Brizard, Alain J.Chan, Anthony A.2022-12-132022-12-132022Brizard, Alain J. and Chan, Anthony A.. "Hamiltonian formulations of quasilinear theory for magnetized plasmas." <i>Frontiers in Astronomy and Space Sciences,</i> 9, (2022) Frontiers Media S.A.: https://doi.org/10.3389/fspas.2022.1010133.https://hdl.handle.net/1911/114100Hamiltonian formulations of quasilinear theory are presented for the cases of uniform and nonuniform magnetized plasmas. First, the standard quasilinear theory of Kennel and Engelmann (Kennel, Phys. Fluids, 1966, 9, 2377) is reviewed and reinterpreted in terms of a general Hamiltonian formulation. Within this Hamiltonian representation, we present the transition from two-dimensional quasilinear diffusion in a spatially uniform magnetized background plasma to three-dimensional quasilinear diffusion in a spatially nonuniform magnetized background plasma based on our previous work (Brizard and Chan, Phys. Plasmas, 2001, 8, 4762–4771; Brizard and Chan, Phys. Plasmas, 2004, 11, 4220–4229). The resulting quasilinear theory for nonuniform magnetized plasmas yields a 3 × 3 diffusion tensor that naturally incorporates quasilinear radial diffusion as well as its synergistic connections to diffusion in two-dimensional invariant velocity space (e.g., energy and pitch angle).engThis is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) and the copyright owner(s) are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.Journal articlefspas-09-1010133https://doi.org/10.3389/fspas.2022.1010133