Landau damping in cilyndrical inhomogeneous plasmas

Hoyos, J.; Valencia, Jose A.; Ramírez, Sebastián

doi:10.1088/1742-6596/1247/1/012006

Cited by 6 publications

(3 citation statements)

References 11 publications

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“…A characteristic methodology in which cubic Hermit interpolation for the simulation of hyper-dimensional Vlasov-Poisson equation in phase space is announced by [24]. Some recent studies regarding mathematical modeling of VMS and their numerical simulations can be seen in Delzanno et al [12,19,28,42]. It is also important to mention here that the study of plasma can also be modeled with the help of fluid models [25,40], but this is quite different, and we consider the VMS system for this study.…”

Section: Introductionmentioning

confidence: 99%

A semi‐relativistic time‐fractional Vlasov–Maxwell code for numerical simulation based on circular polarization and Landau damping instability

Zubair

Usman

2022

Numerical Methods Partial

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The Vlasov-Maxwell system is a revolutionary tool to model and analyze the dynamic behavior of the collisionless plasma in the existence of the electromagnetic field. In this perspective, the investigation of this system with the concept of the time-fractional derivative is the new benchmark and also one of the main objectives of this article. In order to construct the numerical solution, we propose and implement a novel scheme which grounded on finite-difference and spectral approximations. The temporal variable is tackled by using finite-difference approximation, whereas spatial variables approximated via sifted Gegenbauer polynomials. Various simulations are performed to explore new phenomena and demonstrate the accuracy and reliability of the proposed method. Convergence and error bound of the suggested methods are investigated theoretically, whereas stability analysis performed numerically. Moreover, the developed method can be used conveniently to examine the numerical solution of other multidimensional highly nonlinear fractional or variable order problems of physical nature.

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Section: Introductionmentioning

confidence: 99%

A semi‐relativistic time‐fractional Vlasov–Maxwell code for numerical simulation based on circular polarization and Landau damping instability

Zubair

Usman

2022

Numerical Methods Partial

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“…Some recent studies regarding mathematical modeling of VMS and their numerical simulations can be seen in Refs. [4][5][6][7]. It is also important to mention here that the study of plasma can also be modeled with the help of fluid models [8][9][10][11][12], but this is quite different, and we consider the VMS system for this study.…”

Section: Introductionmentioning

confidence: 99%

A novel scheme for time‐fractional semi‐relativistic Vlasov–Maxwell system based on laser‐plasma interaction with linear polarization and Landau damping instability

Zubair

Usman

2020

Numerical Methods Partial

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The Vlasov–Maxwell system is a revolutionary tool to model and analyze the dynamic behavior of the collisionless plasma in the existence of the electromagnetic field. In this perspective, the investigation of this system with the concept of the time‐fractional derivative is the new benchmark and also one of the main objectives of this article. To construct the numerical solution, we propose and implement a novel scheme which grounded on finite‐difference and spectral approximations. The temporal variables are tackled by using finite‐difference approximations, whereas spatial variables approximated via sifted Gegenbauer polynomials. Various simulations are performed to explore new phenomena, demonstrate the accuracy and reliability of the proposed method. Convergence, error bound and stability of the suggested methods are investigated numerically. Moreover, the developed method can be used conveniently to examine the numerical solution of other multidimensional highly nonlinear fractional or variable order problems of physical nature.

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“…Some recent concepts of VMS, FDEs and the numerical simulations can be deliberate from the refs. [8,27,37,38] and [39][40][41][42], respectively. T. Zubair reported in ref.…”

mentioning

confidence: 99%

Higher-Dimensional Fractional Order Modelling for Plasma Particles with Partial Slip Boundaries: A Numerical Study

et al. 2021

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We integrate fractional calculus and plasma modelling concepts with specific geometry in this article, and further formulate a higher dimensional time-fractional Vlasov Maxwell system. Additionally, we develop a quick, efficient, robust, and accurate numerical approach for temporal variables and filtered Gegenbauer polynomials based on finite difference and spectral approximations, respectively. To analyze the numerical findings, two types of boundary conditions are used: Dirichlet and partial slip. Particular methodology is used to demonstrate the proposed scheme’s numerical convergence. A detailed analysis of the proposed model with plotted figures is also included in the paper.

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Landau damping in cilyndrical inhomogeneous plasmas

Cited by 6 publications

References 11 publications

A semi‐relativistic time‐fractional Vlasov–Maxwell code for numerical simulation based on circular polarization and Landau damping instability

A semi‐relativistic time‐fractional Vlasov–Maxwell code for numerical simulation based on circular polarization and Landau damping instability

A novel scheme for time‐fractional semi‐relativistic Vlasov–Maxwell system based on laser‐plasma interaction with linear polarization and Landau damping instability

Higher-Dimensional Fractional Order Modelling for Plasma Particles with Partial Slip Boundaries: A Numerical Study

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