A Comparative Study of Rayleigh–Taylor Instability in Plasmas using Kinetic and Parallel Kinetic-Perpendicular Moment (PKPM) Models

Abstract

Rayleigh-Taylor instability (RTI) is a fundamental instability that occurs when a densermedium is accelerated into a lighter one, and it plays an important role in many plasma systems, including laboratory plasmas, astrophysical flows, and fusion-related environments. While RTI has been studied extensively using fluid models and fully kinetic descriptions, it is less clear how well reduced kinetic-fluid models can reproduce the essential instability physics at a lower computational cost. This thesis examines that question by comparing fully kinetic and Parallel Kinetic-Perpendicular Moment (PKPM) simulations of RTI performed with the Gkeyll framework. The work develops a consistent comparison between the two models using matched initial conditions, common boundary treatments, and contour-based diagnostics for interface evolution and growth-rate extraction. The study focuses on the evolution of density structure, instability growth, and transport behavior under different collisionalities and PKPM field-direction choices. For the Kn = 0.01 case, PKPM reproduces the main qualitative behavior of the kinetic reference, including the interface evolution and fitted growth rate, while showing greater sensitivity in the later nonlinear morphology. The results show that the retained kinetic direction in PKPM acts as an important control on the solution: in-plane field directions remain closest to the kinetic reference, while out-of-plane directions produce broader and more fluid-like interface structures. At Kn = 0.1, the comparison becomes more transport-dominated, and the PKPM field direction more strongly affects whether the interface remains diffusive or develops a clearer RTI head. Overall, the results show that PKPM provides a useful reduced description of RTI. It captures the dominant growth and morphology trends of the fully kinetic model while requiring significantly lower computational cost, making it a practical tool for studying larger and more expensive plasma-instability problems.