Analytical Solution of Mixed Problems for the One-Dimensional Ionization Equations in the Case of Constant Velocities of Atoms and Ions

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Abstract

We consider the main initial–boundary value (mixed) problems for the nonlinear system of one-dimensional gas ionization equations in the case of constant velocities of gas atoms and ions resulting from ionization. The atom and ion concentrations are the unknowns in this system. We find a general formula for a sufficiently smooth solution of the system. It is shown that mixed problems for the system of one-dimensional ionization equations admit integration in closed-form analytical expressions. In the case of a mixed problem for a finite interval, the analytical solution is constructed using recurrence formulas each of which is defined in a triangle belonging to some triangulation, specified in the paper, of the domain where the unknown functions are defined.

About the authors

M. B Gavrikov

Keldysh Institute of Applied Mathematics, Moscow, 125047, Russia

Email: mbgavrikov@yandex.ru
Москва, Россия

A. A Tayurskiy

Keldysh Institute of Applied Mathematics, Moscow, 125047, Russia; Bauman Moscow State Technical University, Moscow, 105005, Russia

Author for correspondence.
Email: tayurskiy2001@mail.ru
Москва, Россия

References

  1. Морозов А.И. Введение в плазмодинамику. М., 2006.
  2. Baranov V.I., Nazarenko Y.S., Petrosov V.A., Vasin A.I., Yashnov Y.M. Theory of oscillations and conductivity for Hall thrusters // 32nd Joint Propulsion Conf. 1996. AIAA 96-3192.
  3. Рождественский Б.Л., Яненко Н.Н. Системы квазилинейных уравнений и их приложения к газовой динамике. М., 1978.
  4. Тихонов А.Н., Самарский А.А. Уравнения математической физики. М., 1977.
  5. Бишаев A.M., Ким В. Исследование локальных параметров плазмы в ускорителе с замкнутым дрейфом электронов и протяжённой зоной ускорения // Журн. техн. физики. 1978. Т. 48. № 9. С. 1853-1857.
  6. Chapurin O., Smolyakov A.I., Hagelaar G., Raitses Y. On the mechanism of ionization oscillations in Hall thrusters // J. Appl. Phys. 2021. V. 129. P. 233307.
  7. Гавриков М.Б., Таюрский А.А. Некоторые математические вопросы ионизации плазмы // Препринты ИПМ им. М.В. Келдыша. 2021. № 94.
  8. Гавриков М.Б., Таюрский А.А. Стационарные и осциллирующие решения уравнений ионизации // Журн. вычислит. математики и мат. физики. 2022. Т. 62. № 7. С. 1158-1179.
  9. Fife J., Martinez-Sanchez M., Szabo J. A numerical study of low-frequency discharge oscillations in Hall thrusters // 33rd Joint Propulsion Conf. 1997. AIAA 97-3052.
  10. Barral S., Ahedo E. On the origin of low frequency oscillations in Hall thrusters // AIP Conf. Proc. 2008. V. 993. P. 439-442.
  11. Dale E., Jorns B. Two-zone Hall thruster breathing mode mechanism. Part I: Theory // 36th Intern. Electric Propulsion Conf. Vienna, 2019.
  12. Boeuf J., Garrigues L. Low frequency oscillations in a stationary plasma thruster // J. Appl. Phys. 1998. V. 84. P. 3541-3554.
  13. Гавриков М.Б., Таюрский А.А. Аналитическое решение смешанных задач для уравнений одномерной ионизации в случае постоянных скоростей атомов и ионов // Препринты ИПМ им. М.В. Келдыша. 2023. № 30.

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