Volume 20, Issue 11, November 2013

In ideal magnetohydrodynamics characterized by an infinite electrical conductivity, the magnetic flux across an arbitrary fluid surface is conserved in time. The magnetofluid then can be partitioned into contiguous subvolumes of fluid, each of which entraps its own subsystem of magnetic flux. During dynamical evolution of the magnetofluid, these subvolumes press into each other; and in the process, two such subvolumes may come into direct contact while ejecting a third interstitial subvolume. Depending on the orientations of magnetic fields of the two interacting subvolumes, the magnetic field at the common surface of interaction may become discontinuous and a current sheet is formed there. This process of current sheet formation and their subsequent decay is believed to be a plausible mechanism for coronal heating and may also be responsible for various eruptive phenomena at the solar corona. In this work, we explore this theoretical concept through numerical simulations of a viscous, incompressible magnetofluid characterized by infinite electrical conductivity. In particular, we show that if the initial magnetic field is prescribed by superposition of two linear forcefree fields with different torsion coefficients, then formation of current sheets are numerically realizable in the neighborhood of magnetic nulls.
 ARTICLES

 Basic Plasma Phenomena, Waves, Instabilities

Current disruption and its spreading in collisionless magnetic reconnection
View Description Hide DescriptionRecent magnetic reconnection experiments (MRX) [Dorfman et al., Geophys. Res. Lett. 40, 233 (2013)] have disclosed current disruption in the absence of an externally imposed guide field. During current disruption in MRX, both the current density and the total observed outofreconnectionplane current drop simultaneous with a rise in outofreconnectionplane electric field. Here, we show that current disruption is an intrinsic property of the dynamic formation of an Xpoint configuration of magnetic field in magnetic reconnection, independent of the model used for plasma description and of the dimensionality (2D or 3D) of reconnection. An analytic expression for the current drop is derived from Ampere's Law. Its predictions are verified by 2D and 3D electronmagnetohydrodynamic (EMHD) simulations. Three dimensional EMHD simulations show that the current disruption due to localized magnetic reconnection spreads along the direction of the electron drift velocity with a speed which depends on the wave number of the perturbation. The implications of these results for MRX are discussed.

Magnetic reconnection in the presence of externally driven and selfgenerated turbulence
View Description Hide DescriptionMagnetic reconnection is an important process that violates flux freezing and induces change of magnetic field topology in conducting fluids and, as a consequence, converts magnetic field energy into particle energy. It is thought to be operative in laboratory, heliophysical, and astrophysical plasmas. These environments exhibit wide variations in collisionality, ranging from collisionless in the Earth's magnetosphere to highly collisional in molecular clouds. A common feature among these plasmas is, however, the presence of turbulence. We review the present understanding of the effects of turbulence on the reconnection rate, discussing both how strong preexisting turbulence modifies SweetParker reconnection and how turbulence may develop as a result of reconnection itself. In steady state, reconnection rate is proportional to the aspect ratio of the diffusion region. Thus, two general MHD classes of models for fast reconnection have been proposed, differing on whether they keep the aspect ratio finite by increasing the width due to turbulent broadening or shortening the length of the diffusion layer due to plasmoid instability. One of the consequences of the plasmoid instability model is the possibility that the current sheet thins down to collisionless scales where kinetic effects become dominant. As a result, kinetic effects may be of importance for many astrophysical applications which were considered to be in the realm of MHD. Whether preexisting turbulence can significantly modify the transition to the kinetic regime is not currently known. Although most studies of turbulent reconnection have been based on MHD, recent advances in kinetic simulations are enabling 3D studies of turbulence and reconnection in the collisionless regime. A summary of these recent works, highlighting similarities and differences with the MHD models of turbulent reconnection, as well as comparison with in situ observations in the magnetosphere and in the solar wind, are presented. The paper concludes with a list of important open questions and suggestions for future work.

Sagdeev potential approach for large amplitude compressional Alfvenic double layers in viscous plasmas
View Description Hide DescriptionSagdeev’s technique is used to study the large amplitude compressional Alfvenic double layers in a magnetohydrodynamic plasma taking into account the small plasma β and small values of kinematic viscosity. Dispersive effect raised by nonideal electron inertia currents perpendicular to the ambient magnetic field. The range of allowed values of the soliton speed, M (Mach number), plasma β (ratio of the plasma thermal pressure to the pressure in the confining magnetic field), and viscosity coefficient, wherein double layer may exist, are determined. In the absence of collisions, viscous dissipation modifies the Sagdeev potential and results in large amplitude compressional Alfvenic double layers. The depth of Sagdeev potential increases with the increasing Mach number and plasma β, however, decreases with the increasing viscosity. The double layer structure increases with the increasing plasma β, but decreases with increasing viscous dissipation .

Electromagnetic fluctuations and normal modes of a drifting relativistic plasma
View Description Hide DescriptionWe present an exact calculation of the power spectrum of the electromagnetic fluctuations in a relativistic equilibrium plasma described by MaxwellJüttner distribution functions. We consider the cases of wave vectors parallel or normal to the plasma mean velocity. The relative contributions of the subluminal and supraluminal fluctuations are evaluated. Analytical expressions of the spatial fluctuation spectra are derived in each case. These theoretical results are compared to particleincell simulations, showing a good reproduction of the subluminal fluctuation spectra.

Interaction of nonthermal muon beam with electronpositronphoton plasma: A thermal field theory approach
View Description Hide DescriptionInteraction of a muon beam with hot dense QED plasma is investigated. Plasma system contains electrons and positrons with FermiDirac distribution and BoseEinstein distributed photons while the beam particles have nonthermal distribution. The energy loss of the beam particles during the interaction with plasma is calculated to complete leading order of interaction in terms of the QED coupling constant using thermal field theory approach. The screening effects of the plasma are computed consistently using resummation of perturbation theory with hard thermal loop approximation according to the BraatenPisarski method. Time evolution of the plasma characteristics and also plasma identifications during the interaction are investigated. Effects of the nonthermal parameter of the beam distribution on the energy exchange and the evolution of plasmabeam system are also explained.

A phenomenological model on the kink mode threshold varying with the inclination of sheath boundary
View Description Hide DescriptionIn nature and many laboratory plasmas, a magnetic flux tube threaded by current or a flux rope has a footpoint at a boundary. The current driven kink mode is one of the fundamental ideal magnetohydrodynamic instabilities in plasmas. It has an instability threshold that has been found to strongly depend on boundary conditions (BCs). We provide a theoretical model to explain the transition of this threshold dependence between nonline tied and line tied boundary conditions. We evaluate model parameters using experimentally measured plasma data, explicitly verify several kink eigenfunctions, and validate the model predictions for boundary conditions BCs that span the range between NLT and LT BCs. Based on this model, one could estimate the kink threshold given knowledge of the displacement of a flux rope end, or conversely estimate flux rope end motion based on knowledge of it kink stability threshold.

Ion finite Larmor radius effects on the interchange instability in an open system
View Description Hide DescriptionA particle simulation of an interchange instability was performed by taking into account the ion finite Larmor radius (FLR) effects. It is found that the interchange instability with large FLR grows in two phases, that is, linearly growing phase and the nonlinear phase subsequent to the linear phase, where the instability grows exponentially in both phases. The linear growth rates observed in the simulation agree well with the theoretical calculation. The effects of FLR are usually taken in the fluid simulation through the gyroviscosity, the effects of which are verified in the particle simulation with large FLR regime. The gyroviscous cancellation phenomenon observed in the particle simulation causes the drifts in the direction of ion diamagnetic drifts.

Constant residual electrostatic electron plasma mode in VlasovAmpere system
View Description Hide DescriptionIn a collisionless VlasovPoisson (VP) electron plasma system, two types of modes for electric field perturbation exist: the exponentially Landau damped electron plasma waves and the initialvalue sensitive ballistic modes. Here, the VP system is modified slightly to a VlasovAmpere (VA) system. A new constant residual mode is revealed. Mathematically, this mode comes from the Laplace transform of an initial electric field perturbation, and physically represents that an initial perturbation (e.g., external electric field perturbation) would not be damped away. Thus, this residual mode is more difficult to be damped than the ballistic mode.

On existence of solitary waves in unmagnetized neutral hot pair plasma
View Description Hide DescriptionWhether the solitary waves exist in unmagnetized neutral hot pair plasma is considered. It is found that for small electrons and positrons longitudinal momentum the solitary waves do not exist under the quasistatic approximation.

Particleincell simulations of magnetic reconnection in laserplasma experiments on ShenguangII facility
View Description Hide DescriptionRecently, magnetic reconnection has been realized in highenergydensity laserproduced plasmas. Plasma bubbles with selfgenerated magnetic fields are created by focusing laser beams to smallscale spots on a foil. The bubbles expand into each other, which may then drive magnetic reconnection. The reconnection experiment in laserproduced plasmas has also been conducted at ShenguangII (SGII) laser facility, and the existence of a plasmoid was identified in the experiment [Dong et al., Phys. Rev. Lett. 108, 215001 (2012)]. In this paper, by performing twodimensional (2D) particleincell simulations, we investigate such a process of magnetic reconnection based on the experiment on SGII facility, and a possible explanation for the formation of the plasmoid is proposed. The results show that before magnetic reconnection occurs, the bubbles squeeze strongly each other and a very thin current sheet is formed. The current sheet is unstable to the tearing mode instability, and we can then observe the formation of plasmoid(s) in such a multiple Xlines reconnection.

Magnetic reconnection under anisotropic magnetohydrodynamic approximation
View Description Hide DescriptionWe study the formation of slowmode shocks in collisionless magnetic reconnection by using one and twodimensional collisionless MHD codes based on the double adiabatic approximation and the Landau closure model. We bridge the gap between the Petschektype MHD reconnection model accompanied by a pair of slow shocks and the observational evidence of the rare occasion of insitu slow shock observations. Our results showed that once magnetic reconnection takes place, a firehosesense pressure anisotropy arises in the downstream region, and the generated slow shocks are quite weak comparing with those in an isotropic MHD. In spite of the weakness of the shocks, however, the resultant reconnection rate is 10%–30% higher than that in an isotropic case. This result implies that the slow shock does not necessarily play an important role in the energy conversion in the reconnection system and is consistent with the satellite observation in the Earth's magnetosphere.

Extended fluid models: Pressure tensor effects and equilibria
View Description Hide DescriptionWe consider the use of “extended fluid models” as a viable alternative to computationally demanding kinetic simulations in order to manage the global large scale evolution of a collisionless plasma while accounting for the main effects that come into play when spatial microscales of the order of the ion inertial scale di and of the thermal ion Larmor radius are formed. We present an extended twofluid model that retains finite Larmor radius (FLR) corrections to the ion pressure tensor while electron inertia terms and heat fluxes are neglected. Within this model we calculate analytic FLR plasma equilibria in the presence of a shear flow and elucidate the role of the magnetic field asymmetry. Using a Hybrid Vlasov code, we show that these analytic equilibria offer a significant improvement with respect to conventional magnetohydrodynamic shearflow equilibria when initializing kinetic simulations.

Simulation and mitigation of the magnetoRayleighTaylor instabilities in Zpinch gas discharge extreme ultraviolet plasma radiation sources
View Description Hide DescriptionThe development and use of a singlefluid twotemperature approximated 2D MagnetoHydrodynamics code is reported. Zpinch dynamics and the evolution of MagnetoRayleighTaylor (MRT) instabilities in a gas jet type Extreme Ultraviolet (EUV) source are investigated with this code. The implosion and stagnation processes of the Zpinch dynamics and the influence of initial perturbations (single mode, multi mode, and random seeds) on MRT instability are discussed in detail. In the case of single mode seeds, the simulation shows that the growth rates for mmscale wavelengths up to 4 mm are between 0.05 and 0.065 ns^{−1}. For multimode seeds, the mode coupling effect leads to a series of other harmonics, and complicates MRT instability evolution. For perturbation by random seeds, the modes evolve to longer wavelengths and finally converge to a mmscale wavelength approximately 1 mm. MRT instabilities can also alter the pinch stagnation state and lead to temperature and density fluctuations along the Z axis, which eventually affects the homogeneity of the EUV radiation output. Finally, the simulation results are related to experimental results to discuss the mitigations of MRT instability.

Wave dispersion in the hybridVlasov model: Verification of Vlasiator
View Description Hide DescriptionVlasiator is a new hybridVlasov plasma simulation code aimed at simulating the entire magnetosphere of the Earth. The code treats ions (protons) kinetically through Vlasov's equation in the sixdimensional phase space while electrons are a massless chargeneutralizing fluid [M. Palmroth et al., J. Atmos. Sol.Terr. Phys. 99, 41 (2013); A. Sandroos et al., Parallel Comput. 39, 306 (2013)]. For first global simulations of the magnetosphere, it is critical to verify and validate the model by established methods. Here, as part of the verification of Vlasiator, we characterize the lowβ plasma wave modes described by this model and compare with the solution computed by the Waves in Homogeneous, Anisotropic Multicomponent Plasmas (WHAMP) code [K. Rönnmark, Kiruna Geophysical Institute Reports No. 179, 1982], using dispersion curves and surfaces produced with both programs. The match between the two fundamentally different approaches is excellent in the lowfrequency, long wavelength range which is of interest in global magnetospheric simulations. The lefthand and righthand polarized wave modes as well as the Bernstein modes in the Vlasiator simulations agree well with the WHAMP solutions. Vlasiator allows a direct investigation of the importance of the Hall term by including it in or excluding it from Ohm's law in simulations. This is illustrated showing examples of waves obtained using the ideal Ohm's law and Ohm's law including the Hall term. Our analysis emphasizes the role of the Hall term in Ohm's law in obtaining wave modes departing from ideal magnetohydrodynamics in the hybridVlasov model.

Modulational instability of spin modified quantum magnetosonic waves in FermiDiracPauli plasmas
View Description Hide DescriptionA theoretical and numerical study of the modulational instability of large amplitude quantum magnetosonic waves (QMWs) in a relativistically degenerate plasma is presented. A modified nonlinear Schrödinger equation is derived by using the reductive perturbation method. The modulational instability regions of the QMWs and the corresponding growth rates are significantly affected by the relativistic degeneracy parameter, the Pauli spin magnetization effects, and the equilibrium magnetic field. The dynamics and nonlinear saturation of the modulational instability of QMWs are investigated numerically. It is found that the increase of the relativistic degeneracy parameter can increase the growth rate of the instability, and the system is saturated nonlinearly by the formation of envelope solitary waves. The current investigation may have relevance to astrophysical magnetized compact objects, such as white dwarfs and pulsar magnetospheres.
 Nonlinear Phenomena, Turbulence, Transport

Ionacoustic doublelayers in a magnetized plasma with nonthermal electrons
View Description Hide DescriptionIn the present work we investigate the existence of obliquely propagating ionacoustic double layers in magnetized twoelectron plasmas. The fluid model is used to describe the ion dynamics, and the hot electron population is modeled via a κ distribution function, which has been proved to be appropriate for modeling nonMaxwellian plasmas. A quasineutral condition is assumed to investigate these nonlinear structures, which leads to the formation of doublelayers propagating with slow ionacoustic velocity. The problem is investigated numerically, and the influence of parameters such as nonthermality is discussed.

Shock formation processes due to interactions of two plasmas in a magnetic field and modified twostream instabilities
View Description Hide DescriptionThe study of interactions of exploding and surrounding plasmas in an external magnetic field [K. Yamauchi and Y. Ohsawa, Phys. Plasmas 14, 053110 (2007)] is verified with twodimensional (2D) electromagnetic particle simulations, for a case in which the initial velocity of the exploding plasma is perpendicular to the external magnetic field. The 2D simulations show essentially the same shockformation processes as those in the previous onedimensional simulation, including penetration of exploding ions into surrounding plasma, formation of a strong magneticfield pulse due to deceleration of the exploding ions, ion reflection by the pulse, and subsequent splitting of the pulse into two magnetosonic pulses which then develop into forward and reverse shock waves. Furthermore, the 2D structure of electromagnetic fields in the region, where the exploding and surrounding ions overlap, is investigated with particular attention to the linear and nonlinear evolution of modified twostream instabilities in the magnetic field that is being gradually compressed. The effects of these instabilities on ion reflection and on 2D magnetic fluctuations in the two generated pulses are also discussed.

Arbitrary amplitude magnetosonic solitary and shock structures in spin quantum plasma
View Description Hide DescriptionA nonlinear analysis is carried out for the arbitrary amplitude magnetosonic solitary and shock structures in spin quantum plasmas. A quantum magnetohydrodynamic model is used to describe the magnetosonic quantum plasma with the Bohm potential and the pressure like spin force for electrons. Analytical calculations are used to simplify the basic equations, which are then studied numerically. It is shown that the magnetic diffusivity is responsible for dissipation, which causes the shocklike structures rather than the soliton structures. Additionally, wave speed, Zeeman energy, and Bohm potential are found to have significant impact on the shock wave structures.

Dissipative kinetic Alfvén solitary waves resulting from viscosity
View Description Hide DescriptionNonlinear smallamplitude kinetic Alfvén solitary waves (KASWs) are investigated with their “anomalous” kinetic viscosity effect on electrons. It is found that the structure of a humptype KASW solution develops into a shocktype (or double layer) KASW solution for large amplitude KASWs when viscosity exists. For small amplitude KASWs, the Kortewegde Vries (KdV) equation with an approximate pseudopotential was solved, and it is found that the humptype KASWs develop into oscillating shocktype (kinktype) KASWs. It is also found that the oscillating scale of this structure is related to the propagation velocity and plasma beta, while the damping scale is inversely proportional to the viscosity.

On the effect of intermittency of turbulence on the parabolic relation between skewness and kurtosis in magnetized plasmas
View Description Hide DescriptionThis paper is aimed to contribute to the scientific discussions that have been triggered by the experimental observation of a quadratic relation between the kurtosis and skewness of turbulent fluctuations present in fusion plasmas and other nonlinear physical systems. In this paper, we offer a general statistical model which attributes the observed relation to the varying intermittency of the experimental signals. The model is a two random variable model constructed to catch the essential intermittent feature of the real signal. One of the variables is the amplitude of the underlying intermittent event (e.g., turbulent structure) while the other is connected to the intermittency level of the system. This simple model can attribute physical meaning to the a and b coefficients, as they characterize the spatiotemporal statistics of intermittent events. By constructing a particleconserving Gaussian model for the underlying coherent structures, the experimentally measured a and b coefficients could be adequately reproduced.