Drift-Kinetic Particle Dynamics in Black Hole Accretion Flows

Abstract

Low density plasmas in curved spacetimes, such as those found in accretion flows around black holes, are challenging to model from first principles, owing to the large scale separation between the characteristic scales of the microscopic processes and large mean-free-paths comparable to the system sizes. Kinetic approaches become necessary to capture the relevant physics but lack the dynamic range to model the global characteristics of the systems. The guiding center formalism has been proposed as a powerful tool to bridge the gap between these scales. Despite its usefulness, the guiding center approach has been formulated successfully only in flat spacetimes, limiting its applicability in astrophysical settings. In this thesis, I develop new covariant guiding center equations of motion for charges in general relativistic spacetimes that are computationally tractable. I derive covariant conservation laws for the motions of the guiding centers and show, through several limiting cases, that the equations contain all known drift mechanisms. Through a variety of experiments, I demonstrate that my equations capture all known gyrocenter drifts while overcoming one severe limitation imposed on numerical algorithms by the fast timescales of the particle gyromotion. I generate a new hybrid numerical algorithm based on this formalism, which evolves the trajectories of charged particles over macroscopic timescales in general relativistic magnetohydrodynamic (GRMHD) backgrounds. I apply my method to GRMHD simulations of black hole accretion flows, demonstrating its accuracy and efficiency across a range of physical conditions. Lastly, I present the general relativistic drift velocities and accompanying parallel and temporal acceleration equations in a 3+1 decomposition applicable in non-spinning black hole spacetimes. The culmination of the work presented in this thesis will enable explorations of a variety of global plasma kinetic phenomena in the curved spacetimes around black holes and neutron stars.