Ion Skin Depth Research Articles

Supersonic regime of the Hall-magnetohydrodynamics resistive tearing instability

An earlier analysis of the Hall-magnetohydrodynamics (MHD) tearing instability [E. Ahedo and J. J. Ramos, Plasma Phys. Controlled Fusion 51, 055018 (2009)] is extended to cover the regime where the growth rate becomes comparable or exceeds the sound frequency. Like in the previous subsonic work, a resistive, two-fluid Hall-MHD model with massless electrons and zero-Larmor-radius ions is adopted and a linear stability analysis about a force-free equilibrium in slab geometry is carried out. A salient feature of this supersonic regime is that the mode eigenfunctions become intrinsically complex, but the growth rate remains purely real. Even more interestingly, the dispersion relation remains of the same form as in the subsonic regime for any value of the instability Mach number, provided only that the ion skin depth is sufficiently small for the mode ion inertial layer width to be smaller than the macroscopic lengths, a generous bound that scales like a positive power of the Lundquist number.

Energy spectrum, dissipation, and spatial structures in reduced Hall magnetohydrodynamic

We analyze the effect of the Hall term in the magnetohydrodynamic turbulence under a strong externally supported magnetic field, seeing how this changes the energy cascade, the characteristic scales of the flow, and the dynamics of global magnitudes, with particular interest in the dissipation. Numerical simulations of freely evolving three-dimensional reduced magnetohydrodynamics are performed, for different values of the Hall parameter (the ratio of the ion skin depth to the macroscopic scale of the turbulence) controlling the impact of the Hall term. The Hall effect modifies the transfer of energy across scales, slowing down the transfer of energy from the large scales up to the Hall scale (ion skin depth) and carrying faster the energy from the Hall scale to smaller scales. The final outcome is an effective shift of the dissipation scale to larger scales but also a development of smaller scales. Current sheets (fundamental structures for energy dissipation) are affected in two ways by increasing the Hall effect, with a widening but at the same time generating an internal structure within them. In the case where the Hall term is sufficiently intense, the current sheet is fully delocalized. The effect appears to reduce impulsive effects in the flow, making it less intermittent.

Characterizing counter-streaming interpenetrating plasmas relevant to astrophysical collisionless shocks

A series of Omega experiments have produced and characterized high velocity counter-streaming plasma flows relevant for the creation of collisionless shocks. Single and double CH2 foils have been irradiated with a laser intensity of ∼ 1016 W/cm2. The laser ablated plasma was characterized 4 mm from the foil surface using Thomson scattering. A peak plasma flow velocity of 2000 km/s, an electron temperature of ∼ 110 eV, an ion temperature of ∼ 30 eV, and a density of ∼ 1018 cm−3 were measured in the single foil configuration. Significant increases in electron and ion temperatures were seen in the double foil geometry. The measured single foil plasma conditions were used to calculate the ion skin depth, c/ωpi∼0.16 mm, the interaction length, ℓint, of ∼ 8 mm, and the Coulomb mean free path, λmfp∼27mm. With c/ωpi≪ℓint≪λmfp, we are in a regime where collisionless shock formation is possible.

Magnetic reconnection from a multiscale instability cascade

Magnetic reconnection, the process whereby magnetic field lines break and then reconnect to form a different topology, underlies critical dynamics of magnetically confined plasmas in both nature and the laboratory. Magnetic reconnection involves localized diffusion of the magnetic field across plasma, yet observed reconnection rates are typically much higher than can be accounted for using classical electrical resistivity. It is generally proposed that the field diffusion underlying fast reconnection results instead from some combination of non-magnetohydrodynamic processes that become important on the 'microscopic' scale of the ion Larmor radius or the ion skin depth. A recent laboratory experiment demonstrated a transition from slow to fast magnetic reconnection when a current channel narrowed to a microscopic scale, but did not address how a macroscopic magnetohydrodynamic system accesses the microscale. Recent theoretical models and numerical simulations suggest that a macroscopic, two-dimensional magnetohydrodynamic current sheet might do this through a sequence of repetitive tearing and thinning into two-dimensional magnetized plasma structures having successively finer scales. Here we report observations demonstrating a cascade of instabilities from a distinct, macroscopic-scale magnetohydrodynamic instability to a distinct, microscopic-scale (ion skin depth) instability associated with fast magnetic reconnection. These observations resolve the full three-dimensional dynamics and give insight into the frequently impulsive nature of reconnection in space and laboratory plasmas.

Local structures of homogeneous Hall MHD turbulence

Local structures of decaying homogeneous and isotropic Hall MHD turbulence are studied by means of direct numerical simulations. Regions of strong vorticity and strong current density in Hall MHD turbulence are compared to those of single-fluid MHD turbulence. An analysis by the use of a low-pass filter reveals that the introduction of the Hall term can modify not only small-scale structures of the current density but also structures of the vorticity field, especially at the scales smaller than the ion skin depth.

FAST MAGNETIC RECONNECTION AND SPONTANEOUS STOCHASTICITY

Magnetic field lines in astrophysical plasmas are expected to be frozen-in at scales larger than the ion gyroradius. The rapid reconnection of magnetic-flux structures with dimensions vastly larger than the gyroradius requires a breakdown in the standard Alfvén flux-freezing law. We attribute this breakdown to ubiquitous MHD plasma turbulence with power-law scaling ranges of velocity and magnetic energy spectra. Lagrangian particle trajectories in such environments become "spontaneously stochastic," so that infinitely many magnetic field lines are advected to each point and must be averaged to obtain the resultant magnetic field. The relative distance between initial magnetic field lines which arrive at the same final point depends upon the properties of two-particle turbulent dispersion. We develop predictions based on the phenomenological Goldreich & Sridhar theory of strong MHD turbulence and on weak MHD turbulence theory. We recover the predictions of the Lazarian & Vishniac theory for the reconnection rate of large-scale magnetic structures. Lazarian & Vishniac also invoked "spontaneous stochasticity," but of the field lines rather than of the Lagrangian trajectories. More recent theories of fast magnetic reconnection appeal to microscopic plasma processes that lead to additional terms in the generalized Ohm's law, such as the collisionless Hall term. We estimate quantitatively the effect of such processes on the inertial-range turbulence dynamics and find them to be negligible in most astrophysical environments. For example, the predictions of the Lazarian & Vishniac theory are unchanged in Hall MHD turbulence with an extended inertial range, whenever the ion skin depth δi is much smaller than the turbulent integral length or injection-scale Li.

Magnetic reconnection in partially ionized plasmas

We review the theory of magnetic reconnection in weakly ionized gases. The theory is relevant to reconnection in the interstellar medium, protostellar and protoplanetary disks, the outer envelopes of cool stars, and a new laboratory experiment. In general, partial ionization introduces three effects beyond the obvious one: increased resistivity due to electron-neutral collisions. First, magnetic neutral sheets are steepened by plasma-neutral drift, setting up the conditions for reconnection. Second, when ion-neutral friction is strong, the effective ion mass is increased by ρ/ρi, the ratio of total to plasma mass density. This reduces the Alfven speed vA by a factor of ρ/ρi and increases the ion skin depth δi by ρ/ρi. As a result, entrainment of neutrals slows MHD reconnection but permits the onset of fast collisionless reconnection at a larger Lundquist number S, or for a longer current sheet, than in the fully ionized plasma case. These effects, taken together, promote fast collisionless reconnection when the ionization fraction is of order 10% to 1%, but reconnection is slowed down for much smaller ionization fractions. Finally, ion-neutral friction can be a strong heating mechanism throughout the inflow and outflow regions. These effects are under study at the Magnetic Reconnection Experiment (MRX).

Analytical and computational study of the ideal full two-fluid plasma model and asymptotic approximations for Hall-magnetohydrodynamics

The 5-moment two-fluid plasma model uses Euler equations to describe the ion and electron fluids and Maxwell’s equations to describe the electric and magnetic fields. Two-fluid physics becomes significant when the characteristic spatial scales are on the order of the ion skin depth and characteristic time scales are on the order of the ion cyclotron period. The full two-fluid plasma model has disparate characteristic speeds ranging from the ion and electron speeds of sound to the speed of light. Two asymptotic approximations are applied to the full two-fluid plasma to arrive at the Hall-MHD model, namely negligible electron inertia and infinite speed of light. The full two-fluid plasma model and the Hall-MHD model are studied for applications to an electromagnetic plasma shock, geospace environmental modeling (GEM challenge) magnetic reconnection, an axisymmetric Z-pinch, and an axisymmetric field reversed configuration (FRC).

Hall magnetohydrodynamic reconnection in the plasmoid unstable regime

A set of reduced Hall magnetohydrodynamic (MHD) equations are used to evaluate the stability of large aspect ratio current sheets to the formation of plasmoids (secondary islands). Reconnection is driven by resistivity in this analysis, which occurs at the resistive skin depth dη≡SL-1/2LνA/γ, where SL is the Lundquist number, L, the length of the current sheet, νA, the Alfvén speed, and γ, the growth rate. Modifications to a recent resistive MHD analysis [N. F. Loureiro et al., Phys. Plasmas 14, 100703 (2007)] arise when collisions are sufficiently weak that dη is shorter than the ion skin depth di ≡ c/ωpi. Secondary islands grow faster in this Hall MHD regime: the maximum growth rate scales as (di/L)6/13SL7/13νA/L and the number of plasmoids as (di/L)1/13SL11/26, compared to SL1/4νA/L and S3/8, respectively, in resistive MHD.

Onset of fast reconnection in Hall magnetohydrodynamics mediated by the plasmoid instability

The role of a super-Alfvénic plasmoid instability in the onset of fast reconnection is studied by means of the largest Hall magnetohydrodynamics simulations to date, with system sizes up to 104 ion skin depths (di). It is demonstrated that the plasmoid instability can facilitate the onset of rapid Hall reconnection, in a regime where the onset would otherwise be inaccessible because the Sweet–Parker width is significantly above di. However, the topology of Hall reconnection is not inevitably a single stable X-point. There exists an intermediate regime where the single X-point topology itself exhibits instability, causing the system to alternate between a single X-point geometry and an extended current sheet with multiple X-points produced by the plasmoid instability. Through a series of simulations with various system sizes relative to di, it is shown that system size affects the accessibility of the intermediate regime. The larger the system size is, the easier it is to realize the intermediate regime. Although our Hall magnetohydrodynamics (MHD) model lacks many important physical effects included in fully kinetic models, the fact that a single X-point geometry is not inevitable raises the interesting possibility for the first time that Hall MHD simulations may have the potential to realize reconnection with geometrical features similar to those seen in fully kinetic simulations, namely, extended current sheets and plasmoid formation.

Effect of Magnetic Field Curvature on Penetration of the Magnetic Field into the Plasma

The penetration of a magnetic field into a cylindrical plasma, in the time scale that is much longer than electron cyclotron period, is studied. A linear wave analysis is shown that the magnetic field penetrates rapidly into the plasma in radii smaller than the ion skin depth. Due to the axial symmetry, the problem reduces to a two-dimensional problem. The magnetic field evolution is numerically calculated. The ion density is also calculated. It is shown that during the penetration of the magnetic field, a gap appears between cathode and plasma. At the early times, at the plasma boundary, electrons move radially, and coupling of the electron velocity and the electric field induces the magnetic field. Electrons then gain a drift due to the field curvature that results in fast penetration of the magnetic field into the plasma.

Alfvén wave phase-mixing and damping in the ion cyclotron range of frequencies

Aims. To determine the effect of the Hall term in the generalised Ohm's law on the damping and phase mixing of Alfven waves in the ion cyclotron range of frequencies in uniform and non-uniform equilibrium plasmas. Methods. Wave damping in a uniform plasma is treated analytically, whilst a Lagrangian remap code (Lare2d) is used to study Hall effects on damping and phase mixing in the presence of an equilibrium density gradient. Results. The magnetic energy associated with an initially Gaussian field perturbation in a uniform resistive plasma is shown to decay algebraically at a rate that is unaffected by the Hall term to leading order in k^2di^2 where k is wavenumber and di is ion skin depth. A similar algebraic decay law applies to whistler perturbations in the limit k^2di^2>>1. In a non-uniform plasma it is found that the spatially-integrated damping rate due to phase mixing is lower in Hall MHD than it is in MHD, but the reduction in the damping rate, which can be attributed to the effects of wave dispersion, tends to zero in both the weak and strong phase mixing limits.

A Proposed Test of Extended MHD Plasmas by Merging of Lithium Ion Plasmas with Pure Electron Plasmas

Recently, extended MHD plasmas have been proposed, especially in both theoretical and computational fields of plasma physics. To test those experimentally, we propose a new project using two nonneutral plasmas: pure ion and electron plasmas. The experiment is performed on a linear machine in which a pair of positive and negative electrostatic potential wells is externally produced. In the positive potential well, an 7Li+ plasma is confined, while an electron plasma in the negative potential one. Then, those nonneutral plasmas are merged into an extended MHD plasma. The most remarkable advantage to employing nonneutral plasmas is that the ion skin depth, that is a typical scale length of the extended MHD plasmas, can be extended to the plasma radius. This actually alleviates experimental difficulties in diagnosing properties of the extended MHD plasmas. With precisely controlling densities of both pure 7Li+ ion and electron plasmas, the proposed method may explore an unrevealed research field of extended MHD plasmas.

Extension of the electron dissipation region in collisionless Hall magnetohydrodynamics reconnection

This paper presents Sweet–Parker type scaling arguments in the context of hyper-resistive Hall magnetohydrodynamics. Numerical experiments suggest that both cusplike and modestly more extended geometries are realizable. However, the length of the electron dissipation region, which is taken as a parameter by several recent studies, is found to depend explicitly on the level of hyper-resistivity. Furthermore, although hyper-resistivity can produce more extended electron dissipation regions, the length of the region remains smaller than one ion skin depth for the largest values of hyper-resistivity considered here, significantly shorter than current sheets seen in many recent kinetic studies. The length of the electron dissipation region is found to depend on electron inertia as well, scaling like (me/mi)3/8. However, the thickness of the region appears to scale similarly, so that the aspect ratio is at most very weakly dependent on (me/mi).

Relative timing of substorm processes as derived from multifluid/multiscale simulations: Internally driven substorms

The role of tail reconnection in initiating substorm onset remains highly controversial. Multifluid/multiscale simulations are used to examine this problem with the unique capability of being able to resolve ion skin depth and ion cyclotron processes within a very thin tail current sheet within a global magnetosphere. It is shown that, consistent with the near‐Earth neutral line model, a thin current sheet forms during the growth phase with the eventual formation of an X line and the ejection of a plasmoid. However, these processes do not produce substorm onset but are precursors to onset. The modeling indicates that in the wake of the plasmoid, a Y line forms within which there is the intermittent generation of flux ropes that can propagate either earthward or tailward with equal probability. The intensity and size of the flux ropes are seen to increase in time up to substorm onset. Depending on the size of the earthward moving flux rope, pseudobreakup or substorm onset occurs when the energy within the earthward moving flux rope is dissipated against the inner edge of the plasma sheet. This interaction leads to rapid (1 min) dipolarization, magnetospheric injection of energetic particles, and intensification of the nightside auroral currents that expand in local time and to higher latitudes. These processes are consistent with the current disruption model where onset occurs as a direct consequence of processes occurring at the inner edge of the plasma sheet. Ionospheric outflows and their energization with the thin current sheet play important roles in the buildup of energy in the plasma sheet that eventually produces substorm onset and drives breakup.

Prevalence of extended reconnection X‐lines in the solar wind at 1 AU

A survey of Wind and ACE data has been performed to address the generality of previous reports of extremely extended reconnection X‐lines in the solar wind. We have studied 51 events in which both Wind and ACE detected the same solar wind current sheets and one of the spacecraft observed a reconnection exhaust. In 50 of the 51 events, the other spacecraft also observed essentially the same reconnection signatures, and all but one of the jets pointed in the same direction at both spacecraft. In 7 of these cases, the X‐line extended more than 100 Earth radii (or 104 ion skin depths). Our findings strongly indicate that reconnection X‐lines in large‐scale current sheets (with magnetic shear >∼70°) are fundamentally extended, and not patchy and randomly distributed in space. Finally, the extended reconnecting current sheets are typically highly planar, indicating no significant current sheet warping associated with the reconnection process.

Multispacecraft observations of the electron current sheet, neighboring magnetic islands, and electron acceleration during magnetotail reconnection

Open questions concerning structures and dynamics of diffusion regions and electron acceleration in collisionless magnetic reconnection are addressed based on data from the four-spacecraft mission Cluster and particle-in-cell simulations. Using time series of electron distribution functions measured by the four spacecraft, distinct electron regions around a reconnection layer are mapped out to set the framework for studying diffusion regions. A spatially extended electron current sheet (ecs), a series of magnetic islands, and bursts of energetic electrons within islands are identified during magnetotail reconnection with no appreciable guide field. The ecs is collocated with a layer of electron-scale electric fields normal to the ecs and pointing toward the ecs center plane. Both the observed electron and ion densities vary by more than a factor of 2 within one ion skin depth north and south of the ecs, and from the ecs into magnetic islands. Within each of the identified islands, there is a burst of suprathermal electrons whose fluxes peak at density compression sites [L.-J. Chen et al., Nat. Phys. 4, 19 (2008)] and whose energy spectra exhibit power laws with indices ranging from 6 to 7.3. These results indicate that the in-plane electric field normal to the ecs can be of the electron scale at certain phases of reconnection, electrons and ions are highly compressible within the ion diffusion region, and for reconnection involving magnetic islands, primary electron acceleration occurs within the islands.

Parametric analysis of the two-fluid tearing instability

A two-fluid analysis of the current driven tearing instability is presented. It concentrates on the systematic investigation of the physics related to the plasma compressibility and to the contribution of the Hall term to the inductive electric field, for arbitrary values of the ion skin depth and of the magnitude of the magnetic guide field. The plasma compressibility is treated consistently for a wide range of the plasma beta that excludes only the extremely cold limit where the mode growth rate would become sonic or supersonic. Conversely, the effects associated with the finite ion gyroradius and the equilibrium density and temperature gradients are neglected. Seven parametric regions are identified, characterized by the relative strengths of the Hall and beta parameters. Five of them are amenable to asymptotic analyses yielding analytic dispersion relations and one allows a semi-analytic treatment. The singular, multi-layer structure of the tearing mode and the conditions under which the different components of the magnetic field diffuse are shown in detail for each of those parametric regions.

ANALYTICAL DESCRIPTION OF STEADY MAGNETIC RECONNECTION IN HALL MAGNETOHYDRODYNAMICS

Steady magnetic reconnection in the framework of incompressible Hall magnetohydrodynamics is considered. The principal role of the Hall effect in the formation of the structure of the reconnecting current sheet is emphasized. Analytical expressions for the velocity and the magnetic field in the sheet are derived, based on the approximation of a weak two dimensionality of the planar components of the solution. The analytical solution illustrates key features of Hall magnetic reconnection, including the reconnection rate enhancement and the sheet thinning due to the Hall effect, the presence of a quadrupolar axial (out-of-the-plane) magnetic field that controls the geometry of the reconnecting planar magnetic field, and the dynamical coupling of the axial and planar components of the solution, with the coupling strength that is proportional to the ion skin depth. Scalings for the sheet thickness, width, and the reconnection inflow and outflow speeds in terms of the electric resistivity and the axial magnetic field are determined. Implications of the results for fast magnetic reconnection in a weakly collisional plasma of the solar corona are discussed.

Spectral properties of electromagnetic turbulence in plasmas

Abstract. We report on the nonlinear turbulent processes associated with electromagnetic waves in plasmas. We focus on low-frequency (in comparison with the electron gyrofrequency) nonlinearly interacting electron whistlers and nonlinearly interacting Hall-magnetohydrodynamic (H-MHD) fluctuations in a magnetized plasma. Nonlinear whistler mode turbulence study in a magnetized plasma involves incompressible electrons and immobile ions. Two-dimensional turbulent interactions and subsequent energy cascades are critically influenced by the electron whisters that behave distinctly for scales smaller and larger than the electron skin depth. It is found that in whistler mode turbulence there results a dual cascade primarily due to the forward spectral migration of energy that coexists with a backward spectral transfer of mean squared magnetic potential. Finally, inclusion of the ion dynamics, resulting from a two fluid description of the H-MHD plasma, leads to several interesting results that are typically observed in the solar wind plasma. Particularly in the solar wind, the high-time-resolution databases identify a spectral break at the end of the MHD inertial range spectrum that corresponds to a high-frequency regime. In the latter, turbulent cascades cannot be explained by the usual MHD model and a finite frequency effect (in comparison with the ion gyrofrequency) arising from the ion inertia is essentially included to discern the dynamics of the smaller length scales (in comparison with the ion skin depth). This leads to a nonlinear H-MHD model, which is presented in this paper. With the help of our 3-D H-MHD code, we find that the characteristic turbulent interactions in the high-frequency regime evolve typically on kinetic-Alfvén time-scales. The turbulent fluctuation associated with kinetic-Alfvén interactions are compressive and anisotropic and possess equipartition of the kinetic and magnetic energies.