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Numerical simulations and quantitative theoretical explanations are presented for the spontaneous formation of a hole–clump pair in phase space. The equilibrium is close to the linear threshold for instability and the destabilizing resonant kinetic drive is nearly balanced by either extrinsic dissipation or a second stabilizing resonant kinetic component. The hole and clump, each support a nonlinear wave where the trapping frequency of the particles is comparable to the kinetic linear growth rate from the destabilizing species alone. The power dissipated is balanced by energy extracted by trapped particles locked to the changing wave-phase velocities. With extrinsic dissipation, phase space structures always form just above the linear instability threshold. With a stabilizing kinetic component, an electrostatic interaction is considered with varying mass ratios of the stabilizing and destabilizing species together with collisional effects. With these input parameters, various nonlinear responses arise, only some of which sweep in frequency.

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The turbulent Ex B drift of a test particle in an inhomogeneous magnetic field is not reducible to a simple diffusion, but rather leads to a biased diffusion producing an inhomogeneous density distribution (pinch effect). The statistical properties of the long-time chaotic two-dimensional drift motion of a charged particle in the magnetic field B(x,y) and the time-dependent electrostatic potential

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We present an alternative approach to statistical analysis of an intermittent ideal magnetohydrodynamics fluid in two dimensions, based on the hydrodynamic discrete vortex model applied to the Elsasser variables. The model contains negative temperature states which predict the formation of magnetic islands, but also includes a natural limit under which the equilibrium states revert to the familiar twin-vortex states predicted by hydrodynamic turbulence theories. Numerical dynamical calculations yield equilibrium spectra in agreement with the theoretical predictions.PACS numbers: 47.65.+a, 52.30.-q, 52.65.+Z Statistical theories of continuous fluids usually are based on some discrete representation of the fluid. Even though such fluids are not in thermodynamic equilibrium at the molecular level, one can expect real systems to tend towards the statistically favored states during time scales for which the model is valid. For numerical simulation, of course, some discretization of a continuous system is always necessary.Hydrodynamic turbulence has been discretized by two methods: a truncated Fourier representation, and a point vortex representation. An analytic statistical Fourier analysis has already been applied to two-dimensional magnetohydrodynamics (MHD) [1]. In this Letter, we show that a point-vortex discretization like that used in hydrodynamics (or the equivalent guiding-center plasma [2]) is also possible for 2D MHD, and we give results of statistical analysis as well as direct numerical simulation of the vortex system.Why is such an approach worth taking? It has been assented [3] that different approaches to discretization of functional integrations cannot in general be expected to yield equivalent results. Indeed, in the hydrodynamic studies, the two different discretization approaches, while both making similar qualitative predictions about a cascade of energy to low wave numbers, do not yield the same results [4]. A neutral 2D fluid with small dissipation is known to form intermediate-scale vorticity distributions, or coherent structures [5], which dominate the nonlinear evolution. Statistical theories based on inviscid equations [6,7] predict evolutionary tendencies suggestive of such structures, although they cannot complete the fully dissipative formation process. Vortices have nevertheless been taken as a starting point for a large body of work and many others). The end states predicted by such models have been observed in direct numerical simulation of the primitive fluid equations [13], and the dynamical approach »to the end state is well described by a modified vortex model [14]. These successes encourage the search for an analogous approach in 2D MHD. Computationally, discrete-vortex models can qualitatively reproduce the behavior of the primitive fluid equations at a lower cost than a spectral or grid point code [15], and allow the possibility of modeling more general large-scale filamentary structures [16,17]. Taking an analogous approach to MHD simulations could lead to similarly efficient n...

We develop a filamentary construct of magnetohydrodynamical plasma dynamics based on the Elsasser variables. This approach is modeled after discrete vortex models of hydrodynamicai turbulence, which cannot be expected in general to produce results identical to ones based on a Fourier decomposition of the fields. La a highly intermittent plasma, the induction force is small compared to the convective motion, and when this force is neglected, the plasma vortex system is described by a Hamiltonian. For a system with many such vortices, we present a statistical treatment of a collection of discrete current-vorticity concentrations. Canonical and microcanonical statistical calculations show that both the vorticity and the current spectra are peaked at long wavelengths, and the expected states revert to known hydrodynamical states as the magnetic field vanishes. These results differ from previous Fourier-based statistical theories, but it is found that when the filament calculation is expanded to include the inductive force, the results approach the Fourier equilibria in the low-temperature limit, and the previous Hamiltonian plasma vortex results in the high-temperature limit. Numerical simulations of a large number of filaments are carried out and support the theory. A three-dimensional vortex model is outlined as weil, which is also Hamiltonian when the inductive force is neglected. A statistical calculi_tion in the canonical ensemble l lnstitute for Fusion Studies,