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

Tamour Zubair,Jan Awrejcewicz,Muhammad Imran Asjad,Muhammad Usman

doi:10.3390/nano11112884

Abstract

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.

Highlights

In the study of plasma [1,2,3,4,5,6,7] particles, there is a ground breaking tool available in the literature named the “Vlasov Maxwell system”, which is the amalgamation of the VlasovKambiz Vafai, Nanomaterials11, I.x AbdelsalamFOR PEER and REVIEW equation and Maxwell equations
The main idea of this paper is that we formulated an extended version of VMS using the concepts of fractional calculus and further numerical simulations of the problem, which is influenced by the concepts of partial slip boundaries [22,23,24], with the help of a modified algorithm
The Dirichlet boundary conditions are included to numerical convergence of the formulated algorithm

Summary

Introduction

In the study of plasma [1,2,3,4,5,6,7] particles, there is a ground breaking tool available in the literature named the “Vlasov Maxwell system”, which is the amalgamation of the Vlasov. The main idea of this paper is that we formulated an extended version of VMS using the concepts of fractional calculus and further numerical simulations of the problem, which is influenced by the concepts of partial slip boundaries [22,23,24], with the help of a modified algorithm. For this purpose, we strategized a specific geometry with partial slip boundaries and further verbalized the assumptions using the basic perceptions and theorems available in the literature [9,37,43,44]. REVIEW literature detailed ther motivate the readers to extend it to the Boltzmann approximations

Formulation of Numerical Scheme

Discussion about Numerical Results

Discussion about Numerical

Concluding Remarks

Results