A time-implicit numerical method and benchmarks for the relativistic Vlasov–Ampere equations

Carrie, Michael; Shadwick, B. A.

doi:10.1063/1.4938035

Cited by 3 publications

(1 citation statement)

References 41 publications

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“…The exact conservation of enstrophy guarantees nonlinear numerical stability. The split form of this algorithm has been extended to the relativistic Vlasov–Poisson system (Carrié & Shadwick 2016), yielding identical conservation and stability properties.…”

Section: Discussionmentioning

confidence: 99%

An unconditionally stable, time-implicit algorithm for solving the one-dimensional Vlasov–Poisson system

Carrie

Shadwick

2022

J. Plasma Phys.

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The development of an implicit, unconditionally stable, numerical method for solving the Vlasov–Poisson system in one dimension using a phase-space grid is presented. The algorithm uses the Crank–Nicolson discretization scheme and operator splitting allowing for direct solution of the finite difference equations. This method exactly conserves particle number, enstrophy and momentum. A variant of the algorithm which does not use splitting also exactly conserves energy but requires the use of iterative solvers. This algorithm has no dissipation and thus fine-scale variations can lead to oscillations and the production of negative values of the distribution function. We find that overall, the effects of negative values of the distribution function are relatively benign. We consider a variety of test cases that have been used extensively in the literature where numerical results can be compared with analytical solutions or growth rates. We examine higher-order differencing and construct higher-order temporal updates using standard composition methods.

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Section: Discussionmentioning

confidence: 99%

An unconditionally stable, time-implicit algorithm for solving the one-dimensional Vlasov–Poisson system

Carrie

Shadwick

2022

J. Plasma Phys.

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Transition from convective to absolute Raman instability via the longitudinal relativistic effect by using Vlasov-Maxwell simulations

et al. 2018

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The longitudinal relativistic effect on stimulated Raman backscattering (SRBS) is investigated by using one-dimensional (1D) Vlasov-Maxwell simulations. Using a short backscattered light seed pulse with a very small amplitude, the linear gain spectra of SRBS in the strongly convective regime is presented by combining the relativistic and non-relativistic 1D Vlasov-Maxwell simulations, which is in agreement with the steady-state linear theory. More interestingly, by considering transition from convective to absolute instability due to electron trapping, we successfully predict the critical duration of the seed which can just trigger the kinetic inflation of the excited SRBS after the seed leaves the simulation box. The critical duration in the relativistic case is much shorter than that in the nonrelativistic case, which indicates that the kinetic inflation more easily occurs in the relativistic case than in the nonrelativistic case. In the weakly convective regime, the transition from convective to absolute instability for SRBS can directly occur in the linear regime due to the longitudinal relativistic modification. For the same pump, our simulations first demonstrate that the SRBS excited by a short and small seed pulse is a convective instability in the nonrelativistic case but becomes an absolute instability due to the decrease of the linear Landau damping from the longitudinal relativistic modification in the relativistic case. In more detail, the growth rate of the backscattered light is also in excellent agreement with theoretical prediction.

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Eulerian Finite-Difference Vlasov Solver with a Non-Uniform Momentum Grid

Shadwick,

Hesse

2023

2023 IEEE International Conference on Plasma Science (ICOPS)

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A time-implicit numerical method and benchmarks for the relativistic Vlasov–Ampere equations

Cited by 3 publications

References 41 publications

An unconditionally stable, time-implicit algorithm for solving the one-dimensional Vlasov–Poisson system

An unconditionally stable, time-implicit algorithm for solving the one-dimensional Vlasov–Poisson system

Transition from convective to absolute Raman instability via the longitudinal relativistic effect by using Vlasov-Maxwell simulations

Eulerian Finite-Difference Vlasov Solver with a Non-Uniform Momentum Grid

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