[en] Gyrocenter-gauge kinetic theory is developed as an extension of the existing gyrokinetic theories. In essence, the formalism introduced here is a kinetic description of magnetized plasmas in the gyrocenter coordinates which is fully equivalent to the Vlasov--Maxwell system in the particle coordinates. In particular, provided the gyroradius is smaller than the scale-length of the magnetic field, it can treat high-frequency range as well as the usual low-frequency range normally associated with gyrokinetic approaches. A significant advantage of this formalism is that it enables the direct particle-in-cell simulations of compressional Alfven waves for magnetohydrodynamic (MHD) applications and of rf (radio frequency) waves relevant to plasma heating in space and laboratory plasmas. The gyrocenter-gauge kinetic susceptibility for arbitrary wavelength and arbitrary frequency electromagnetic perturbations in a homogeneous magnetized plasma is shown to recover exactly the classical result obtained by integrating the Vlasov--Maxwell system in the particle coordinates. This demonstrates that all the waves supported by the Vlasov--Maxwell system can be studied using the gyrocenter-gauge kinetic model in the gyrocenter coordinates. This theoretical approach is so named to distinguish it from the existing gyrokinetic theory, which has been successfully developed and applied to many important low-frequency and long parallel wavelength problems, where the conventional meaning of ''gyrokinetic'' has been standardized. Besides the usual gyrokinetic distribution function, the gyrocenter-gauge kinetic theory emphasizes as well the gyrocenter-gauge distribution function, which sometimes contains all the physics of the problems being studied, and whose importance has not been realized previously. The gyrocenter-gauge distribution function enters Maxwell's equations through the pull-back transformation of the gyrocenter transformation, which depends on the perturbed fields. The efficacy of the gyrocenter-gauge kinetic approach is largely due to the fact that it directly decouples particle's gyromotion from its gyrocenter motion in the gyrocenter coordinates. As in the case of kinetic theories using guiding center coordinates, obtaining solutions for this kinetic system involves only following particles along their gyrocenter orbits. However, an added advantage here is that unlike the guiding center formalism, the gyrocenter coordinates used in this theory involves both the equilibrium and the perturbed components of the electromagnetic field. In terms of solving the kinetic system using particle simulation methods, the gyrocenter-gauge kinetic approach enables the reduction of computational complexity without the loss of important physical content

[en] It is found that the thermal fluctuation level of the shear-Alfven waves in a gyrokinetic plasma is dependent on plasma β((equivalent to)c_s²/v_A²), where c_s is the ion acoustic speed and v_A is the Alfven velocity. This unique thermodynamic property based on the fluctuation--dissipation theorem is verified in this paper using a new gyrokinetic particle simulation scheme, which splits the particle distribution function into the equilibrium part as well as the adiabatic and nonadiabatic parts. The numerical implication of this property is discussed

[en] The effort to obtain a set of MagnetoHydroDynamic (MHD) equations for a magnetized collisionless plasma was started nearly 60 years ago by Chew et al. [Proc. R. Soc. London, Ser. A 236(1204), 112–118 (1956)]. Many attempts have been made ever since. Here, we will show the derivation of a set of these equations from the gyrokinetic perspective, which we call it gyrokinetic MHD, and it is different from the conventional ideal MHD. However, this new set of equations still has conservation properties and, in the absence of fluctuations, recovers the usual MHD equilibrium. Furthermore, the resulting equations allow for the plasma pressure balance to be further modified by finite-Larmor-radius effects in regions with steep pressure gradients. The present work is an outgrowth of the paper on “Alfven Waves in Gyrokinetic Plasmas” by Lee and Qin [Phys. Plasmas 10, 3196 (2003)].

[en] The relevance of the gyrokinetic fluctuation-dissipation theorem (FDT) to thermal equilibrium and nonequilibrium states of the gyrokinetic plasma is explored, with particular focus being given to the contribution of weakly damped normal modes to the fluctuation spectrum. It is found that the fluctuation energy carried in the normal modes exhibits the proper scaling with particle count (as predicted by the FDT in thermal equilibrium) even in the presence of drift waves, which grow linearly and attain a nonlinearly saturated steady state. This favorable scaling is preserved, and the saturation amplitude of the drift wave unaffected, for parameter regimes in which the normal modes become strongly damped and introduce a broad spectrum of discreteness-induced background noise in frequency space

[en] In this paper, a simple iterative procedure is presented for obtaining the higher order ExB and dE/dt (polarization) drifts associated with the gyrokinetic Vlasov-Poisson equations in the long wavelength limit of k_{perpendicular}ρ_i∼o(ε) and k_{perpendicular}L∼o(1), where ρ_i is the ion gyroradius, L is the scale length of the background inhomogeneity, and ε is a smallness parameter. It can be shown that these new higher order k_{perpendicular}ρ_i terms, which are also related to the higher order perturbations of the electrostatic potential φ, should have negligible effects on turbulent and neoclassical transport in tokamaks regardless of the form of the background distribution and the amplitude of the perturbation. To address further the issue of a non-Maxwellian plasma, higher order finite Larmor radius terms in the gyrokinetic Poisson's equation have been studied and shown to be unimportant as well. On the other hand, the terms of o(k_{perpendicular}²ρ_i²) and k_{perpendicular}L∼o(1) can, indeed, have an impact on microturbulence, especially in the linear stage, such as those arising from the difference between the guiding center and the gyrocenter densities due to the presence of the background gradients. These results will be compared to a recent study questioning the validity of the commonly used gyrokinetic equations for long time simulations.

[en] A new split-weight perturbative particle simulation scheme for finite-β plasmas in the presence of background inhomogeneities is presented. The scheme is an improvement over the original split-weight scheme, which splits the perturbed particle response into adiabatic and non-adiabatic parts to improve numerical properties. In the new scheme, by further separating out the adiabatic response of the particles associated with the quasi-static bending of the magnetic field lines in the presence of background inhomogeneities of the plasma, we are able to demonstrate the finite-β stabilization of drift waves and ion temperature gradient modes using a simple gyrokinetic particle code based on realistic fusion plasma parameters. However, for βm_i/m_e ≫ 1, it becomes necessary to use the electron skin-depth as the grid size of the simulation to achieve accuracy in solving the resulting equations, unless special numerical arrangement is made for the cancelling of the two large terms on the either side of the governing equation. The proposed scheme is most suitable for studying shear-Alfvén physics in general geometry using straight field line coordinates for microturbulence and magnetic reconnection problems

[en] We show in this response that the nonlinear Poisson's equation in our original paper derived from the drift kinetic approach can be verified by using the nonlinear gyrokinetic Poisson's equation of Dubin et al. [Phys. Fluids 26, 3524 (1983)]. This nonlinear contribution in φ² is indeed of the order of k_{perpendicular})⁴ in the long wavelength limit and remains finite for zero ion temperature, in contrast with the nonlinear term by Parra and Catto [Plasma Phys. Controlled Fusion 50, 065014 (2008)], which is of the order of k_{perpendicular}² and diverges for T_i→0. For comparison, the leading term for the gyrokinetic Poisson's equation in this limit is of the order of k_{perpendicular}²φ.

[en] High frequency gyrokinetic (HFGK) algorithm for particle-in-cell (PIC) simulation has been developed based on the gyrocenter-gauge kinetic theory. This new algorithm takes advantage of the separation of gyrocenter and gyrophase motions introduced by the gyrokinetic formalism. The 6D version of the algorithm is equivalent to the direct 6D Lorentz-force simulation in the limit of small gyroradius (compared to the ambient magnetic field). Since the gyrocenter dynamics is slow, one is allowed to use large time step for pushing gyrocenters in the 6D HFGK algorithm, which results in saving in computing time. Using simple electrostatic collisionless system in slab geometry, we perform nonlinear PIC simulation of the ion cyclotron instability and nonlinear ion perpendicular heating dynamics using new 6D HFGK algorithm. Comparisons with a conventional 6D Lorentz-force code are presented

[en] The gyrokinetic approach for arbitrary frequency dynamics in magnetized plasmas is explored, using the gyrocenter-gauge kinetic theory. Contrary to low-frequency gyrokinetics, which views each particle as a rigid charged ring, arbitrary frequency response of a particle is described by a quickly changing Kruskal ring. This approach allows the separation of gyrocenter and gyrophase responses and thus allows for, in many situations, larger time steps for the gyrocenter push than for the gyrophase push. The gyrophase response which determines the shape of Kruskal rings can be described by a Fourier series in gyrophase for some problems, thus allowing control over the cyclotron harmonics at which the plasma responds. A computational algorithm for particle-in-cell simulation based on this concept has been developed. An example of the ion Bernstein wave is used to illustrate its numerical properties, and comparison with a direct Lorentz-force approach is presented

[en] An efficient numerical method for treating electrons in magnetized plasmas has been developed. The scheme, which is based on the perturbative (δf) gyrokinetic particle simulation, splits the particle electron responses into adiabatic and nonadiabatic parts. The former is incorporated into the gyrokinetic Poisson's equation, while the latter is calculated dynamically with the aid of the charge conservation equation. The new scheme affords us the possibility of suppressing unwanted high-frequency oscillations and, in the meantime, relaxing the Courant condition for the thermal particles moving in the parallel direction. It is most useful for studying low-frequency phenomena in plasmas. As an example, one-dimensional drift wave simulation has been carried out using the scheme and the results are presented in this paper. This methodology can easily be generalized to problems in three-dimensional toroidal geometry, as well as those in unmagnetized plasmas. (c) 2000 American Institute of Physics