Hall Magnetohydrodynamics Model Research Articles

Counter‐Helical Magnetic Flux Ropes From Magnetic Reconnections in Space Plasmas

AbstractMagnetic flux ropes are ubiquitous in various space environments, including the solar corona, interplanetary solar wind, and planetary magnetospheres. When these flux ropes intertwine, magnetic reconnection may occur at the interface, forming disentangled new ropes. Some of these newly formed ropes contain reversed helicity along their axes, diverging from the traditional flux rope model. We introduce new observations and interpretations of these newly formed flux ropes from existing Hall Magnetohydrodynamics model results. We first examine the time‐varying local magnetic field direction at the impact interface to assess the likelihood of reconnection. Then we investigate the electric current system to describe the evolution of these structures, which potentially accelerate particles and heat the plasma. This study offers novel insights into the dynamics of space plasmas and suggests a potential solar wind heating source, calling for further synthetic observations.

Analytic Hall magnetohydrodynamics toroidal equilibria via the energy-Casimir variational principle

Equilibrium equations for magnetically confined, axisymmetric plasmas are derived by means of the energy-Casimir variational principle in the context of Hall magnetohydrodynamics (MHD). This approach stems from the noncanonical Hamiltonian structure of Hall MHD, the simplest, quasineutral two-fluid model that incorporates contributions due to ion Hall drifts. The axisymmetric Casimir invariants are used, along with the Hamiltonian functional to apply the energy-Casimir variational principle for axisymmetric two-fluid plasmas with incompressible ion flows. This results in a system of equations of the Grad–Shafranov–Bernoulli (GSB) type with four free functions. Two families of analytic solutions to the GSB system are then calculated, based on specific choices for the free functions. These solutions are subsequently applied to Tokamak-relevant configurations using proper boundary shaping methods. The Hall MHD model predicts a departure of the ion velocity surfaces from the magnetic surfaces which are frozen in the electron fluid. This separation of the characteristic surfaces is corroborated by the analytic solutions calculated in this study. The equilibria constructed by these solutions exhibit favorable characteristics for plasma confinement, for example they possess closed and nested magnetic and flow surfaces with pressure profiles peaked at the plasma core. The relevance of these solutions to laboratory and astrophysical plasmas is finally discussed, with particular focus on systems that involve length scales on the order of the ion skin depth.

Global Hall MHD Simulations of Mercury's Magnetopause Dynamics and FTEs Under Different Solar Wind and IMF Conditions

AbstractMercury possesses a miniature but dynamic magnetosphere driven primarily by the solar wind through magnetic reconnection. A prominent feature of the dayside magnetopause reconnection that has been frequently observed is flux transfer events (FTEs), which are thought to be an important player in driving the global convection at Mercury. Using the BATSRUS Hall magnetohydrodynamics model with coupled planetary interior, we have conducted a series of global simulations to investigate the generation and characteristics of FTEs under different solar wind Alfvénic Mach numbers (MA) and interplanetary magnetic field (IMF) orientations. An automated algorithm was also developed to consistently identify FTEs and extract their key properties from the simulations. In all simulations driven by steady upstream conditions, FTEs are formed quasi‐periodically with recurrence time ranging from 2 to 9 s, and their characteristics vary in time as they evolve and interact with the surrounding plasma and magnetic field. Our statistical analysis of the simulated FTEs reveals that the key properties of FTEs, including spatial size, traveling speed and core field strength, all exhibit notable dependence on the solar wind MA and IMF orientation, and the trends identified from the simulations are generally consistent with previous MErcury Surface Space ENvironment, GEochemistry, and Ranging observations. It is also found that FTEs formed in the simulations contribute about 3%–13% of the total open flux created at the dayside magnetopause that participates in the global circulation, suggesting that FTEs indeed play an important role in driving the Dungey cycle at Mercury.

Blowup of Dyadic MHD Models with Forward Energy Cascade

Abstract A particular type of dyadic model for the magnetohydrodynamics (MHD) with dominating forward energy cascade is studied. The model includes intermittency dimension $\delta $ in the nonlinear scales. It is shown that when $\delta $ is small, positive solution with large initial data for either the dyadic MHD or the dyadic Hall MHD model develops blowup in finite time. Moreover, for a class of positive initial data with large velocity components and small magnetic field components, we prove that there exists a positive solution that blows up at a finite time.

Investigation of the fast magnetosonic wave excited by the Alfvén wave phase mixing by using the Hall–MHD model in inhomogeneous plasma

The inhomogeneity is introduced by a nonzero density gradient which separates the plasma into two different regions where plasma density are constant. The Alfvén waves, the phase mixing and the fast magnetosonic wave are excited by the boundary condition in inhomogeneous magnetized plasma. By using the Hall–magnetohydrodynamics (MHD) model, it is found that there are Alfvén waves in the homogeneous regions, while the phase mixing appears in the inhomogeneous region. The interesting result is that a fast magnetosonic wave is excited in a different direction which has a nonzero angle between the wave propagation direction and the direction of the background magnetic field. The dependence of the propagation direction of the excited fast magnetosonic wave and its strength of the magnetic field on the plasma parameters are given numerically. The results show that increasing both the driving frequency and the ratio of magnetic pressure to thermal pressure will increase the acceleration of the electrons. The electron acceleration also depends on the inhomogeneity parameters.

Temporal Evolution of Flux Rope/Tube Entanglement in 3‐D Hall MHD Simulations

AbstractAt the Earth’s magnetopause, flux tubes observed by the Magnetospheric Multiscale (MMS) spacecraft in “entangled” pairs have been interpreted as a precursory stage to the formation of a new pair of flux tubes by magnetic reconnection, of which one reconnected tube joins the magnetosphere. Understanding the connectivity of these tubes before and after the entanglement is essential to understanding the transport of particles and energy between the magnetosphere and the solar wind. In this study, we use a three‐dimensional Hall Magnetohydrodynamics (MHD) model to simulate the interaction of two entangled flux tubes in the ambient plasma. Four types of interactions are simulated: Two types of magnetic field geometry (flux tube‐flux tube and flux rope‐flux rope) are tested separately, each under two different boundary conditions. With the boundary condition that drives the interaction with ambient flow, magnetic reconnection transforms the two tubes/ropes into new pairs. The process is performed under plasma conditions comparable to those of such events identified in recent MMS observations. The detailed three‐dimensional evolution is shown at representative stages, with key parameters shown across the entanglement interface. The shape of the central current sheet and evolution of magnetic field curvature are also discussed. Our study supports the feasibility of reconnection between entangled flux tubes, recognizes the importance of ambient plasma conditions for the completion of such processes, and quantifies how such structures evolve to modify the solar wind‐geomagnetic field interaction. In addition, this model is applicable to flux rope interactions in the solar corona.

Impulse-driven Richtmyer-Meshkov instability in Hall-magnetohydrodynamics

We utilize the incompressible, Hall-magnetohydrodynamics (MHD) model for conducting fluids to investigate the effect of Hall current on the stability of an impulsively accelerated, perturbed density interface, or contact discontinuity (CD) separating two fluids in the presence of a background magnetic field. This is used as a simple model, in a conducting fluid, of a Richtmyer-Meshkov type flow that is characterized in a neutral fluid by a shock-wave-density-interface interaction. Two versions of the Hall-MHD equations are explored. In the first, the ions are treated as an incompressible fluid but the electron gas retains its compressibility, while for the second version the incompressible limit for both species is invoked. The linearized equations of motion are first formulated for a sinusoidal interface perturbation and then solved as an initial-value problem using a Laplace transform method with general numerical inversion but with analytical inversion for some limiting-parameter cases. While the field equations are identical for both Hall-MHD models, the CD-jump conditions differ leading to qualitatively similar but quantitatively different CD dynamics. For both models, the presence of the magnetic field is found to suppress the incipient interfacial growth associated with neutral-gas, Richtmyer-Meshkov instability (RMI). When the ion skin depth is finite, the vorticity dynamics that drive the suppression of the RMI differ markedly from the ideal MHD, RMI flow. On the interface, the Hall-MHD description allows the presence of a tangential slip velocity which leads to finite circulation deposition. Away from the interface, vorticity is produced by the perturbed magnetic fields and transported to infinity by a dispersive wave system. This leads to decay of the velocity slip at the interface with the effect that interface growth remains bounded but distorted by damped oscillations associated with the ion cyclotron effect. The flow behavior for several limits of the ion skin depth and the Larmor radius is explored. Specific comparisons with the results from both models against ideal MHD are presented.

Modeling aperiodic magnetospheric oscillations.

We present an analysis of a Hall-magnetohydrodynamics model of the magnetospheric plasma with finite Larmor radius effect. Through a bifurcation analysis of the resultant nonlinear system, we show that this nonlinear model does not possess a limit cycle, which rules out regular periodic oscillations with constant amplitude. However, it does result in a train of magnetosonic solitons, localized in space, with amplitudes increasing in time, which are largely in agreement with what is usually observed in the magnetopause region. We call these oscillations aperiodic magnetospheric oscillations. We emphasize that most of the train of solitary oscillations observed by the Cluster fleet and other spacecrafts do not have constant amplitudes: they either continuously increase or decrease. These train of solitons with nonconstant amplitudes is a primary solution of our model.

Analytical studies on the evolution processes of rarefied deuterium plasma shell Z-pinch by PIC and MHD simulations**Projected supported by the National Natural Science Foundation of China (Grant Nos. 11675025, 11135007, and 11405012).

In this paper, we analytically explore the magnetic field and mass density evolutions obtained in particle-in-cell (PIC) and magnetohydrodynamics (MHD) simulations of a rarefied deuterium shell Z-pinch and compare those results, and also we study the effects of artificially increased Spitzer resistivity on the magnetic field evolution and Z-pinch dynamic process in the MHD simulation. There are significant differences between the profiles of mass density in the PIC and MHD simulations before 45 ns of the Z-pinch in this study. However, after the shock formation in the PIC simulation, the mass density profile is similar to that in the MHD simulation in the case of using multiplier 2 to modify the Spitzer resistivity. Compared with the magnetic field profiles of the PIC simulation of the shell, the magnetic field diffusion has still not been sufficiently revealed in the MHD simulation even though their convergence ratios become the same by using larger multipliers in the resistivity. The MHD simulation results suggest that the magnetic field diffusion is greatly enhanced by increasing the Spitzer resistivity used, which, however, causes the implosion characteristic to change from shock compression to weak shock, even shockless evolution, and expedites the expansion of the shell. Too large a multiplier is not suggested to be used to modify the resistivity in some Z-pinch applications, such as the Z-pinch driven inertial confinement fusion (ICF) in a dynamic hohlraum. Two-fluid or Hall MHD model, even the PIC/fluid hybrid simulation would be considered as a suitable physical model when there exist the plasma regions with very low density in the simulated domain.

Alfvénic localized structures in partially ionized plasmas

The existence and dynamics of Alfvénic localized structures are investigated in partially ionized plasmas. We have employed the Hall magnetohydrodynamics model for partially ionized plasmas and shown that the evolution of a weakly nonlinear and weakly dispersive Alfvén wave is governed by a derivative nonlinear Schrödinger (DNLS) type equation. In the Hall effect domination limit, this equation reduces to a standard DNLS equation that possesses localized solutions in the form of solitons and rogue waves. The dependence of the profile of these structures on the Hall parameter is addressed. When the ohmic and ambipolar effects are small but finite in comparison to the Hall effect, the evolution equation takes the form of a perturbed DNLS equation. In this limit, the dynamics of envelope soliton solution is examined by means of the soliton perturbation method, the moment method, to be precise.

Comparison of multi-fluid moment models with particle-in-cell simulations of collisionless magnetic reconnection

We introduce an extensible multi-fluid moment model in the context of collisionless magnetic reconnection. This model evolves full Maxwell equations and simultaneously moments of the Vlasov-Maxwell equation for each species in the plasma. Effects like electron inertia and pressure gradient are self-consistently embedded in the resulting multi-fluid moment equations, without the need to explicitly solving a generalized Ohm's law. Two limits of the multi-fluid moment model are discussed, namely, the five-moment limit that evolves a scalar pressures for each species and the ten-moment limit that evolves the full anisotropic, non-gyrotropic pressure tensor for each species. We first demonstrate analytically and numerically that the five-moment model reduces to the widely used Hall magnetohydrodynamics (Hall MHD) model under the assumptions of vanishing electron inertia, infinite speed of light, and quasi-neutrality. Then, we compare ten-moment and fully kinetic particle-in-cell (PIC) simulations of a large scale Harris sheet reconnection problem, where the ten-moment equations are closed with a local linear collisionless approximation for the heat flux. The ten-moment simulation gives reasonable agreement with the PIC results regarding the structures and magnitudes of the electron flows, the polarities and magnitudes of elements of the electron pressure tensor, and the decomposition of the generalized Ohm's law. Possible ways to improve the simple local closure towards a nonlocal fully three-dimensional closure are also discussed.

Two-way coupling of a global Hall magnetohydrodynamics model with a local implicit particle-in-cell model

Computational models based on a fluid description of the plasma, such as magnetohydrodynamic (MHD) and extended magnetohydrodynamic (XMHD) codes are highly efficient, but they miss the kinetic effects due to the assumptions of small gyro radius, charge neutrality, and Maxwellian thermal velocity distribution. Kinetic codes can properly take into account the kinetic effects, but they are orders of magnitude more expensive than the fluid codes due to the increased degrees of freedom. If the fluid description is acceptable in a large fraction of the computational domain, it makes sense to confine the kinetic model to the regions where kinetic effects are important. This coupled approach can be much more efficient than a pure kinetic model. The speed up is approximately the volume ratio of the full domain relative to the kinetic regions assuming that the kinetic code uses a uniform grid. This idea has been advocated by [1] but their coupling was limited to one dimension and they employed drastically different grid resolutions in the fluid and kinetic models.We describe a fully two-dimensional two-way coupling of a Hall MHD model BATS-R-US with an implicit Particle-in-Cell (PIC) model iPIC3D. The coupling can be performed with identical grid resolutions and time steps. We call this coupled computational plasma model MHD-EPIC (MHD with Embedded PIC regions). Our verification tests show that MHD-EPIC works accurately and robustly. We show a two-dimensional magnetosphere simulation as an illustration of the potential future applications of MHD-EPIC.

Modeling of strongly collimated jets produced by high energy density plasmas on COBRA

Jet collimation in astrophysical plasmas and in the laboratory has recently received much attention. When the magnetohydrodynamics (MHD) model is used to represent both systems, scale invariance allows for the simple extension of the parameters encountered in laboratory experiments to much larger systems, like astrophysical outflows. However, the validation of such a model requires a precise comparison of numerical simulations with experimental data. Using radial foils as an experimental setup to generate strongly collimated plasma jets, we show that the Hall MHD model included in the PERSEUS code does well to capture the plasma dynamics of collimated jets, even with restrictive conditions such as a constant ionization number and the neglect of normally important transport processes. Very importantly, we show that jet collimation is not only the result of magnetic forces, but also converging radial flows.

Structure of intermediate shocks in collisionless anisotropic Hall-magnetohydrodynamics plasma models

The existence of discontinuities within the double-adiabatic Hall-magnetohydrodynamics (MHD) model is discussed. These solutions are transitional layers where some of the plasma properties change from one equilibrium state to another. Under the assumption of traveling wave solutions with velocity C and propagation angle θ with respect to the ambient magnetic field, the Hall-MHD model reduces to a dynamical system and the waves are heteroclinic orbits joining two different fixed points. The analysis of the fixed points rules out the existence of rotational discontinuities. Simple considerations about the Hamiltonian nature of the system show that, unlike dissipative models, the intermediate shock waves are organized in branches in parameter space, i.e., they occur if a given relationship between θ and C is satisfied. Electron-polarized (ion-polarized) shock waves exhibit, in addition to a reversal of the magnetic field component tangential to the shock front, a maximum (minimum) of the magnetic field amplitude. The jumps of the magnetic field and the relative specific volume between the downstream and the upstream states as a function of the plasma properties are presented. The organization in parameter space of localized structures including in the model the influence of finite Larmor radius is discussed.

Alfven wave interactions within the Hall-MHD description

AbstractWe show that comparatively simple expressions for the Alfven wave coupling coefficients can be deduced from the well-known Hall-magnetohydrodynamics (MHD) model equations.

Generalized shock conditions and the contact discontinuity in the Hall-magnetohydrodynamics model

It is shown that shocks and contact discontinuities in the Hall-magnetohydrodynamics (HMHD) model must satisfy solvability conditions that replace some of the familiar Rankine-Hugoniot jump conditions when the latter do not apply due to singular behavior of fluxes of conserved quantities. Some of these conditions depend on the larger topology of the plasma and magnetic field and are not merely “local.” The contact discontinuity which separates two adjoining plasma regions or plasma and vacuum regions is the simplest case where the new jump conditions are applicable and is discussed for a toroidal plasma with sheared magnetic field such as the tokamak, but with no initial mass flow. It is proven that a static discontinuous tokamak-like equilibrium is linearly stable in the HMHD model if it is linearly stable within the ideal magnetohydrodynamics model, provided that the electron pressure depends only on the density, and some other restrictions on the ratio of pressure to density gradients also apply. When the electron pressure does depend on two thermodynamic variables, a sufficient condition for Hall-MHD plasma stability is derived as well.

Effects of out-of-plane shear flows on fast reconnection in a two-dimensional Hall magnetohydrodynamics model

Effects of out-of-plane shear flows on fast magnetic reconnection in Hall magnetohydrodynamics approximation are studied in a slab model with an initial Harris sheet equilibrium. It is found that the out-of-plane shear flows can also generate a series of out-of-plane magnetic perturbations that significantly modify the out-of-plane quadrupolar magnetic perturbation induced by the Hall effect in magnetic reconnection. The modification to out-of-plane magnetic perturbations then considerably affects the magnetic reconnection process. Particularly, flows along the X-line can either enhance or reduce the reconnection rate, even altering the X-point to an O-point and resulting in a secondary island. The impact on satellite observations is also discussed.

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.

Compressible Hall magnetohydrodynamics in a strong magnetic field

Plasma dynamics becomes anisotropic in the presence of a strong background magnetic field, a feature that may be exploited to yield reduced fluid models. The reduced Hall-magnetohydrodynamics model derived in a recent work by Gomez et al. [Phys. Plasmas 15, 102303 (2008)], reflecting two-fluid effects such as the Hall current and the electron pressure, is extended to account for a crucial aspect of the role of the plasma compressibility, i.e., the compression of the guide field. This reduced model constitutes therefore a description of the two-fluid plasma dynamics in a strong external magnetic field, which can be used also for values of the plasma pressure parameter β of the order of unity or smaller.

On Hall magnetohydrodynamics equilibria

Steady states are studied in the framework of the ideal Hall magnetohydrodynamics (HMHD) model in arbitrary and axisymmetric geometries. In arbitrary geometry, conditions are found under which certain magnetohydrodynamics (MHD) equilibrium solutions can also satisfy the HMHD equations. For axisymmetric plasmas reduced equations are derived for uniform electron temperatures on magnetic surfaces and either barotropic ions or incompressible ion flows. The Hall and electron pressure gradient terms result in a deviation of the magnetic from the ion velocity surfaces, and consequently, the axisymmetric equilibria obey a set of coupled partial differential equations: one for the poloidal magnetic flux function and the other for a flux function labeling the ion velocity surfaces. Furthermore, the characteristics of certain classes of axisymmetric steady states with side conditions, as flows parallel to the magnetic field or purely poloidal incompressible flows, are identified and compared with respective MHD equilibria. Unlike in the frame of MHD, steady states with parallel axisymetric flows must be incompressible and equilibria with purely poloidal incompressible flows are possible. Certain analytic axisymmetric solutions are also constructed.