Abstract
For the Vlasov equation with a self-consistent field, a connection is established between the dispersion relation and the Schur algebraic complement of the generator of the corresponding dynamical system. An estimate of the instability index is obtained in terms of the Hankel transform of the background distribution of electrons, the sign of which is determined using the saddle point method.
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The authors are grateful to the referee for the suggestions for improving the presentation and bibliography comments.
Funding
The research was supported by the Russian Foundation for Basic Research (project No. 19-01-00474).
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Translated from Teoreticheskaya i Matematicheskaya Fizika, 2022, Vol. 210, pp. 442-454 https://doi.org/10.4213/tmf10175.
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Stepin, S.A., Tarasov, A.G. Dispersion relation in the kinetic model of collisionless plasma. Theor Math Phys 210, 386–397 (2022). https://doi.org/10.1134/S0040577922030096
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DOI: https://doi.org/10.1134/S0040577922030096