle method, generalized Ohm's law, plasma ionization, kinetic equations, equation of characteristics.

Bibliographie

[1] K. N. Kozubsky, V. M. Murashko, V. P. Rylov, Yu. V. Trifonov, V. P. Khodenko, V. P. Kim, G. A. Popov, V. A. Obukhov, “SPD rabotaet v kosmose”, Fizika plazmy, 29:3 (2003), 277–792

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

[3] V. P. Kim, A. V. Semenkin, S. A. Khartov, Konstruktivnye i fizicheskie osobennosti dvigatelei s zamknutym dreifom elektronov, Izd-vo MAI, M., 2016, 160 pp.

[4] A. I. Morozov, Vvedenie v plazmodinamiku, Fizmatlit, M., 2006, 576 pp.

[5] O. A. Mitrofanova, R. Yu. Gnizdor, V. M. Murashko, A. I. Koryakin, A. N. Nesterenko, “New Generation of SPT-100”, 32nd International Electric Propulsion Conference (September 11-15, 2011, Wiesbaden, Germany), IEPC-2011-041, 7 pp.

[6] L. Garrigues, A. H-ron, J. C. Adam, J. P. Boeuf, “Hybrid and Particle-In-Cell Models of a Stationary Plasma Thruster”, Plasma Source Sci. Technol., 2000, no. 9, 219–226 | DOI

[7] A. A. Bykov, V. Iu. Popov, A. G. Sveshnikov, S. A. Iakunin, “Vnutrennie perekhodnye sloi potentsiala v silno zamagnichennoi plazme”, Matematicheskoe modelirovanie, 1:6 (1989), 33–47 | Zbl

[8] A. I. Morozov, V. V. Savelyev, “Fundamentals of Stationary Plasma Thruster Theory”, Reviews of Plasma Physics, 21 (2000), 203–391 | DOI

[9] B. I. Volkov, S. A. Iakunin, Matematicheskie zadachi plazmooptiki, Novoe v zhizni, nauke I tekhnike. Ser. “Matematika, kibernetika”, 11, Znanie, M., 1982, 64 pp.

[10] G. I. Budker, Sobranie trudov, Nauka, M., 1982, 576 pp.

[11] A. I. Morozov, L. S. Solov'ev, “Steady-state plasma flow in a magnetic field”, Rev. Plasma Phys., 8, ed. M.A. Leontovich, 1980, 1–104

[12] M. B. Gavrikov, Dvukhzhidkostnaia elektromagnitnaia gidrodinamika, KRASAND, M., 2018, 584 pp.

[13] V. A. Vshivkov, G. I. Dudnikova, Iu. P. Zakharov, A. M. Orishich, Generatsiia plazmennykh vozmushchenii pri besstolknovitelnom vzimodeistvii plazmennykh potokov, preprint 20-87, ITPM SO AN SSSR, Novosibirsk, 1987, 48 pp.

[14] L. Vshivkova, G. Dudnikova, K. Vshivkov, “Hybrid Numerical Model of Shock Waves in Collisionless Plasma”, Proc. AIP Conf., 1773 (2016), 110017 | DOI

[15] L. Spitzer, Physics of Fully Ionized Gases, 2nd ed, Interscience, New York, 1962, 170 pp. | MR

[16] V. S. Imshennik, “O teploprovodnosti plazmy”, Astronomicheskii Zhurnal, 38:4 (1961), 652–655

[17] S. Chapman, T. G. Cowling, The Mathematical Theory of Non-uniform Gase, Cambridge University Press, 1952 | MR | MR

[18] L. D. Landau, “Kineticheskoe uravnenie v sluchae kulonovskogo vzaimodeistviia”, JETF, 7:2 (1937), 203–209 | Zbl

[19] J. P. Boeuf, “Tutorial: Physics and modeling of Hall thrusters”, Journal of Applied Physics, 121 (2017), 011101 | DOI

[20] A. I. Morozov, “Effect pristenochnoi provodimosti v khorosho zamagnichennoi plazme”, PMTF, 1968, no. 3, 19–23

[21] Iu. S. Sigov, Vuchislitelnyi eksperiment: most mezhdu proshlym i budushchim fiziki plazmy. Izbrannye trudy, Sost. G.I. Zmievskaia, V.D. Levchenko, Fizmatlit, M., 2001, 288 pp.

[22] Iu. A. Berezin, V. A. Vshivkov, Metod chastits v dinamike razriazhennoi plazmy, Nauka, Novosibirsk, 1980, 95 pp. | MR

[23] R.W. Hockney, J.W. Eastwood, Computer simulation using particles, McGraw-Hill, NY, 1981, 640 pp.

[24] C. K. Birdsall, A. B. Langdon, Plasma Physics via Computer Simulation, McGraw-Hill, NY, 1985

[25] A. A. Arsen'ev, Lektsii o kineticheskikh uravneniiakh, Nauka, M., 1992, 216 pp.

[26] M. B. Gavrikov, A. A. Taiurskii, “Gibridnaia model statsionarnogo plazmennogo dvigatelia”, Keldysh Institute preprints, 2021, 035, 48 pp.

[27] H. A. Lorentz, De theorie van Maxwell (1900–1902), Brill, Leiden, 1925