{'fraction_non_alphanumeric': 0.022222222222222223, 'fraction_numerical': 0.0, 'mean_word_length': 5.597560975609756, 'pattern_counts': {'":': 0, '<': 0, '<?xml version=': 0, '>': 0, 'https://': 0, 'lorem ipsum': 0, 'www.': 0, 'xml': 0}, 'pii_count': 0, 'substrings_counts': 0, 'word_list_counts': {'cursed_substrings.json': 0, 'profanity_word_list.json': 0, 'sexual_word_list.json': 0, 'zh_pornsignals.json': 0}}
Finite-dimensional collisionless kinetic theory

A collisionless kinetic plasma model may often be cast as an infinite-dimensional noncanonical Hamiltonian system. I show that, when this is the case, the model can be discretized in space and particles while preserving its Hamiltonian structure, thereby producing a finite-dimensional Hamiltonian system that approximates the original kinetic model. I apply the general theory to two example systems: the relativistic Vlasov-Maxwell system with spin and a gyrokinetic Vlasov-Maxwell system.