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Register a new userExact Vlasov-Maxwell equilibria for asymmetric current sheets
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The NASA Magnetospheric Multiscale mission has made in situ diffusion region and kinetic-scale resolution measurements of asymmetric magnetic reconnection for the first time, in the Earths magnetopause. The principal theoretical tool currently used to model collisionless asymmetric reconnection is particle-in-cell simulations. Many particle-in-cell simulations of asymmetric collisionless reconnection start from an asymmetric Harris-type magnetic field but with distribution functions that are not exact equilibrium solutions of the Vlasov equation. We present new and exact equilibrium solutions of the Vlasov-Maxwell system that are self-consistent with one-dimensional asymmetric current sheets, with an asymmetric Harris-type magnetic field profile, plus a constant nonzero guide field. The distribution functions can be represented as a combination of four shifted Maxwellian distribution functions. This equilibrium describes a magnetic field configuration with more freedom than the previously known exact solution and has different bulk flow properties.
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Using fully kinetic simulations, we study the suppression of asymmetric reconnection in the limit where the diamagnetic drift speed >> Alfven speed and the magnetic shear angle is moderate. We demonstrate that the slippage between electrons and the magnetic flux facilitates reconnection, and can even result in fast reconnection that lacks one of the outflow jets. Through comparing a case where the diamagnetic drift is supported by the temperature gradient with a companion case that has a density gradient instead, we identify a robust suppression mechanism. The drift of the x-line is slowed down locally by the asymmetric nature of the current sheet and the resulting tearing modes, then the x-line is run over and swallowed by the faster-moving following flux.
The hybrid Vlasov-Maxwell system of equations is suitable to describe a magnetized plasma at scales of the order of or larger than proton kinetic scales. An exact stationary solution is presented by revisiting previous results with a uniform-density shear flow, directed either parallel or perpendicular to a uniform magnetic field, and by adapting the solution to the hybrid Vlasov-Maxwell model. A quantitative characterization of the equilibrium distribution function is provided by studying both analytically and numerically the temperature anisotropy and gyrotropy and the heat flux. In both cases, in the shear region, the velocity distribution significantly departs from local thermodynamical equilibrium. A comparison between the time behavior of the usual fluid-like equilibrium shifted Maxwellian and the exact stationary solutions is carried out by means of numerical simulations of the hybrid Vlasov-Maxwell equations. These hybrid equilibria can be employed as an unperturbed states for numerous problems which involve sheared flows, such as the wave propagation in inhomogeneous background and the onset of the Kelvin-Helmholtz instability.
To explain energy dissipation via turbulence in collisionless, magnetized plasmas, the existence of a dual real- and velocity-space cascade of ion-entropy fluctuations below the ion gyroradius has been proposed. Such a dual cascade, predicted by the gyrokinetic theory, has previously been observed in gyrokinetic simulations of two-dimensional, electrostatic turbulence. For the first time we show evidence for a dual phase-space cascade of ion-entropy fluctuations in a three-dimensional simulation of hybrid-kinetic, electromagnetic turbulence. Some of the scalings observed in the energy spectra are consistent with a generalized theory for the cascade that accounts for the spectral anisotropy of critically balanced, intermittent, sub-ion-Larmor-scale fluctuations. The observed velocity-space cascade is also anisotropic with respect to the magnetic-field direction, with linear phase mixing along magnetic-field lines proceeding mainly at spatial scales above the ion gyroradius and nonlinear phase mixing across magnetic-field lines proceeding at perpendicular scales below the ion gyroradius. Such phase-space anisotropy could be sought in heliospheric and magnetospheric data of solar-wind turbulence and has far-reaching implications for the dissipation of turbulence in weakly collisional astrophysical plasmas.
Motivated by recent discussions on the possible role of quantum computation in plasma simulations, here we present different approaches to Koopmans Hilbert-space formulation of classical mechanics in the context of Vlasov-Maxwell kinetic theory. The celebrated Koopman-von Neumann construction is provided with two different Hamiltonian structures: one is canonical and recovers the usual Clebsch representation of the Vlasov density, the other is noncanonical and appears to overcome certain issues emerging in the canonical formalism. Furthermore, the canonical structure is restored for a variant of the Koopman-von Neumann construction that carries a different phase dynamics. Going back to van Hoves prequantum theory, the corresponding Koopman-van Hove equation provides an alternative Clebsch representation which is then coupled to the electromagnetic fields. Finally, the role of gauge transformations in the new context is discussed in detail.
We use a numerical nonlinear multigrid magnetic relaxation technique to investigate the generation of current sheets in three-dimensional magnetic flux braiding experiments. We are able to catalogue the relaxed nonlinear force-free equilibria resulting from the application of deformations to an initially undisturbed region of plasma containing a uniform, vertical magnetic field. The deformations are manifested by imposing motions on the bounding planes to which the magnetic field is anchored. Once imposed the new distribution of magnetic footpoints are then taken to be fixed, so that the rest of the plasma must then relax to a new equilibrium configuration. For the class of footpoint motions we have examined, we find that singular and nonsingular equilibria can be generated. By singular we mean that within the limits imposed by numerical resolution we find that there is no convergence to a well-defined equilibrium as the number of grid points in the numerical domain is increased. These singular equilibria contain current sheets of ever-increasing current intensity and decreasing width; they occur when the footpoint motions exceed a certain threshold, and must include both twist and shear to be effective. On the basis of these results we contend that flux braiding will indeed result in significant current generation. We discuss the implications of our results for coronal heating.
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