High precision methods for solving a system of cold plasma equations taking into account electron–ion collisions
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Eugene V. Chizhonkov
,
Mariya I. Delova
Abstract
High precision simulation algorithms are proposed and justified for modelling cold plasma oscillations taking into account electron–ion collisions in the non-relativistic case. The specific feature of the approach is the use of Lagrangian variables for approximate solution of the problem formulated initially in Eulerian variables. High accuracy is achieved both through the use of analytical solutions on trajectories of particles and due to sufficient smoothness of the solution in numerical integration of Cauchy problems. Numerical experiments clearly illustrate the obtained theoretical results. As a practical application, a simulation of the well-known breaking effect of multi-period relativistic oscillations is carried out. It is shown that with an increase in the collision coefficient one can observe that the breaking process slows down until it is completely eliminated.
Funding statement: The work was partially supported by the Moscow Center for Fundamental and Applied Mathematics.
References
[1] A. F. Aleksandrov, L. S. Bogdankevich, and A. A. Rukhadze, Principles of Plasma Electrodynamics. Springer, New York, 1984.10.1007/978-3-642-69247-5Suche in Google Scholar
[2] S. I. Braginskii, Transport phenomena in plasma. In: Problems of Plasma Theory. Gosatomizdat, Moscow, 1963, pp. 183–285 (in Russian).Suche in Google Scholar
[3] E. V. Chizhonkov, Mathematical Aspects of Modelling Oscillations and Wake Waves in Plasma. CRC Press, Boca Raton, 2019.10.1201/9780429288289Suche in Google Scholar
[4] C. M. Dafermos, Hyperbolic Conservation Laws in Continuum Physics. Springer, Berlin–Heidelberg, 2016.10.1007/978-3-662-49451-6Suche in Google Scholar
[5] R. C. Davidson, Methods in Nonlinear Plasma Theory. Acad. Press, New York, 1972.Suche in Google Scholar
[6] J. M. Dawson, Nonlinear electron oscillations in a cold plasma. Phys. Review 113 (1959), No. 2, 383–387.10.1103/PhysRev.113.383Suche in Google Scholar
[7] A. A. Frolov and E. V. Chizhonkov, Influence of electron collisions on the breaking of plasma oscillations. Plasma Physics Reports 44 (2018), No. 4, 398–404.10.1134/S1063780X18040049Suche in Google Scholar
[8] V. L. Ginsburg and A. A. Rukhadze, Waves in Magnetoactive Plasma. Nauka, Moscow, 1975 (in Russian).Suche in Google Scholar
[9] E. Infeld, G. Rowlands, and A. A. Skorupski, Analytically solvable model of nonlinear oscillations in a cold but viscous and resistive plasma. Phys. Rev. Lett. 102 (2009), 145005.10.1103/PhysRevLett.102.145005Suche in Google Scholar PubMed
[10] D. Kahaner, C. Moler, and S. Nash, Numerical Methods and Software. Prentice-Hall International, Inc., New Jersey, 1989.Suche in Google Scholar
[11] W. T. Reid, Riccati Differential Equations. Academic Press, New York, 1972.Suche in Google Scholar
[12] O. S. Rozanova and E. V. Chizhonkov, On the existence of a global solution of a hyperbolic problem. Doklady Math. 101 (2020), No. 3, 254–256.10.1134/S1064562420030163Suche in Google Scholar
[13] O. Rozanova, E. Chizhonkov, and M. Delova, Exact thresholds in the dynamics of cold plasma with electron–ion collisions. AIP Conf. Proc. 2302 (2020), No. 1, 060012.10.1063/5.0033619Suche in Google Scholar
[14] O. S. Rozanova and E. V. Chizhonkov, On the conditions for the breaking of oscillations in a cold plasma. Z. Angew. Math. Phys. 72 (2021), 13. doi: 10.1007/s00033-020-01440-3.10.1007/s00033-020-01440-3Suche in Google Scholar
[15] B. L. Rozhdestvenskii and N. N. Yanenko, Systems of Quasilinear Equations and Their Applications to Gas Dynamics. Amer. Math. Soc., 1983.Suche in Google Scholar
[16] M. H. Schultz, Spline Analysis. Prentice-Hall, Englewood Cliffs, New Jersey, 1973.Suche in Google Scholar
[17] C. J. R. Sheppard, Cylindrical lenses — focusing and imaging: a review. Applied Optics 52 (2013), No. 4, 538–545.10.1364/AO.52.000538Suche in Google Scholar PubMed
[18] V. P. Silin, Introduction to Kinetic Theory of Gases. Nauka, Moscow, 1971 (in Russian).Suche in Google Scholar
[19] V. P. Silin and A. A. Rukhadze, Electromagnetic Properties of Plasma and Plasma-Like Media. Librokom, Moscow, 2012 (in Russian).Suche in Google Scholar
[20] P. S. Verma, J. K. Soni, S. Segupta, and P. K. Kaw, Nonlinear oscillations in a cold dissipative plasma. Physics of Plasmas 17 (2010), 044503.10.1063/1.3389227Suche in Google Scholar
[21] Ya. B. Zeldovich and A. D. Myshkis, Elements of Mathematical Physics. Nauka, Moscow, 1973 (in Russian).Suche in Google Scholar
© 2021 Walter de Gruyter GmbH, Berlin/Boston
Artikel in diesem Heft
- Frontmatter
- Maximum cross section method in the filtering problem for continuous systems with Markovian switching
- High precision methods for solving a system of cold plasma equations taking into account electron–ion collisions
- A diffusion–convection problem with a fractional derivative along the trajectory of motion
- An implicit scheme for simulation of free surface non-Newtonian fluid flows on dynamically adapted grids
- Model reduction for Smoluchowski equations with particle transfer
Artikel in diesem Heft
- Frontmatter
- Maximum cross section method in the filtering problem for continuous systems with Markovian switching
- High precision methods for solving a system of cold plasma equations taking into account electron–ion collisions
- A diffusion–convection problem with a fractional derivative along the trajectory of motion
- An implicit scheme for simulation of free surface non-Newtonian fluid flows on dynamically adapted grids
- Model reduction for Smoluchowski equations with particle transfer
