2015/09/13 by J. W. Burby, Burby, J. W. · 1 citation
Earth and Planetary Sciences · Engineering · Mathematics · Physics and Astronomy · #FOS: Physical sciences #Geophysics and Sensor Technology #High-pressure geophysics and materials #Mathematical Physics (math-ph) #Plasma Physics (physics.plasm-ph) #Quantum and Classical Electrodynamics #math-ph #math.MP #physics.plasm-ph
paper · pdf · doi:10.48550/arxiv.1509.04551
Princeton University thesis
arxiv created 2015/09/13 · openalex publication_date 2015/09/13 · arxiv updated 2015/09/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 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.