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Abstract <p>For the kinetic plasma model based on the relativistic Vlasov–Ampère equations, the implicit MacCormack-type scheme is constructed. Compared to the explicit scheme, it has a weaker stability constraint, but retains the same computational efficiency; i.e., it does not use internal iterations. In this case, the error in the total energy corresponds to the second order of accuracy of the algorithm, and the total charge (number of particles) is preserved at the grid level. The formation of plasma waves excited by a short powerful laser pulse is considered as the simulated physical process. For a weakly relativistic initial distribution function, a scaling of the problem is proposed that allows numerical analysis of the perturbation parameters in a wide range.</p>

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On the Numerical Solution of Relativistic Vlasov–Ampère Equations

  • 期刊论文

  • 发表日期：

    2025年10月21日

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  • A. A. Frolov,
  • E. V. Chizhonkov

摘要

Abstract

For the kinetic plasma model based on the relativistic Vlasov–Ampère equations, the implicit MacCormack-type scheme is constructed. Compared to the explicit scheme, it has a weaker stability constraint, but retains the same computational efficiency; i.e., it does not use internal iterations. In this case, the error in the total energy corresponds to the second order of accuracy of the algorithm, and the total charge (number of particles) is preserved at the grid level. The formation of plasma waves excited by a short powerful laser pulse is considered as the simulated physical process. For a weakly relativistic initial distribution function, a scaling of the problem is proposed that allows numerical analysis of the perturbation parameters in a wide range.