A semi-relativistic time-fractional Vlasov-Maxwell code for numerical simulation based on circular polarization and symmetric two-stream instability

Abstract

The “Vlasov-Maxwell system” is a groundbreaking differential procedure to visualize, model, simulate and further analyze the vigorous performance of plasma (collisionless) in the presence of the different fields (electromagnetic). In this frame of reference, the analysis of “Vlasov-Maxwell system” with the deep conceptions of (time-fractional) calculus is a novel benchmark and also the key intentions of this study. For this purpose, (1D + 1P) dimensional semi-relativistic time-fractional Vlasov-Maxwell system is formulated with the physical significances of the geometry. Furthermore, to fabricate the numerical consequences, we suggest (and also implement) an innovative algorithm which based on spectral and finite-difference estimations. The spatial and temporal variables are handled by using sifted Gegenbauer polynomials and finite-difference calculations respectively. Numerous simulations are executed to validate the reliability and accuracy of anticipated method. Error bound convergence and stability of the method is inspected numerically. Moreover, the established technique can be used conveniently to observe the numerical result of other multi-dimensional fraction (variable) order problems of physical nature.

Keywords

• (1D+1P) dimensional Vlasov-Maxwell system
• Shifted Gegenbauer polynomials
• Fractional order matrices