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

Area of Science:

• Plasma Physics
• Fractional Calculus
• Computational Electromagnetics

Background:

• The Vlasov Maxwell system describes plasma behavior.
• Fractional calculus offers advanced modeling capabilities.
• Efficient numerical methods are crucial for complex systems.

Purpose of the Study:

• To formulate a higher dimensional time-fractional Vlasov Maxwell system.
• To develop an efficient and accurate numerical approach for the system.
• To analyze the model's behavior using Dirichlet and partial slip boundary conditions.

Main Methods:

• Integration of fractional calculus and plasma modeling.
• Development of a numerical scheme using finite difference and spectral approximations.
• Application of filtered Gegenbauer polynomials for temporal variables.

Main Results:

• A robust numerical scheme was developed for the fractional Vlasov Maxwell system.
• Numerical convergence was demonstrated using a specific methodology.
• The model's behavior was analyzed under different boundary conditions.

Conclusions:

• The proposed numerical method is efficient and accurate for the fractional Vlasov Maxwell system.
• The study provides a framework for analyzing complex plasma phenomena using fractional calculus.