Chasing Hamiltonian structure in gyrokinetic theory

Abstract

Hamiltonian structure is pursued and uncovered in collisional and collisionless gyrokinetic theory. A new Hamiltonian formulation of collisionless electromagnetic theory is presented that is ideally suited to implementation on modern supercomputers. The method used to uncover this structure is described in detail and applied to a number of examples, where several well-known plasma models are endowed with a Hamiltonian structure for the first time. The first energy- and momentum-conserving formulation of full-F collisional gyrokinetics is presented. In an effort to understand the theoretical underpinnings of this result at a deeper level, a \emph{stochastic} Hamiltonian modeling approach is presented and applied to pitch angle scattering. Interestingly, the collision operator produced by the Hamiltonian approach is equal to the Lorentz operator plus higher-order terms, but does not exactly conserve energy. Conversely, the classical Lorentz collision operator is provably not Hamiltonian in the stochastic sense.

Princeton University thesis

Cited by in corpus (9)

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• Discovering exact, gauge-invariant, local energy-momentum conservation laws for the electromagnetic gyrokinetic system by high-order field theory on heterogeneous manifolds
• Hamiltonian structure of the guiding center plasma model
• The initial value problem in Lagrangian drift kinetic theory
• Electron inertia and quasi-neutrality in the Weibel instability
• Hamiltonian structure of the guiding-center Vlasov-Maxwell equations
• Improved accuracy in degenerate variational integrators for guiding center and magnetic field line flow