Ideal MHD Simulations Research Articles

Variable-spectrum mode control of high poloidal beta discharges

DIII-D experiments demonstrate that high pressure, broad current profile equilibria can be accessed in the high poloidal beta regime by optimizing the MHD mode control poloidal spectrum. A novel, variable spectrum (VS) magnetic feedback scheme implemented using the DIII-D internal non-axisymmetric coils (I-coils) facilitated access to reduced internal inductance ℓi operation above the no-wall beta limit compared with both no feedback and fixed spectrum feedback. In addition, the VS feedback helped avoid beta collapses caused by marginally unstable resistive wall mode activity. The lower and upper I-coil rows were configured in two independent feedback loops, allowing the feedback field’s poloidal spectrum to vary and track changes in the plasma mode structure as the edge safety factor q 95 varied from 11 to 6 during the discharges. The q 95 dependence of the measured phase difference between the lower and upper I-coil rows during VS feedback is qualitatively compatible with ideal MHD simulations of the least-stable plasma kink mode and with plasma response simulations that included kinetic modifications to ideal MHD. The VS feedback approach is a straightforward way to improve resilience to variations in mode structure that occur as plasma parameters change. The demonstrated expansion of the operating space to lower ℓi is expected to improve the coupling of the plasma kink mode to external fields and beneficial wall eddy currents, and is compatible with high bootstrap fraction operation.

A global 3D simulation of magnetospheric accretion – I. Magnetically disrupted discs and surface accretion

ABSTRACT We present a 3D ideal MHD simulation of magnetospheric accretion on to a non-rotating star. The accretion process unfolds with intricate 3D structures driven by various mechanisms. First, the disc develops filaments at the magnetospheric truncation radius (RT) due to magnetic interchange instability. These filaments penetrate deep into the magnetosphere, form multiple accretion columns, and eventually impact the star at ∼30o from the poles at nearly the free-fall speed. Over 50 per cent (90 per cent) of accretion occurs on just 5 per cent (20 per cent) of the stellar surface. Secondly, the disc region outside RT develops large-scale magnetically dominated bubbles, again due to magnetic interchange instability. These bubbles orbit at a sub-Keplerian speed, persisting for a few orbits while leading to asymmetric mass ejection. The disc outflow is overall weak because of mostly closed field lines. Thirdly, magnetically supported surface accretion regions appear above the disc, resembling a magnetized disc threaded by net vertical fields, a departure from traditional magnetospheric accretion models. Stellar fields are efficiently transported into the disc region due to above instabilities, contrasting with the ‘X-wind’ model. The accretion rate on to the star remains relatively steady with a 23 per cent standard deviation. The periodogram reveals variability occurring at around 0.2 times the Keplerian frequency at RT, linked to the large-scale magnetic bubbles. The ratio of the spin-up torque to $\dot{M}(GM_*R_T)^{1/2}$ is around 0.8. Finally, after scaling the simulation, we investigate planet migration in the inner protoplanetary disc. The disc driven migration is slow in the MHD turbulent disc beyond RT, while aerodynamic drag plays a significant role in migration within RT.

The persistence of magneto-rotational turbulence in gravitationally turbulent accretion disks

Aims. Our main goal is to probe the persistence of turbulence originating from the magneto-rotational instability (MRI) in gravito-turbulent disks. This state is referred to here as GI-MRI coexistence, with GI standing for gravitational instability. We test the influence of GI strength, controlled by the cooling law, and the impact of Ohmic resistivity. Methods. Our starting point was three-dimensional, ideal, magnetohydrodynamic (MHD) simulations of gravitational turbulence in the local shearing-box approximation using the code Athena. We introduced a zero-net-flux magnetic seed field in a GI-turbulent state and investigated the nonlinear evolution. The GI strength was varied by modifying the cooling parameters. We tested the cooling times τcΩ0 = 10, τcΩ0 = 20, and τcΩ0 = 10, with additional background heating. For some resistive cases, ideal-MHD simulations, which had already developed GI-MRI coexistence, were restarted with a finite Ohmic resistivity enabled at the moment of restart. Results. It appears that there are two possible saturated dynamo states in the ideal-MHD regime: a state of GI-MRI coexistence (for low GI activity) and a strong-GI dynamo. The cases with lower GI activity eventually develop a clearly visible butterfly pattern. For the case with the highest GI activity (τcΩ0 = 10, no heating), a clearly visible butterfly pattern is absent, though more chaotic field reversals are observed above (and below) the mid-plane. We were also able to reproduce the results of previous simulations. With Ohmic resistivity, the simulation outcome can be substantially different. There exists a critical magnetic Reynolds number, ⟨Rm⟩ ∼ 500, below which the ideal-MHD outcome is replaced by a new dynamo state. For larger Reynolds numbers, one recovers turbulent states that are more reminiscent of the ideal-MHD states, and especially the strong-GI case. This new state leads to oscillations, which are caused by a significant heat production due to the resistive dissipation of magnetic energy. The additional heat periodically quenches GI, and the quenching events correspond to maxima of the Toomre value, Q.

Global Magnetohydrodynamic Magnetosphere Simulation With an Adaptively Embedded Particle‐In‐Cell Model

AbstractWe perform a geomagnetic event simulation using a newly developed magnetohydrodynamic with adaptively embedded particle‐in‐cell (MHD‐AEPIC) model. We have developed effective criteria to identify reconnection sites in the magnetotail and cover them with the PIC model. The MHD‐AEPIC simulation results are compared with Hall MHD and ideal MHD simulations to study the impacts of kinetic reconnection at multiple physical scales. At the global scale, the three models produce very similar SYM‐H and SuperMag Electrojet indexes, which indicates that the global magnetic field configurations from the three models are very close to each other. We also compare the ionospheric solver results and all three models generate similar polar cap potentials and field‐aligned currents. At the mesoscale, we compare the simulations with in situ Geotail observations in the tail. All three models produce reasonable agreement with the Geotail observations. At the kinetic scales, the MHD‐AEPIC simulation can produce a crescent shape distribution of the electron velocity space at the electron diffusion region, which agrees very well with MMS observations near a tail reconnection site. These electron scale kinetic features are not available in either the Hall MHD or ideal MHD models. Overall, the MHD‐AEPIC model compares well with observations at all scales, it works robustly, and the computational cost is acceptable due to the adaptive adjustment of the PIC domain. It remains to be determined whether kinetic physics can play a more significant role in other types of events, including but not limited to substorms.

Non-Linear Damping of Surface Alfvén Waves Due to Uniturbulence

This investigation is concerned with uniturbulence associated with surface Alfvén waves that exist in a Cartesian equilibrium model with a constant magnetic field and a piece-wise constant density. The surface where the equilibrium density changes in a discontinuous manner are the source of surface Alfvén waves. These surface Alfvén waves create uniturbulence because of the variation of the density across the background magnetic field. The damping of the surface Alfvén waves due to uniturbulence is determined using the Elsässer formulation. Analytical expressions for the wave energy density, the energy cascade, and the damping time are derived. The study of uniturbulence due to surface Alfvén waves is inspired by the observation that (the fundamental radial mode of) kink waves behave similarly to surface Alfvén waves. The results for this relatively simple case of surface Alfvén waves can help us understand the more complicated case of kink waves in cylinders. We perform a series of 3D ideal MHD simulations for a numerical demonstration of the non-linearly self-cascading model of unidirectional surface Alfvén waves using the code MPI-AMRVAC. We show that surface Alfvén waves damping time in the numerical simulations follows well our analytical prediction for that quantity. Analytical theory and the simulations show that the damping time is inversely proportional to the amplitude of the surface Alfvén waves and the density contrast. This unidirectional cascade may play a role in heating the coronal plasma.

Implementation of the Hll-Grp Solver for Multidimensional Ideal Mhd Simulations Based on Finite Volume Method

Implementation of the Hll-Grp Solver for Multidimensional Ideal Mhd Simulations Based on Finite Volume Method

Overdense Threads in the Solar Corona Induced by Torsional Alfvén Waves

Abstract High-resolution and high-cadence observations have shown that Alfvén waves are ubiquitous in the solar atmosphere. Theoretical works suggest their ability to transfer large energy fluxes from the photosphere to the corona and solar wind. In this proof-of-concept Letter we show that torsional Alfvén waves can induce the formation of filamentary plasma structures in the solar corona. We perform high-resolution 3D ideal MHD simulations in an initially uniform coronal plasma permeated by a line-tied twisted magnetic field. We find that torsional Alfvén waves develop Kelvin–Helmholtz instabilities as a result of the phase mixing process. The Kelvin–Helmholtz instability drives plasma compression that breaks the uniformity of density, creating elongated overdense threads aligned with the direction of the magnetic field. With synthetic modeling of SDO/AIA imaging we show that the overdense filaments could be seen in observations as fine strands that illuminate the underlying magnetic structure.

A 3D magnetohydrodynamic simulation of the propagation of a plasma plume transverse to applied magnetic field

We have carried out a 3D ideal-MHD (magnetohydrodynamic) simulation to study the evolution of a laser-generated plasma plume in a moderate external magnetic field (0.13 T) oriented perpendicular to the flow direction of the plasma plume. The simulation shows that the plasma plume pushes the external magnetic field lines outward in the direction of the expansion. This leads to the compression and bending of the magnetic field lines. The force resulting from the change in shape and the density of the magnetic field lines opposes the expansion of the plume. An elliptic layer of shocked plasma is formed at the plasma/external field interface leaving a cavity in the plume core due to the outward expansion and the inertia of the plume. As the plasma pressure drops due to expansion, the imbalance between the magnetic energy and the internal energy results in the collapse of the cavity. These observations have striking similarities with the observations of the experiments (Behera et al 2017 Phys. Plasmas 24 033511) performed recently to study the plasma plume expansion in the presence of an external transverse magnetic field. This similarity indicates that the physical mechanisms dominantly governing the plasma plume expansion in the moderate magnetic field are aptly described in the ideal MHD regime. The studies thus show that the laser-generated plasma plume can be utilized to carry out interesting experiments on MHD phenomena in a simple laboratory setup.

Magnetized decaying turbulence in the weakly compressible Taylor-Green vortex

Magnetohydrodynamic (MHD) turbulence affects both terrestrial and astrophysical plasmas. The properties of magnetized turbulence must be better understood to more accurately characterize these systems. This work presents ideal MHD simulations of the compressible Taylor-Green vortex under a range of initial subsonic Mach numbers and magnetic field strengths. We find that regardless of the initial field strength, the magnetic energy becomes dominant over the kinetic energy on all scales after at most several dynamical times. The spectral indices of the kinetic and magnetic energy spectra become shallower than k^{-5/3} over time and generally fluctuate. Using a shell-to-shell energy transfer analysis framework, we find that the magnetic fields facilitate a significant amount of the energy flux and that the kinetic energy cascade is suppressed. Moreover, we observe nonlocal energy transfer from the large-scale kinetic energy to intermediate and small-scale magnetic energy via magnetic tension. We conclude that even in intermittently or singularly driven weakly magnetized systems, the dynamical effects of magnetic fields cannot be neglected.

On the study of hydrodynamic instabilities in the presence of background magnetic fields in high-energy-density plasmas

Blast-wave-driven hydrodynamic instabilities are studied in the presence of a background B-field through experiments and simulations in the high-energy-density (HED) physics regime. In experiments conducted at the Laboratoire pour l’utilisation des lasers intenses (LULI), a laser-driven shock-tube platform was used to generate a hydrodynamically unstable interface with a prescribed sinusoidal surface perturbation, and short-pulse x-ray radiography was used to characterize the instability growth with and without a 10-T B-field. The LULI experiments were modeled in FLASH using resistive and ideal magnetohydrodynamics (MHD), and comparing the experiments and simulations suggests that the Spitzer model implemented in FLASH is necessary and sufficient for modeling these planar systems. These results suggest insufficient amplification of the seed B-field, due to resistive diffusion, to alter the hydrodynamic behavior. Although the ideal-MHD simulations did not represent the experiments accurately, they suggest that similar HED systems with dynamic plasma-β (=2μ0ρv2/B2) values of less than ∼100 can reduce the growth of blast-wave-driven Rayleigh–Taylor instabilities. These findings validate the resistive-MHD FLASH modeling that is being used to design future experiments for studying B-field effects in HED plasmas.

Evolution of Earth-like extended exospheres orbiting solar-like stars

ABSTRACT Recent observations of the Earth’s exosphere revealed the presence of an extended hydrogenic component that could reach distances beyond 40 planetary radii. Detection of similar extended exospheres around Earth-like exoplanets could reveal crucial facts in terms of habitability. The presence of these rarified hydrogen envelopes is extremely dependent on the planetary environment, dominated by the ionizing radiation and plasma winds coming from the host star. Radiation and fast wind particles ionize the uppermost layers of planetary atmospheres, especially for planets orbiting active, young stars. The survival of the produced ions in the exosphere of such planets is subject to the action of the magnetized stellar winds, particularly for unmagnetized bodies. In order to address these star–planet interactions, we have carried out numerical 2.5D ideal MHD simulations using the pluto code to study the dynamical evolution of tenuous, hydrogen-rich, Earth-like extended exospheres for an unmagnetized planet, at different stellar evolutionary stages: from a very young, solar-like star of 0.1 Gyr to a 5.0 Gyr star. For each star–planet configuration, we show that the morphology of extended Earth-like hydrogen exospheres is strongly dependent on the incident stellar winds and the produced ions present in these gaseous envelopes, showing that the ionized component of Earth-like exospheres is quickly swept by the stellar winds of young stars, leading to large bow shock formation for later stellar ages.

Global 3D radiation magnetohydrodynamic simulations for FU Ori’s accretion disc and observational signatures of magnetic fields

ABSTRACT FU Ori is the prototype of FU Orionis systems that are outbursting protoplanetary discs. Magnetic fields in FU Ori’s accretion discs have previously been detected using spectropolarimetry observations for Zeeman effects. We carry out global radiation ideal MHD simulations to study FU Ori’s inner accretion disc. We find that (1) when the disc is threaded by vertical magnetic fields, most accretion occurs in the magnetically dominated atmosphere at z ∼ R, similar to the ‘surface accretion’ mechanism in previous locally isothermal MHD simulations. (2) A moderate disc wind is launched in the vertical field simulations with a terminal speed of ∼300–500 km s−1 and a mass-loss rate of 1–10 per cent the disc accretion rate, which is consistent with observations. Disc wind fails to be launched in simulations with net toroidal magnetic fields. (3) The disc photosphere at the unit optical depth can be either in the wind launching region or the accreting surface region. Magnetic fields have drastically different directions and magnitudes between these two regions. Our fiducial model agrees with previous optical Zeeman observations regarding both the field directions and magnitudes. On the other hand, simulations indicate that future Zeeman observations at near-IR wavelengths or towards other FU Orionis systems may reveal very different magnetic field structures. (4) Due to energy loss by the disc wind, the disc photosphere temperature is lower than that predicted by the thin disc theory, and the previously inferred disc accretion rate may be lower than the real accretion rate by a factor of ∼2–3.

The role of turbulence during the formation of circumbinary discs

Most stars form in binaries and the evolution of their discs remains poorly understood. To shed light on this subject, we carry out 3D ideal MHD simulations with the AMR code FLASH of binary star formation for separations of $10-20\,\mathrm{AU}$. We run a simulation with no initial turbulence (NT), and two with turbulent Mach numbers of $\mathcal{M} = \sigma_v/c_s = 0.1$ and $0.2$ (T1 and T2) for $5000\,\mathrm{yr}$ after protostar formation. By the end of the simulations the circumbinary discs in NT and T1, if any, have radii of $\lesssim20\,\mathrm{AU}$ with masses $\lesssim0.02\,\mathrm{M}_\odot$, while T2 hosts a circumbinary disc with radius $\sim70-80\,\mathrm{AU}$ and mass $\sim0.12\,\mathrm{M}_\odot$. These circumbinary discs formed from the disruption of circumstellar discs and harden the binary orbit. Our simulated binaries launch large single outflows. We find that NT drives the most massive outflows, and also removes large quantities of linear and angular momentum. T2 produces the least efficient outflows concerning mass, momentum and angular momentum ($\sim$61 per cent, $\sim$71 per cent, $\sim$68 per cent of the respective quantities in NT). We conclude that while turbulence helps to build circumbinary discs which organise magnetic fields for efficient outflow launching, too much turbulence may also disrupt the ordered magnetic field structure required for magneto-centrifugal launching of jets and outflows. We also see evidence for episodic accretion during the binary star evolution. We conclude that the role of turbulence in building large circumbinary discs may explain some observed very old ($>10\,\mathrm{Myr}$) circumbinary discs. The longer lifetime of circumbinary discs may increase the likelihood of planet formation.

JCMT POL-2 and ALMA Polarimetric Observations of 6000–100 au Scales in the Protostar B335: Linking Magnetic Field and Gas Kinematics in Observations and MHD Simulations

Abstract We present our analysis of the magnetic field structures from 6000 to 100 au scales in the Class 0 protostar B335 inferred from our James Clerk Maxwell telescope (JCMT) POL-2 observations and ALMA archival polarimetric data. To interpret the observational results, we perform a series of (non)ideal MHD simulations of the collapse of a rotating nonturbulent dense core, whose initial conditions are adopted to be the same as observed in B335, and generate synthetic polarization maps. The comparison of our JCMT and simulation results suggests that the magnetic field on a 6000 au scale in B335 is pinched and well aligned with the bipolar outflow along the east–west direction. Among all our simulations, the ALMA polarimetric results are best explained with weak magnetic field models having an initial mass-to-flux ratio of 9.6. However, we find that with a weak magnetic field, the rotational velocity on a 100 au scale and the disk size in our simulations are larger than the observational estimates by a factor of several. An independent comparison of our simulations and the gas kinematics in B335 observed with the SMA and ALMA favors strong magnetic field models with an initial mass-to-flux ratio smaller than 4.8. We discuss two possibilities resulting in the different magnetic field strengths inferred from the polarimetric and molecular-line observations: (1) overestimated rotational-to-gravitational energy in B335, and (2) additional contributions in the polarized intensity due to scattering on a 100 au scale.

MHD simulations of the formation and propagation of protostellar jets to observational length-scales

We present 2.5-D global, ideal MHD simulations of magnetically and rotationally driven protostellar jets from Keplerian accretion discs, wherein only the initial magnetic field strength at the inner radius of the disc, $B_{\rm i}$, is varied. Using the AMR-MHD code AZEUS, we self-consistently follow the jet evolution into the observational regime ($>10^3\,\mathrm{AU}$) with a spatial dynamic range of $\sim6.5\times10^5$. The simulations reveal a three-component outflow: 1) A hot, dense, super-fast and highly magnetised 'jet core'; 2) a cold, rarefied, trans-fast and highly magnetised 'sheath' surrounding the jet core and extending to a tangential discontinuity; and 3) a warm, dense, trans-slow and weakly magnetised shocked ambient medium entrained by the advancing bow shock. The simulations reveal power-law relationships between $B_{\rm i}$ and the jet advance speed, $v_{\rm jet}$, the average jet rotation speed, $\langle v_\varphi\rangle$, as well as fluxes of mass, momentum, and kinetic energy. Quantities that do not depend on $B_{\rm i}$ include the plasma-$\beta$ of the transported material which, in all cases, seems to asymptote to order unity. Jets are launched by a combination of the 'magnetic tower' and 'bead-on-a-wire' mechanisms, with the former accounting for most of the jet acceleration---even for strong fields---and continuing well beyond the fast magnetosonic point. At no time does the leading bow shock leave the domain and, as such, these simulations generate large-scale jets that reproduce many of the observed properties of protostellar jets including their characteristic speeds and transported fluxes.

Does Misalignment between Magnetic Field and Angular Momentum Enhance or Suppress Circumstellar Disk Formation?

Abstract The effect of misalignment between the magnetic field and the angular momentum of molecular cloud cores on the angular momentum evolution during the gravitational collapse is investigated by ideal and non-ideal MHD simulations. For the non-ideal effect, we consider the ohmic and ambipolar diffusion. Previous studies that considered the misalignment reported qualitatively contradicting results. Magnetic braking was reported as being either strengthened or weakened by misalignment in different studies. We conducted simulations of cloud core collapse by varying the stability parameter α (the ratio of the thermal to gravitational energy of the core) with and without including magnetic diffusion. The non-ideal MHD simulations show the central angular momentum of the core, with θ = 0° ( ) being always greater than that with θ = 90° ( ), independently of α, meaning that circumstellar disks form more easily in a core with θ = 0°. The ideal MHD simulations, in contrast, show the central angular momentum of the core with θ = 90° being greater than with θ = 0° for small α and smaller for large α. Inspection of the angular momentum evolution of the fluid elements reveals three mechanisms contributing to the evolution of the angular momentum: (i) magnetic braking in the isothermal collapse phase, (ii) selective accretion of the rapidly (for θ = 90°) or slowly (for θ = 0°) rotating fluid elements to the central region, and (iii) magnetic braking in the first core and the disk. The difference between the ideal and non-ideal simulations arises from the different efficiencies of (iii).

3D global simulations of RIAFs: convergence, effects of azimuthal extent, and dynamo

We study the long-term evolution of non-radiative geometrically thick ($H/R\approx 0.5$) accretion flows using 3D global ideal MHD simulations and a pseudo-Newtonian gravity. We find that resolving the scale height with 42 grid points is adequate to obtain convergence with the product of quality factors $\langle \langle Q_{\theta} \rangle \rangle \langle \langle Q_{\phi} \rangle \rangle \geq 300$ and magnetic tilt angle $\theta_B \sim 13^{\circ}-14^{\circ}$. Like previous global isothermal thin disk simulations, we find stronger mean magnetic fields for the restricted azimuthal domains. Imposing periodic boundary conditions with the azimuthal extent smaller than $2\pi$ make the turbulent field at low $m$ appear as a mean field in the runs with smaller azimuthal extent. But unlike previous works, we do not find a monotonic trend in turbulence with the azimuthal extent. We conclude that the minimum azimuthal extent should be $\geq \pi/2$ to capture the flow structure, but a full $2 \pi$ extent is necessary to study the dynamo. We find an intermittent dynamo cycle, with $\alpha$-quenching playing an important role in the nonlinear saturated state. Unlike previous local studies, we find almost similar values of kinetic and magnetic $\alpha$-s, giving rise to an irregular distribution of dynamo-$\alpha$. The effects of dynamical quenching are shown explicitly for the first time in global simulations of accretion flows.

Global Evolution of an Accretion Disk with a Net Vertical Field: Coronal Accretion, Flux Transport, and Disk Winds

Abstract We report results from global ideal MHD simulations that study thin accretion disks (with thermal scale height H/R = 0.1 and 0.05) threaded by net vertical magnetic fields. Our computations span three orders of magnitude in radius, extend all the way to the pole, and are evolved for more than 1000 innermost orbits. We find that (1) inward accretion occurs mostly in the upper magnetically dominated regions of the disk at z ∼ R, similar to predictions from some previous analytical work and the “coronal accretion” flows found in GRMHD simulations. (2) A quasi-static global field geometry is established in which flux transport by inflows at the surface is balanced by turbulent diffusion. The resulting field is strongly pinched inwards at the surface. A steady-state advection–diffusion model, with a turbulent magnetic Prandtl number of order unity, reproduces this geometry well. (3) Weak unsteady disk winds are launched beyond the disk corona with the Alfvén radius R A /R 0 ∼ 3. Although the surface inflow is filamentary and the wind is episodic, we show that the time-averaged properties are well-described by steady-wind theory. Even with strong fields, β 0 = 103 at the midplane initially, only 5% of the angular momentum transport is driven by the wind, and the wind mass flux from the inner decade of the radius is only ∼0.4% of the mass accretion rate. (4) Within the disk, most of the accretion is driven by the Rϕ stress from the MRI and global magnetic fields. Our simulations have many applications to astrophysical accretion systems.

Nonlinear Dynamics of Non-uniform Current-Vortex Sheets in Magnetohydrodynamic Flows

A theoretical model is proposed to describe fully nonlinear dynamics of interfaces in two-dimensional MHD flows based on an idea of non-uniform current-vortex sheet. Application of vortex sheet model to MHD flows has a crucial difficulty because of non-conservative nature of magnetic tension. However, it is shown that when a magnetic field is initially parallel to an interface, the concept of vortex sheet can be extended to MHD flows (current-vortex sheet). Two-dimensional MHD flows are then described only by a one-dimensional Lagrange parameter on the sheet. It is also shown that bulk magnetic field and velocity can be calculated from their values on the sheet. The model is tested by MHD Richtmyer–Meshkov instability with sinusoidal vortex sheet strength. Two-dimensional ideal MHD simulations show that the nonlinear dynamics of a shocked interface with density stratification agrees fairly well with that for its corresponding potential flow. Numerical solutions of the model reproduce properly the results of the ideal MHD simulations, such as the roll-up of spike, exponential growth of magnetic field, and its saturation and oscillation. Nonlinear evolution of the interface is found to be determined by the Alfven and Atwood numbers. Some of their dependence on the sheet dynamics and magnetic field amplification are discussed. It is shown by the model that the magnetic field amplification occurs locally associated with the nonlinear dynamics of the current-vortex sheet. We expect that our model can be applicable to a wide variety of MHD shear flows.

Global multifluid simulations of the magnetorotational instability in radially stratified protoplanetary discs

The redistribution of angular momentum is a long standing problem in our understanding of protoplanetary disk (PPD) evolution. The magnetorotational instability (MRI) is considered a likely mechanism. We present the results of a study involving multifluid global simulations including Ohmic dissipation, ambipolar diffusion and the Hall effect in a dynamic, self-consistent way. We focus on the turbulence resulting from the non-linear development of the MRI in radially stratified PPDs and compare with ideal MHD simulations. In the multifluid simulations the disk is initially set up to transition from a weak Hall dominated regime, where the Hall effect is the dominant non-ideal effect but approximately the same as or weaker than the inductive term, to a strong Hall dominated regime, where the Hall effect dominates the inductive term. As the simulations progress a substantial portion of the disk develops into a weak Hall dominated disk. We find a transition from turbulent to laminar flow in the inner regions of the disk, but without any corresponding overall density feature. We introduce a dimensionless parameter, $\alpha_\mathrm{RM}$, to characterise accretion with $\alpha_\mathrm{RM} \gtrsim 0.1$ corresponding to turbulent transport. We calculate the eddy turnover time, $t_\mathrm{eddy}$, and compared this with an effective recombination timescale, $t_\mathrm{rcb}$, to determine whether the presence of turbulence necessitates non-equilibrium ionisation calculations. We find that $t_\mathrm{rcb}$ is typically around three orders of magnitude smaller than $t_\mathrm{eddy}$. Also, the ionisation fraction does not vary appreciably. These two results suggest that these multifluid simulations should be comparable to single fluid non-ideal simulations.