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1. Exact conservation laws for gauge-free electromagnetic gyrokinetic equations

   https://doi.org/10.1017/S0022377821000519  

   Brizard, Alain J. (June 2021, Journal of Plasma Physics)

   null (Ed.)

   The exact energy and angular momentum conservation laws are derived by the Noether method for the Hamiltonian and symplectic representations of the gauge-free electromagnetic gyrokinetic Vlasov–Maxwell equations. These gyrokinetic equations, which are solely expressed in terms of electromagnetic fields, describe the low-frequency turbulent fluctuations that perturb a time-independent toroidally-axisymmetric magnetized plasma. The explicit proofs presented here provide a complete picture of the transfer of energy and angular momentum between the gyrocentres and the perturbed electromagnetic fields, in which the crucial roles played by gyrocentre polarization and magnetization effects are highlighted. In addition to yielding an exact angular momentum conservation law, the gyrokinetic Noether equation yields an exact momentum transport equation, which might be useful in more general equilibrium magnetic geometries. 

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2. Improved multispecies Dougherty collisions

   https://doi.org/10.1017/S0022377822000289  

   Francisquez, Manaure; Juno, James; Hakim, Ammar; Hammett, Gregory W.; Ernst, Darin R. (June 2022, Journal of Plasma Physics)

   The Dougherty model Fokker–Planck operator is extended to describe nonlinear full- $$f$$ (  f is the distribution function) collisions between multiple species in plasmas. Simple relations for cross-species primitive moments are developed which obey conservation laws, and reproduce familiar velocity and temperature relaxation rates. This treatment of multispecies Dougherty collisions, valid for arbitrary mass ratios, avoids unphysical temperatures and satisfies the $$H$$ -theorem ( H is related to the entropy) unlike an analogous Bhatnagar–Gross–Krook operator. Formulas for both a Cartesian velocity space and a gyroaveraged operator are provided for use in Vlasov as well as long-wavelength gyrokinetic models. We present an algorithm for the discontinuous Galerkin discretization of this operator, and provide results from relaxation and Landau damping benchmarks. 

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3. Characterizing velocity–space signatures of electron energization in large-guide-field collisionless magnetic reconnection

   https://doi.org/10.1063/5.0082213  

   McCubbin, Andrew J.; Howes, Gregory G.; TenBarge, Jason M. (May 2022, Physics of Plasmas)

   Magnetic reconnection plays an important role in the release of magnetic energy and consequent energization of particles in collisionless plasmas. Energy transfer in collisionless magnetic reconnection is inherently a two-step process: reversible, collisionless energization of particles by the electric field, followed by collisional thermalization of that energy, leading to irreversible plasma heating. Gyrokinetic numerical simulations are used to explore the first step of electron energization, and we generate the first examples of field–particle correlation signatures of electron energization in 2D strong-guide-field collisionless magnetic reconnection. We determine these velocity space signatures at the x-point and in the exhaust, the regions of the reconnection geometry in which the electron energization primarily occurs. Modeling of these velocity–space signatures shows that, in the strong-guide-field limit, the energization of electrons occurs through bulk acceleration of the out-of-plane electron flow by the parallel electric field that drives the reconnection, a non-resonant mechanism of energization. We explore the variation of these velocity–space signatures over the plasma beta range 0.01≤βi≤1. Our analysis goes beyond the fluid picture of the plasma dynamics and exploits the kinetic features of electron energization in the exhaust region to propose a single-point diagnostic, which can potentially identify a reconnection exhaust region using spacecraft observations. 

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4. Characterizing Velocity-Space Signatures of Electron Energization in Large-Guide-Field Collisionless Magnetic Reconnection

   McCubbin, Andrew J.; Howes, Gregory G.; TenBarge, Jason M. (December 2021, ArXivorg)

   Magnetic reconnection plays an important role in the release of magnetic energy and consequent energization of particles in collisionless plasmas. Energy transfer in collisionless magnetic reconnection is inherently a two-step process: reversible, collisionless energization of particles by the electric field, followed by collisional thermalization of that energy, leading to irreversible plasma heating. Gyrokinetic numerical simulations are used to explore the first step of electron energization, and we generate the first examples of field-particle correlation (FPC) signatures of electron energization in 2D strong-guide-field collisionless magnetic reconnection. We determine these velocity space signatures at the x-point and in the exhaust, the regions of the reconnection geometry in which the electron energization primarily occurs. Modeling of these velocity-space signatures shows that, in the strong-guide-field limit, the energization of electrons occurs through bulk acceleration of the out-of-plane electron flow by parallel electric field that drives the reconnection, a non-resonant mechanism of energization. We explore the variation of these velocity-space signatures over the plasma beta range 0.01 < beta_i < 1. Our analysis goes beyond the fluid picture of the plasma dynamics and exploits the kinetic features of electron energization in the exhaust region to propose a single-point diagnostic which can potentially identify a reconnection exhaust region using spacecraft observations. 

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5. Fast spectral separation method for kinetic equation with anisotropic non-stationary collision operator retaining micro-model fidelity

   Zhao, Yue; Lei, Huan (August 2025, arXivorg)

   In this paper, we present a generalized, data-driven collisional operator for one-component plasmas, learned from molecular dynamics simulations, to extend the collisional kinetic model beyond the weakly coupled regime. The proposed operator features an anisotropic, non-stationary collision kernel that accounts for particle correlations typically neglected in classical Landau formulations. To enable efficient numerical evaluation, we develop a fast spectral separation method that represents the kernel as a low-rank tensor product of univariate basis functions. This formulation admits an O(N log N) algorithm via fast Fourier transforms and preserves key physical properties, including discrete conservation laws and the H-theorem, through a structure-preserving central difference discretization. Numerical experiments demonstrate that the proposed model accurately captures plasma dynamics in the moderately coupled regime beyond the standard Landau model while maintaining high computational efficiency and structure-preserving properties. 

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