Hall Magnetohydrodynamic Simulations Research Articles

LAPS: An MPI-parallelized 3D pseudo-spectral Hall-MHD simulation code incorporating the expanding box model

Numerical simulations have been an increasingly important tool in space physics. Here, we introduce an open-source three-dimensional compressible Hall-Magnetohydrodynamic (MHD) simulation code LAPS (UCLA-Pseudo-Spectral, https://github.com/chenshihelio/LAPS). The code adopts a pseudo-spectral method based on Fourier Transform to evaluate spatial derivatives, and third-order explicit Runge-Kutta method for time advancement. It is parallelized using Message-Passing-Interface (MPI) with a “pencil” parallelization strategy and has very high scalability. The Expanding-Box-Model is implemented to incorporate spherical expansion effects of the solar wind. We carry out test simulations based on four classic (Hall)-MHD processes, namely, 1) incompressible Hall-MHD waves, 2) incompressible tearing mode instability, 3) Orszag-Tang vortex, and 4) parametric decay instability. The test results agree perfectly with theory predictions and results of previous studies. Given all its features, LAPS is a powerful tool for large-scale simulations of solar wind turbulence as well as other MHD and Hall-MHD processes happening in space.

Comparative simulations of Kelvin–Helmholtz induced magnetic reconnection at the Earth's magnetospheric flanks

This study presents three-dimensional (3D) resistive Hall-magnetohydrodynamic simulations of the Kelvin–Helmholtz instability (KHI) dynamics at Earth's magnetospheric flanks during northward interplanetary magnetic field periods. By comparing two simulations with and without initial magnetic shear, we analyze the impact of distinct magnetic field orientations on plasma dynamics and magnetic reconnection events taking into account 3D mechanisms, such as KHI high latitude stabilization. The identical nature of the simulations, except for the presence/absence of an initial magnetic shear, enables, for the first time, a complete and coherent comparative analysis of the latitudinal distribution of KH vortices, current sheets, reconnection events, and the evolution of the mixing layer. In one configuration, a uniform magnetic field leads to double mid-latitude reconnection (MLR), while in the other, magnetic shear induces both type I vortex-induced reconnection (VIR) and MLR. Notably, the type I VIR observed in this second scenario results from the combined action of line advection and vortex-induced current sheet pinching (the classic mechanism driving two-dimensional type I VIR). Of particular importance is our quantification of newly closed field lines that experienced double reconnection, ultimately becoming embedded in solar wind plasma at low latitudes while remaining connected to magnetospheric plasma at high latitudes. The varying abundance of such lines in the two simulations holds implications for plasma transport at the magnetopause.

Hall-magnetohydrodynamic simulations of X-ray photoevaporative protoplanetary disc winds

ABSTRACT Understanding the evolution and dispersal via energetic stellar radiation of protoplanetary discs (PPDs) is a prominent challenge in astrophysics. It has been established that X-ray luminosity from the central protostar can significantly heat the surface of the disc, causing powerful photoevaporative winds that eject a considerable fraction of the disc’s mass. Recent work in the field has moreover shown the importance of global PPD simulations that simultaneously take into account non-ideal magnetohydrodynamic (MHD) effects and detailed thermochemistry. In this paper, we combine these two aspects and figure out how they interact. Focus is put on the Hall Effect (HE) and the impact it has on the overall field topology and mass-loss/accretion rates. Utilizing a novel X-ray temperature parametrization, we perform 2D-axisymmetric MHD simulations with the nirvana-iii fluid code, covering all non-ideal effects. We find that, in the aligned orientation, the HE causes prominent inward displacement of the poloidal field lines that increase the accretion rate through a laminar Maxwell stress. We find that outflows are mainly driven by photoevaporation – unless the magnetic field strength is considerable (i.e. βp ≤ 103) or the X-ray luminosity low enough (i.e. log LX ≤ 29.3). Inferred mass-loss rate are in the range of the expected values 10−8–$10^{-7}\, M_\odot \, {\rm yr}^{-1}$. Moreover, we performed pure hydrodynamic (HD) runs and compared them with the equivalent MHD runs. We concluded that the magnetic field does indeed contribute to the mass-loss rate, albeit only discernibly so for low enough LX (i.e. log LX ≤ 30.8).

Deflection of O2 + Ion Flow by Magnetic Fields in the Martian Ionosphere

The effect of the Martian crustal magnetic field on ion escape is the focus of considerable interest. Directions of magnetic fields near Mars determined by the interaction between Mars’ crustal and interplanetary magnetic fields have been suggested to play a significant role on ion transport around Mars. In this study we investigate the physical mechanism of deflection of ion flow in two typical magnetic field orientations at the horizontal plane in the Martian ionosphere by performing 3D multifluid Hall magnetohydrodynamic simulations. Cross validation of the simulation results from two cases with the G110 crustal field model and equivalent source dipole model reveals that due to the Hall electric force, ion flow tends to be accelerated eastwards in the region occupied by outward magnetic fields, and westwards in the region with inward magnetic fields. These results are helpful for understanding the impact of magnetic fields on the deflection of ionospheric ions in the Martian space environment.

Hall Magnetohydrodynamics Simulations of Hall-Physics-Driven Effects in Low-Density Plasmas Surrounding Dense Z-Pinch Liners

Hall Magnetohydrodynamics Simulations of Hall-Physics-Driven Effects in Low-Density Plasmas Surrounding Dense Z-Pinch Liners

Magnetotail reconnection asymmetries in an ion-scale, Earth-like magnetosphere

Abstract. We use a newly developed global Hall magnetohydrodynamic (MHD) code to investigate how reconnection drives magnetotail asymmetries in small, ion-scale magnetospheres. Here, we consider a magnetosphere with a similar aspect ratio to Earth but with the ion inertial length (δi) artificially inflated by a factor of 70: δi is set to the length of the planetary radius. This results in a magnetotail width on the order of 30 δi, slightly smaller than Mercury's tail and much smaller than Earth's with respect to δi. At this small size, we find that the Hall effect has significant impact on the global flow pattern, changing from a symmetric, Dungey-like convection under resistive MHD to an asymmetric pattern similar to that found in previous Hall MHD simulations of Ganymede's subsonic magnetosphere as well as other simulations of Mercury's using multi-fluid or embedded kinetic physics. We demonstrate that the Hall effect is sufficient to induce a dawnward asymmetry in observed dipolarization front locations and find quasi-periodic global-scale dipolarizations under steady, southward solar wind conditions. On average, we find a thinner current sheet dawnward; however, the measured thickness oscillates with the dipolarization cycle. During the flux-pileup stage, the dawnward current sheet can be thicker than the duskward sheet. This could be an explanation for recent observations that suggest Mercury's current sheet is actually thicker on the duskside: a sampling bias due to a longer lasting “thick” state in the sheet.

Spectral Transfer and Kármán–Howarth–Monin Equations for Compressible Hall Magnetohydrodynamics

Abstract We derive two new forms of the Kármán–Howarth–Monin (KHM) equation for decaying compressible Hall magnetohydrodynamic (MHD) turbulence. We test them on results of a weakly compressible, 2D, moderate-Reynolds-number Hall MHD simulation and compare them with an isotropic spectral transfer (ST) equation. The KHM and ST equations are automatically satisfied during the whole simulation owing to the periodic boundary conditions and have complementary cumulative behavior. They are used here to analyze the onset of turbulence and its properties when it is fully developed. These approaches give equivalent results characterizing the decay of the kinetic + magnetic energy at large scales, the MHD and Hall cross-scale energy transfer/cascade, the pressure dilatation, and the dissipation. The Hall cascade appears when the MHD one brings the energy close to the ion inertial range and is related to the formation of reconnecting current sheets. At later times, the pressure dilatation energy exchange rate oscillates around zero, with no net effect on the cross-scale energy transfer when averaged over a period of its oscillations. A reduced 1D analysis suggests that all three methods may be useful to estimate the energy cascade rate from in situ observations.

Axial magnetic flux amplification in Hall-magnetohydrodynamic simulations of externally magnetized z-pinches

It is shown that externally magnetized gas-puff z-pinches under compression can exhibit robust axial flux amplification under suitable axial boundary conditions. This effect relies upon the Hall term in the generalized Ohm's law to generate azimuthal currents in the presence of a driving axial electric field. Under dynamic compression, the total current tends to flow in a mostly force-free boundary layer, separating the predominately azimuthal field outside the layer and the predominately axial field inside the layer. The effect only appears to occur if the axial boundaries allow for outflow or absorption of electromagnetic energy. The effect is mitigated by imposing either periodic or conducting axial boundary conditions. A semi-analytic equilibrium analysis agrees with steady-state solutions of the time-dependent electron-magnetohydrodynamic equations and provides an estimate of the scaling of the boundary layer as well as suggesting a scenario for the formation of the boundary layer. When operative, the effect can significantly impede plasma compression due to the increase in axial flux that diffuses into the pre-compressed plasma or through the presence of conductors that inhibit movement of the generated axial flux. Several facilities have noted unusual implosion behavior in z-pinch experiments with applied axial fields that does not appear to be explainable within the standard magnetohydrodynamic model. It is suggested that these experiments can be explained by the axial flux amplification and concentration effect.

The Convective Electric Field Influence on the Cold Plasma and Diamagnetic Cavity of Comet 67P

Abstract We studied the distribution of cold electrons (<1 eV) around comet 67P/Churyumov–Gerasimenko with respect to the solar wind convective electric field direction. The cold plasma was measured by the Langmuir Probe instrument and the direction of the convective electric field conv = − × was determined from magnetic field ( ) measurements inside the coma combined with an assumption of a purely radial solar wind velocity . We found that the cold plasma is twice as likely to be observed when the convective electric field at Rosetta’s position is directed toward the nucleus (in the − conv hemisphere) compared to when it is away from the nucleus (in the + conv hemisphere). Similarly, the diamagnetic cavity, in which previous studies have shown that cold plasma is always present, was also found to be observed twice as often when in the − conv hemisphere, linking its existence circumstantially to the presence of cold electrons. The results are consistent with hybrid and Hall magnetohydrodynamic simulations as well as measurements of the ion distribution around the diamagnetic cavity.

Evolution of Kelvin–Helmholtz Instability on the Venusian Ionopause with the Influence of Hall Effect

Abstract It has been demonstrated that Kelvin–Helmholtz (KH) instability is an essential large-scale mechanism to generate plasma waves along the boundary layers of Venus. In this paper, evolution of KH instability on the Venusian ionopause with the influence of the Hall effect was investigated under Hall magnetohydrodynamic (MHD) simulations. Linear and nonlinear physical behaviors of KH instability with different wavelengths of perturbation, magnetic field configurations, and ion inertial lengths were studied. Numerical results indicate that, for perturbation with short wavelength, the circulation area of matter becomes small and the driving force is weakened. The combined effect of short wavelength and the antiparallel magnetic field leads to longer linear growth time, while the antiparallel magnetic field tends to enlarge the pressure gradient. As for the moderate wavelength of perturbation, the growth rate reaches its peak value, whereas the maximal y component of total kinetic energy increases significantly with the wavelength. Hall MHD simulations indicate that the Hall effect does not change the growth rates for different ion inertial lengths at all. However, the Hall effect has a depression effect on small structures at the nonlinear stage of KH instability.

Extended magnetohydrodynamics with embedded particle‐in‐cell simulation of Ganymede's magnetosphere

AbstractWe have recently developed a new modeling capability to embed the implicit particle‐in‐cell (PIC) model iPIC3D into the Block‐Adaptive‐Tree‐Solarwind‐Roe‐Upwind‐Scheme magnetohydrodynamic (MHD) model. The MHD with embedded PIC domains (MHD‐EPIC) algorithm is a two‐way coupled kinetic‐fluid model. As one of the very first applications of the MHD‐EPIC algorithm, we simulate the interaction between Jupiter's magnetospheric plasma and Ganymede's magnetosphere. We compare the MHD‐EPIC simulations with pure Hall MHD simulations and compare both model results with Galileo observations to assess the importance of kinetic effects in controlling the configuration and dynamics of Ganymede's magnetosphere. We find that the Hall MHD and MHD‐EPIC solutions are qualitatively similar, but there are significant quantitative differences. In particular, the density and pressure inside the magnetosphere show different distributions. For our baseline grid resolution the PIC solution is more dynamic than the Hall MHD simulation and it compares significantly better with the Galileo magnetic measurements than the Hall MHD solution. The power spectra of the observed and simulated magnetic field fluctuations agree extremely well for the MHD‐EPIC model. The MHD‐EPIC simulation also produced a few flux transfer events (FTEs) that have magnetic signatures very similar to an observed event. The simulation shows that the FTEs often exhibit complex 3‐D structures with their orientations changing substantially between the equatorial plane and the Galileo trajectory, which explains the magnetic signatures observed during the magnetopause crossings. The computational cost of the MHD‐EPIC simulation was only about 4 times more than that of the Hall MHD simulation.

Two-fluid and magnetohydrodynamic modelling of magnetic reconnection in the MAST spherical tokamak and the solar corona

Twisted magnetic flux ropes are ubiquitous in laboratory and astrophysical plasmas, and the merging of such flux ropes through magnetic reconnection is an important mechanism for restructuring magnetic fields and releasing free magnetic energy. The merging-compression scenario is one possible start-up scheme for spherical tokamaks, which has been used on the Mega Amp Spherical Tokamak (MAST). Two current-carrying plasma rings or flux ropes approach each due to mutual attraction, forming a current sheet and subsequently merge through magnetic reconnection into a single plasma torus, with substantial plasma heating. Two-dimensional resistive and Hall-magnetohydrodynamic simulations of this process are reported, including a strong guide field. A model of the merging based on helicity-conserving relaxation to a minimum energy state is also presented, extending previous work to tight-aspect-ratio toroidal geometry. This model leads to a prediction of the final state of the merging, in good agreement with simulations and experiment, as well as the average temperature rise. A relaxation model of reconnection between two or more flux ropes in the solar corona is also described, allowing for different senses of twist, and the implications for heating of the solar corona are discussed.

Three-dimensional fast magnetic reconnection driven by relativistic ultraintense femtosecond lasers.

Three-dimensional fast magnetic reconnection driven by two ultraintense femtosecond laser pulses is investigated by relativistic particle-in-cell simulation, where the two paralleled incident laser beams are shot into a near-critical plasma layer to form a magnetic reconnection configuration in self-generated magnetic fields. A reconnection X point and out-of-plane quadrupole field structures associated with magnetic reconnection are formed. The reconnection rate is found to be faster than that found in previous two-dimensional Hall magnetohydrodynamic simulations and electrostatic turbulence contribution to the reconnection electric field plays an essential role. Both in-plane and out-of-plane electron and ion accelerations up to a few MeV due to the magnetic reconnection process are also obtained.

Study of the effects of guide field on Hall reconnection

The results from guide field studies on the Magnetic Reconnection Experiment (MRX) are compared with results from Hall magnetohydrodynamic (HMHD) reconnection simulation with guide field. The quadrupole field, a signature of two-fluid reconnection at zero guide field, is modified by the presence of a finite guide field in a manner consistent with HMHD simulation. The modified Hall current profile contains reduced electron flows in the reconnection plane, which quantitatively explains the observed reduction of the reconnection rate. The present results are consistent with the hypothesis that the local reconnection dynamics is dominated by Hall effects in the collisionless regime of the MRX plasmas. While very good agreement is seen between experiment and simulations, we note that an important global feature of the experiments, a compression of the guide field by the reconnecting plasma, is not represented in the simulations.

Hall magnetohydrodynamic effects for three‐dimensional magnetic reconnection with finite width along the direction of the current

We performed three‐dimensional Hall magnetohydrodynamic (MHD) simulations of magnetic reconnection with finite width along the direction perpendicular to the antiparallel magnetic field (i.e., the direction of the electric current). Previous similar simulations including the Hall term have shown that the localized reconnection region itself can broaden in the anticurrent direction when the initial current is carried only by electrons. However, there is still no clear understanding of the behavior of the reconnection region in the presence of the initial ion current as in the Earth's magnetotail plasma sheet since no simulations have been carried out under such situations. In this study, we performed a systematic parametric survey considering the cases in which the initial current is carried not only by electrons but also by ions and found that the speed and direction of the current‐aligned broadening of the reconnection region are almost equal to those of background ion and electron flows that carry the current. This result means that location and size of the localized reconnection region vary with time, depending on plasma conditions in the background current sheet in Hall MHD regime. The rate of the localized reconnection can reach close to the value in the two‐dimensional case, even when reconnection starts in an extremely narrow region with its current‐aligned width equal to an ion inertial length. The localized reconnection process also produces the asymmetry of the current‐aligned structure of the reconnection jet. These results can explain various observational features related to magnetic reconnection in the near‐Earth magnetotail.

Comparison of a statistical model for magnetic islands in large current layers with Hall MHD simulations and Cluster FTE observations

[1] Magnetic islands have been observed in long current layers for various space plasmas, including the magnetopause and solar corona. In previous work exploring these magnetic islands, a statistical model was developed that described their formation, growth, convection, and coalescence in very large systems, for which simulations prove inadequate. An integro-differential equation was derived for the island distribution function, which characterized islands by the flux they contain ψ and the cross-sectional area they enclose A. The steady-state solution of the evolution equation predicted a distribution of islands. Here, we use a Hall MHD (magnetohydrodynamic) simulation of a very long current sheet with large numbers of magnetic islands to explore their dynamics, specifically their growth via two distinct mechanisms: quasi-steady reconnection and merging. We then use the simulation to validate the statistical model and benchmark its parameters. A database of 1,098 flux transfer events (FTEs) observed by Cluster between 2001 and 2003 is also compared with the model's predictions. In both simulations and observations, island merging plays a significant role. This suggests that the magnetopause is populated by many FTEs too small to be recognized by spacecraft instrumentation.

A study of shear flows induced by nonlinear evolution of double tearing modes in Hall magnetohydrodynamics

Shear flows induced by the nonlinear evolution of double tearing modes are studied numerically using Hall magnetohydrodynamics simulations in a slab geometry. The Hall effect is shown to plays an important role when the thickness of current sheets decrease and falls in the range of ion inertia length d i . Effective shear flows in the magnetic islands are generated during the process of magnetic reconnection and disappear finally. The induced toroidal velocity are shown to be more sensitive than the induced poloidal velocities in the Hall dominant systems. Moreover, the temporal evolution of the shear flows in the Tokamak resonant surface is studied and 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.

Three-dimensional simulations of the orientation and structure of reconnection X-lines

This letter employs Hall magnetohydrodynamic simulations to study X-lines formed during the reconnection of magnetic fields with differing strengths and orientations embedded in plasmas of differing densities. Although random initial perturbations trigger the growth of X-lines with many orientations, a few robust X-lines sharing an orientation consistent with the direction of maximal outflow speed, as predicted by Swisdak and Drake [Geophys. Res. Lett. 34, L11106 (2007)] eventually dominate the system. Reconnection in the geometry examined here contradicts the suggestion of Sonnerup [J. Geophys. Res. 79, 1546 (1974)] that it occurs in a plane normal to the equilibrium current. At late time, the X-lines' growth stagnates, leaving them shorter than the simulation domain.

Nonlinear electromagnetic wave interactions in Hall–MHD plasmas

AbstractWe have developed a massively parallelized fully three-dimensional (3D) compressible Hall–magnetohydrodynamic (MHD) code to investigate inertial range electromagnetic wave cascades and dissipative processes in the regime, where characteristic length scales associated with plasma fluctuations are smaller than ion gyroradii. Such regime is ubiquitously present in the solar wind and many other collisionless space plasmas. Particularly, in the solar wind, the high time resolution databases depict a spectral break near the end of the 5/3 spectrum that corresponds to a high-frequency regime where the electromagnetic turbulent cascades cannot be explained by the usual MHD models. This refers to a second inertial range, where turbulent cascades follow a k−7/3 (where k is a wavenumber) spectrum in which the characteristic electromagnetic fluctuations evolve typically on kinetic Alfvén time scales. In this paper, we describe results from our 3D compressible Hall–MHD simulations that explain the observed k−7/3 spectrum in the solar wind plasma, energy cascade, anisotropy, and other spectral features.