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This Letter reports on a metriplectic formulation of a collisional, nonlinear full-f electromagnetic gyrokinetic theory compliant with energy conservation and monotonic entropy production. In an axisymmetric background magnetic field, the toroidal angular momentum is also conserved. Notably, a new collisional current, contributing to the gyrokinetic Maxwell–Ampère equation and the gyrokinetic charge conservation law, is discovered.

Tmore » he Hamiltonian formulations for the perturbed Vlasov–Maxwell equations and the perturbed ideal magnetohydrodynamics (MHD) equations are expressed in terms of the perturbation derivative $\partial \mathcal{F}/\partial ϵ\equiv [\mathcal{F},\mathcal{S}]$ of an arbitrary functional $\mathcal{F}\left[\mathit{\psi }\right]$ of the Vlasov–Maxwell fields $\mathit{\psi }=(\mathrm{f},\mathbf{E},\mathbf{B})$ or the ideal MHD fields $\mathit{\psi }=(\rho ,\mathbf{u},s,\mathbf{B})$, which are assumed to depend continuously on the (dimensionless) perturbation parameter ϵ. In this study, $[,]$ denotes the functional Poisson bracket for each set of plasma equations and the perturbation action functional $\mathcal{S}$ is said to generate dynamically accessible perturbations of the plasma fields. he new Hamiltonian perturbation formulation introduces a framework for functional perturbation methods in plasma physics and highlights the crucial roles played by polarization and magnetization in Vlasov–Maxwell and ideal MHD perturbation theories. One application considered in this paper is a formulation of plasma stability that guarantees dynamical accessibility and leads to a natural generalization to higher-order perturbation theory.« less

The goal of this project is to develop new Lie-transform methods for the purpose of deriving advanced reduced plasma models (including hybrid kinetic-MHD models) used to investigate energetic-particle effects in magnetized fusion plasmas. Two classes of energetic particles are considered: fusion products and energetic (e.g., runaway) electrons, which have their respective importance in determining the path of a hightemperature magnetized plasma toward the burning-plasma state.

The perturbative variational formulation of the Vlasov-Maxwell equations is presented up to the third order in the perturbation analysis. From the second and third-order Lagrangian densities, the first-order and second-order Vlasov-Maxwell equations are expressed in gauge-invariant and gauge-independent forms, respectively. Upon deriving the reduced second-order Vlasov-Maxwell Lagrangian for the linear nonadiabatic gyrokinetic Vlasov-Maxwell equations, the reduced Lagrangian densities for the linear drift-wave equation and the linear hybrid kinetic-magnetohydrodynamic (MHD) equations are derived, with their associated wave-action conservation laws obtained by the Noether method. The exact wave-action conservation law for the linear hybrid kinetic-MHD equations is written explicitly. To conclude, amore » new form of the third-order Vlasov-Maxwell Lagrangian is derived in which ponderomotive effects play a crucial role.« less

A new gauge-free electromagnetic gyrokinetic theory is developed, in which the gyrocenter equations of motion and the gyrocenter phase-space transformation are expressed in terms of the perturbed electromagnetic fields, instead of the usual perturbed potentials. Gyrocenter polarization and magnetization are derived explicitly from the gyrocenter Hamiltonian, up to first order in the gyrocenter perturbation expansion. In conclusion, expressions for the sources in Maxwell's equations are derived in a form that is suitable for simulation studies, as well as kinetic-gyrokinetic hybrid modeling.

The nonlinear (full-f) electromagnetic gyrokinetic Vlasov-Maxwell equations are derived in the parallel-symplectic representation from an Eulerian gyrokinetic variational principle. The gyrokinetic Vlasov-Maxwell equations are shown to possess an exact energy conservation law, which is derived by the Noether method from the gyrokinetic variational principle. Here, the gyrocenter Poisson bracket and the gyrocenter Jacobian contain contributions from the perturbed magnetic field. Lastly, in the full-f formulation of the gyrokinetic Vlasov-Maxwell theory presented here, the gyrocenter parallel-Ampere equation contains a second-order contribution to the gyrocenter current density that is derived from the second-order gyrocenter ponderomotive Hamiltonian.

The use of supersonic rotation of a plasma in mirror geometry has distinct advantages for thermonuclear fusion. The device is steady state, there are no disruptions, the loss cone is almost closed, sheared rotation stabilizes magnetohydrodynamic instabilities as well as plasma turbulence, there are no runaway electrons, and the coil configuration is simple. In this work, we examine the effect of rotation on mirror confinement using a full cyclotron orbit code. The full cyclotron simulations give a much more complete description of the particle energy distribution and losses than the use of guiding center equations. Both collisionless loss as amore » function of rotation and the effect of collisions are investigated. Although the cross field diffusion is classical, we find that the local rotating Maxwellian is increased to higher energy, increasing the fusion rate and also enhancing the radial diffusion. We find a loss channel not envisioned with a guiding center treatment, but a design can be chosen that can satisfy the Lawson criterion for ions. Of course, the rotation has a minimal effect on the alpha particle birth distribution, so there is initially loss through the usual loss cone, just as in a mirror with no rotation. However after this loss, the alphas slow down on the electrons with little pitch angle scattering until reaching low energy, so over half of the initial alpha energy is transferred to the electrons. The important problem of energy confinement, with losses primarily through the electron channel, is not addressed in this work. In conclusion, we also discuss the use of rotating mirror geometry to produce an ion thruster.« less

The motion of a charged particle in a nonuniform straight magnetic field with a constant magnetic-field gradient is solved exactly in terms of elliptic functions. The connection between this problem and the guiding-center approximation is discussed. Here, it is shown that, for this problem, the predictions of higher-order guiding-center theory agree very well with the orbit-averaged particle motion and hold well beyond the standard guiding-center limit $$\epsilon$$ $$\equiv$$ p/L << 1, where p is the gyromotion length scale and L is the magnetic-field gradient length scale.

The compressional component of magnetic perturbation δB-_|| to can play an important role in drift-Alfvenic instabilities in tokamaks, especially as the plasma β increases (β is the ratio of kinetic pressure to magnetic pressure). In this work, we have formulated a gyrokinetic particle simulation model incorporating δB-_||, and verified the model in kinetic Alfven wave simulations using the Gyrokinetic Toroidal Code in slab geometry. Simulations of drift-Alfvenic instabilities in tokamak geometry shows that the kinetic ballooning mode (KBM) growth rate decreases more than 20% when δB-_|| is neglected for β_e = 0.02, and that δB-_|| to has stabilizing effects onmore » the ion temperature gradient instability, but negligible effects on the collisionless trapped electron mode. Lastly, the KBM growth rate decreases about 15% when equilibrium current is neglected.« less

In this paper, the variational formulations of guiding-center Vlasov-Maxwell theory based on Lagrange, Euler, and Euler-Poincaré variational principles are presented. Each variational principle yields a different approach to deriving guiding-center polarization and magnetization effects into the guiding-center Maxwell equations. Finally, the conservation laws of energy, momentum, and angular momentum are also derived by Noether method, where the guiding-center stress tensor is now shown to be explicitly symmetric.