Higher dimensional semi-relativistic time-fractional Vlasov-Maxwell code for numerical simulation based on linear polarization and 2D Landau damping instability

Abstract

The “Vlasov-Maxwell system” is a groundbreaking algorithm to model, simulate and further analyze the vigorous performance of the collisionless plasma in the presence of the electromagnetic fields. In this frame of reference, the inquiry of this system with the deep conceptions of the time-fractional derivative is a novel benchmark and also the key intentions of this study. For this purpose, higher 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 an innovative algorithm which based on spectral and finite-difference approximations. The spatial and temporal variables are handled by using shifted Gegenbauer polynomials and finite-difference approximations respectively. Numerous simulations are carried out to validate the reliability and accuracy of the anticipated method. Error bound convergence and stability of the method is inspected numerically. Furthermore, the established technique can be used conveniently to observe the numerical result of other multi-dimensional time-fraction with variable-order problems of physical nature.