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KIAM Preprint  94, Moscow, 2021
Authors: Gavrikov M.B., Tayurskiy A.A.
Some mathematical questions of plasma ionization
Abstract:
A number of mathematical problems of the theory of ionization in relation to processes in stationary plasma thrusters (SPT) are solved in this work. Two main one-dimensional mathematical models of ionization are considered hydrodynamic and kinetic. The main question is the existence of ionization oscillations (breathing modes). On the basis of a hydrodynamic model, a boundary value problem for stationary ionization equations is solved. Its unique solvability and the absence of breathing modes are proved. In the case when the ion velocity in the flow region has a single zero with a positive derivative, it is proved that the stationary boundary value problem has a countable number of solutions, and a necessary and sufficient condition for the existence of breathing modes is formulated. Finally, an analytical solution of the ionization equations is given in the case of constant velocities of atoms and ions, and the formulas obtained are applied to the solution of the Cauchy problem, boundary value and mixed problems in the simplest regions. In the case of the kinetic model of ionization, the existence of breathing modes is numerically shown and the results obtained are compared with the hydrodynamic case.
Keywords:
ionization oscillations, breathing modes, characteristics
Publication language: russian,  pages: 48
Research direction:
Mathematical modelling in actual problems of science and technics
Russian source text:
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About authors:
  • Gavrikov Mikhail Borisovich,  orcid.org/0000-0001-7165-8318KIAM RAS
  • Tayurskiy Aleksei Aleksandrovich,  orcid.org/0000-0001-6027-5119KIAM RAS