Classical Magnetohydrodynamics Research Articles

Dust Dynamics in Hall-effected Protoplanetary Disks. I. Background Drift Hall Instability

Recent studies have shown that the large-scale gas dynamics of protoplanetary disks (PPDs) are controlled by nonideal magnetohydrodynamics (MHD), but how this influences dust dynamics is not fully understood. To this end, we investigate the stability of dusty, magnetized disks subject to the Hall effect, which applies to planet-forming regions of PPDs. We find a novel background drift Hall instability (BDHI) that may facilitate planetesimal formation in Hall-effected disk regions. Through a combination of linear analysis and nonlinear simulations, we demonstrate the viability and characteristics of BDHI. We find it can potentially dominate over the classical streaming instability (SI) and standard MHD instabilities at low dust-to-gas ratios and weak magnetic fields. We also identify magnetized versions of the classic SI, but these are usually subdominant. We highlight the complex interplay between magnetic fields and dust-gas dynamics in PPDs, underscoring the need to consider nonideal MHD like the Hall effect in the broader narrative of planet formation.

Numerical model of restrikes in gliding arc discharges

Abstract Direct current (DC) electric arcs are of particular interest because they can produce large volumes of thermal plasmas with controlled energy deposition. When such discharges are applied in a gas flow, convection displaces the top of the arc downstream while the arc roots remain attached to the electrodes, thus increasing the length of the arc over time. However, this growth is limited by a restrike phenomenon, which starts from streamers appearing in high electric field regions and shortcutting the long, stretched electric arc. From a numerical point of view, DC arcs can be efficiently simulated with a resistive magneto-hydrodynamics (MHD) model, with numerical requirements in terms of spatial and temporal discretization that are compatible with classic fluid dynamics and combustion simulations. However, arc restrikes rely on the propagation of streamer discharges that are highly non-neutral phenomena, whereas classical MHD assumes neutrality. To tackle this problem, we propose in this paper a model of restrike that can be used in an MHD approach. After describing the ideas of the model, we perform a parametric study of the input parameters to examine its influence on the discharge dynamics.

A 4th-order accurate finite volume method for ideal classical and special relativistic MHD based on pointwise reconstructions

We present a novel implementation of a genuinely 4th-order accurate finite volume scheme for multidimensional classical and special relativistic magnetohydrodynamics (MHD) based on the constrained transport (CT) formalism. The scheme introduces several novel aspects when compared to its predecessors yielding a more efficient computational tool. Among the most relevant ones, our scheme exploits pointwise to pointwise reconstructions (rather than one-dimensional finite volume ones), employs the generic upwind constrained transport averaging and sophisticated limiting strategies that include both a discontinuity detector and an order reduction procedure. Selected numerical benchmarks demonstrate the accuracy and robustness of the method.

The moving finite element method with streamline-upwind Petrov–Galerkin for magnetohydrodynamic flows problems at high Hartmann numbers

It is widely acknowledged that both the streamline-upwind Petrov–Galerkin (SUPG) method and moving mesh method can enhance the stability of finite element method in solving convection-dominated convection–diffusion problems. However, in the case of strong convection-dominated conditions, they still exhibit numerical oscillations and the solutions will not even converge. In order to address similar phenomena observed in solving magnetohydrodynamic (MHD) flow problems at high Hartmann numbers with strong convective dominance, the MHD equation was first decoupled into two convection–diffusion equations. Subsequently, a new approach called the moving mesh streamline-upwind Petrov–Galerkin method (MM-SUPG) was proposed by coupling the moving mesh technique with SUPG method. The MM-SUPG method contains two independent part: the finite element method with SUPG for solving the decoupled MHD equation and a mesh-redistribution algorithm. To verify its effectiveness for solving the MHD equation at high Hartmann number, a classical MHD fluid flow problem was numerically tested using both the MM-SUPG method and the moving finite element method (MFEM). Compared to the MFEM, the proposed method not only yields stable numerical solutions under strong convective dominance while reducing unnecessary false oscillations, but also improves calculation accuracy to some extent using the same mesh.

Nonlinear Damping and Field-aligned Flows of Propagating Shear Alfvén Waves with Braginskii Viscosity

Braginskii magnetohydrodynamics (MHD) provides a more accurate description of many plasma environments than classical MHD since it actively treats the stress tensor using a closure derived from physical principles. Stress tensor effects nonetheless remain relatively unexplored for solar MHD phenomena, especially in nonlinear regimes. This paper analytically examines nonlinear damping and longitudinal flows of propagating shear Alfvén waves. Most previous studies of MHD waves in Braginskii MHD have considered the strict linear limit of vanishing wave perturbations. We show that those former linear results only apply to Alfvén wave amplitudes in the corona that are so small as to be of little interest, typically a wave energy less than 10−11 times the energy of the background magnetic field. For observed wave amplitudes, the Braginskii viscous dissipation of coronal Alfvén waves is nonlinear and a factor around 109 stronger than predicted by the linear theory. Furthermore, the dominant damping occurs through the parallel viscosity coefficient η 0, rather than the perpendicular viscosity coefficient η 2 in the linearized solution. This paper develops the nonlinear theory, showing that the wave energy density decays with an envelope . The damping length L d exhibits an optimal damping solution, beyond which greater viscosity leads to lower dissipation as the viscous forces self-organize the longitudinal flow to suppress damping. Although the nonlinear damping greatly exceeds the linear damping, it remains negligible for many coronal applications.

Suppression mechanism of Richtmyer–Meshkov instability by transverse magnetic field with different strengths

The Richtmyer–Meshkov instability (RMI) is caused by an incident planar shock wave impinging on the heavy-gas-density interface. We have numerically investigated the RMI controlled by different transverse magnetic-field strengths based on the ideal compressible magnetohydrodynamics (MHD) equations. The MHD equations are solved by the corner transport upwind + constrained transport algorithm, which guarantees a divergence-free constraint on the magnetic field. We discuss the flow characteristics and shock patterns in both classical hydrodynamic and MHD situations and verify our conclusions by comparing the experimental results with the numerical results. The results show that the magnetic field modifies the pressure-gradient distribution, and the baroclinic vorticity splits and attaches to the MHD shock waves. In addition, the results indicate that the interaction of shock wave and density interface changes the distribution of magnetic-field energy and distorts the magnetic induction line in the region of magnetic-field energy accumulation. The distortion of the magnetic induction lines alters the magnetic field gradient and creates a magnetic tension that produces a torque opposing that generated by the shear force on the vorticity layer, so the Kelvin–Helmholtz instability is effectively suppressed and no Kelvin–Helmholtz vortex appears on the vorticity layer. The result is that the interface instability is suppressed.

PLASMA AND MAGNETIC FIELD DYNAMICS IN POS: PIC SIMULATIONS

2D3V particle in cell computer simulations for plasma, magnetic field and current density spatio-temporal dynamics in plasma opening switch (POS) are presented for various initial plasma densities. The current channel formation in the POS’s plasma, its passage through the plasma bridge, and its destruction at the boundary of the plasma jumper are studied. It is shown, that during the penetration of the magnetic field into the POS's plasma and current channel formation, electron vortices are excited. The passage speed of the POS's plasma by vortices decreases with increasing plasma density, which is qualitatively consistent with estimates based on classical electron magnetohydrodynamics (EMHD).

Nonlinear approximation for buoyancy-driven mixed convection heat and mass transfer flow over an inclined porous plate with Joule heating, nonlinear thermal radiation, viscous dissipation and thermophoresis effects

This study considered a classical magnetohydrodynamics (MHD) mixed convection heat and mass transfer flow over an inclined porous plate with thermophoresis, Joule heating, viscous dissipation, and nonlinear thermal radiation. The impact of nonlinear density variation with temperature and concentration (NDTC) in the buoyancy term is also taken into consideration. The mathematical model is first transformed into ordinary differential equations (ODEs) by similarity variables. The reduced ODEs are solved through the classical Runge–Kutta algorithm after utilizing the shooting technique. Some major findings of the analysis include; the heat transfer rate increases with the fluid injection but it decreases the rate of particle deposition and skin friction. Regarding the fluid suction, the heat transfer rate is observed to decrease as the fluid suction intensifies whereas increases the particle deposition and shear stress at the plate surface. As (a classical horizontal flat plate), the rate of heat transfer enhances but decreases the particle deposition rate and plate shear stress. With blowing/suction and in the presence of the magnetic parameter, the plate shear stress and heat transfer increase with nonlinear thermal radiation propagation whereas decreases the particle deposition. The species concentration near the porous plate, velocity, and temperature curves is enhanced by escalating the dissipation parameter. The radiative heat flux boosts the fluid temperature that consequently enhanced the velocity and the species concentration near the porous plate. The fluid velocity past the porous plate is higher in the case of a vertical plate () compared to the classical flow over a horizontal porous plate ().

Charged space debris induced nonlinear magnetosonic waves using inertial magnetohydrodynamics

The excitations of nonlinear magnetosonic waves in the presence of charged space debris objects in the low Earth orbital (LEO) plasma region are investigated by taking into account the effects of electron inertia in the framework of classical magnetohydrodynamics (MHD); which is also referred to as inertial magnetohydrodynamics. The magnetosonic waves are found to be governed by a forced Kadomtsev–Petviashvili (KP) equation with the forcing term representing the effects of space debris objects. The dynamical behaviours of both slow and fast magnetosonic solitary waves are explored in detail. Exact pinned accelerated magnetosonic lump wave solutions are shown to be stable for the entire region in the parameter space of slow waves and a large region in the parameter space of fast waves. In a similar way, exact pinned curved magnetosonic solitary wave solutions become stable for a small region in the parameter space of fast waves. These exact solutions with special properties are derived for some specific choices of the forcing debris functions. These novel results can have potential applications in the scientific and technological aspects of the space debris detection and mitigation in the near-Earth space.

Generation of Reverse Meniscus Flow by Applying An Electromagnetic Brake

A numerical study is presented that deals with the flow in the mold of a continuous slab caster under the influence of a DC magnetic field (electromagnetic brakes (EMBrs)). The arrangement and geometry investigated here is based on a series of previous experimental studies carried out at the mini-LIMMCAST facility at the Helmholtz-Zentrum Dresden-Rossendorf (HZDR). The magnetic field models a ruler-type EMBr and is installed in the region of the ports of the submerged entry nozzle (SEN). The current article considers magnet field strengths up to 441 mT, corresponding to a Hartmann number of about 600, and takes the electrical conductivity of the solidified shell into account. The numerical model of the turbulent flow under the applied magnetic field is implemented using the open-source CFD package OpenFOAM®. Our numerical results reveal that a growing magnitude of the applied magnetic field may cause a reversal of the flow direction at the meniscus surface, which is related the formation of a “multiroll” flow pattern in the mold. This phenomenon can be explained as a classical magnetohydrodynamics (MHD) effect: (1) the closure of the induced electric current results not primarily in a braking Lorentz force inside the jet but in an acceleration in regions of previously weak velocities, which initiates the formation of an opposite vortex (OV) close to the mean jet; (2) this vortex develops in size at the expense of the main vortex until it reaches the meniscus surface, where it becomes clearly visible. We also show that an acceleration of the meniscus flow must be expected when the applied magnetic field is smaller than a critical value. This acceleration is due to the transfer of kinetic energy from smaller turbulent structures into the mean flow. A further increase in the EMBr intensity leads to the expected damping of the mean flow and, consequently, to a reduction in the size of the upper roll. These investigations show that the Lorentz force cannot be reduced to a simple damping effect; depending on the field strength, its action is found to be topologically complex.

Mixed properties of magnetohydrodynamic waves undergoing resonant absorption in the cusp continuum

Context. Observations of magnetohydrodynamic (MHD) waves in the structured solar atmosphere have shown that these waves are damped and can thus contribute to atmospheric heating. In this paper, we focus on the damping mechanism of resonant absorption in the cusp continuum. This process takes places when waves travel through an inhomogeneous plasma. Aims. Our aim is to determine the properties of MHD waves undergoing resonant absorption in the cusp continuum in the transition layer of a cylindrical solar atmospheric structure, such as a photospheric pore or a coronal loop. Depending on which quantities dominate, one can assess what type of classical MHD wave the modes in question resemble most. Methods. In order to study the properties of these waves, we analytically determine the spatial profiles of compression, displacement, and vorticity for waves with frequencies in the cusp continuum, which undergo resonant absorption. We confirm these analytical derivations via numerical calculations of the profiles in the resistive MHD framework. Results. We show that the dominant quantities for the modes in the cusp continuum are the displacement parallel to the background magnetic field and the vorticity component in the azimuthal direction (i.e. perpendicular to the background magnetic field and along the loop boundary).

Modeling the lightning continuing current electric arc discharge and material thermal damage: Effects of combinations of amplitude and duration

The damage depth of a material is a key parameter for industrial objects in consideration of the lightning threat. The continuing current component in a multiple lightning sequence features a large charge transfer, which often leads to the dominant damage depth for electrically conductive materials. Laboratory simulation of the lightning continuing current is prone to misinterpretation due to various combinations of the current amplitude and duration in fulfillment of the fixed charge requirement of 200 C (±20%) in standards. This study employs a Unified Plasma-Material Finite Element Model (UPM-FEM) that is developed based on the classical magnetohydrodynamics method to analyze the influence of the current amplitude-duration combinations on the arc-material interactions. The energy originated from different physical processes, the heat flux and current density on material surface, and the material damage response are predicted using the UPM-FEM and compared for different amplitude-duration combinations at a fixed transfer charge. We report that the Joule heating, thermal conduction, radiative emission, and electronic enthalpic flux jointly determine the energy budget injected to materials at low current levels (≤300 A). While at higher currents (≥500 A), the thermal conduction contributes less significantly compared to the other energy items. The more pronounced increase of radiative emission heat loss will bring a saturation trend in arc properties and the material damage. A combination with a big current amplitude is recommended for achieving consistent arc properties and material damage in lightning continuing current test.

Generation of chiral asymmetry via helical magnetic fields

It is well known that helical magnetic fields undergo a so-called inverse cascade by which their correlation length grows due to the conservation of magnetic helicity in classical ideal magnetohydrodynamics (MHD). At high energies above approximately $10$ MeV, however, classical MHD is necessarily extended to chiral MHD and then the conserved quantity is $\langle\mathcal{H}\rangle + 2 \langle\mu_5\rangle / \lambda$ with $\langle\mathcal{H}\rangle$ being the mean magnetic helicity and $\langle\mu_5\rangle$ being the mean chiral chemical potential of charged fermions. Here, $\lambda$ is a (phenomenological) chiral feedback parameter. In this paper, we study the evolution of the chiral MHD system with the initial condition of nonzero $\langle\mathcal{H}\rangle$ and vanishing $\mu_5$. We present analytic derivations for the time evolution of $\langle\mathcal{H}\rangle$ and $\langle\mu_5\rangle$ that we compare to a series of laminar and turbulent three-dimensional direct numerical simulations. We find that the late-time evolution of $\langle\mathcal{H}\rangle$ depends on the magnetic and kinetic Reynolds numbers ${\rm Re}_{_\mathrm{M}}$ and ${\rm Re}_{_\mathrm{K}}$. For a high ${\rm Re}_{_\mathrm{M}}$ and ${\rm Re}_{_\mathrm{K}}$ where turbulence occurs, $\langle\mathcal{H}\rangle$ eventually evolves in the same way as in classical ideal MHD where the inverse correlation length of the helical magnetic field scales with time $t$ as $k_\mathrm{p} \propto t^{-2/3}$. For a low Reynolds numbers where the velocity field is negligible, the scaling is changed to $k_\mathrm{p} \propto t^{-1/2}\mathrm{ln}\left(t/t_\mathrm{log}\right)$. After being rapidly generated, $\langle\mu_5\rangle$ always decays together with $k_\mathrm{p}$, i.e. $\langle\mu_5\rangle \approx k_\mathrm{p}$, with a time evolution that depends on whether the system is in the limit of low or high Reynolds numbers.

Shock waves and characteristic discontinuities in ideal compressible two-fluid MHD

We are concerned with a model of ideal compressible isentropic two-fluid magnetohydrodynamics (MHD). Introducing an entropy-like function, we reduce the equations of two-fluid MHD to a symmetric form which looks like the classical MHD system written in the nonconservative form in terms of the pressure, the velocity, the magnetic field and the entropy. This gives a number of instant results. In particular, we conclude that all compressive extreme shock waves exist locally in time in the limit of weak magnetic field. We write down a condition sufficient for the local-in-time existence of current-vortex sheets in two-fluid flows. For the 2D case and a particular equation of state, we make the conclusion that contact discontinuities in two-fluid MHD flows exist locally in time provided that the Rayleigh-Taylor sign condition on the jump of the normal derivative of the pressure is satisfied at the first moment.

A divergence-free semi-implicit finite volume scheme for ideal, viscous, and resistive magnetohydrodynamics.

SummaryIn this paper, we present a novel pressure‐based semi‐implicit finite volume solver for the equations of compressible ideal, viscous, and resistive magnetohydrodynamics (MHD). The new method is conservative for mass, momentum, and total energy, and in multiple space dimensions, it is constructed in such a way as to respect the divergence‐free condition of the magnetic field exactly, also in the presence of resistive effects. This is possible via the use of multidimensional Riemann solvers on an appropriately staggered grid for the time evolution of the magnetic field and a double curl formulation of the resistive terms. The new semi‐implicit method for the MHD equations proposed here discretizes the nonlinear convective terms as well as the time evolution of the magnetic field explicitly, whereas all terms related to the pressure in the momentum equation and the total energy equation are discretized implicitly, making again use of a properly staggered grid for pressure and velocity. Inserting the discrete momentum equation into the discrete energy equation then yields a mildly nonlinear symmetric and positive definite algebraic system for the pressure as the only unknown, which can be efficiently solved with the (nested) Newton method of Casulli et al. The pressure system becomes linear when the specific internal energy is a linear function of the pressure. The time step of the scheme is restricted by a CFL condition based only on the fluid velocity and the Alfvén wave speed and is not based on the speed of the magnetosonic waves. Being a semi‐implicit pressure‐based scheme, our new method is therefore particularly well suited for low Mach number flows and for the incompressible limit of the MHD equations, for which it is well known that explicit density‐based Godunov‐type finite volume solvers become increasingly inefficient and inaccurate because of the more and more stringent CFL condition and the wrong scaling of the numerical viscosity in the incompressible limit. We show a relevant MHD test problem in the low Mach number regime where the new semi‐implicit algorithm is a factor of 50 faster than a traditional explicit finite volume method, which is a very significant gain in terms of computational efficiency. However, our numerical results confirm that our new method performs well also for classical MHD test cases with strong shocks. In this sense, our new scheme is a true all Mach number flow solver.

Normal modes in magnetized two-fluid spin quantum plasmas

We extend the classical two-fluid magnetohydrodynamic (MHD) formalism to include quantum effects such as electron Fermi pressure, Bohm pressure and spin couplings. At scales smaller than the electron skin-depth, the Hall effect and electron inertia must be taken into account, and can overlap with the quantum effects. We write down the full set of two-fluid quantum MHD (QMHD) and analyze the relative importance ofthese effects in the high density environments of neutron star atmospheres and white dwarf interiors, finding that for a broad range of parameters all these effects are operative. Of all spin interactions we analyze only the spin-magnetic coupling, as it is linear in $\hbar$ and consequently it is the strongest spin effect. We re-obtain the classical two-fluid MHD dispersion relations corresponding to the magnetosonic and Alfv\'en modes, modified by quantum effects. In the zero-spin case, for propagation parallel to the magnetic field, we find that the frequency of the fast mode is due to quantum effects modified by electron inertia, while the frequency of the Alfv\'en-slow sector has no quantum corrections. For perpendicular propagation, the fast-mode frequency is the same as for the parallel propagation plus a correction due only to classical two-fluid effects. When spin is considered, a whistler mode appears, which is due to two-fluid spin-magnetic interaction. There are no modifications due to spin for parallel propagation of magnetosonic and Alfv\'en waves, while for perpendicular prop agation a dispersive term due to spin arises in the two-fluid expression for the fast magnetosonic mode.

CAFE-Q: Code Designed to Solve the Resistive MHD Equations With Thermal Conductivity

We present a new code designed to solve the equations of classical magnetohydrodynamics in 3-D under the effects of magnetic resistivity and heat transfer. The purpose of the code centers on the analysis of solar phenomena within the photosphere–corona region and the study of the propagation of coronal mass ejections in the interplanetary medium. We present 1-D and 2-D standard tests to demonstrate the quality of the numerical results obtained with our code. As a new code test, we include a system directly related to solar physics: the formation of a jet triggered by magnetic reconnection. The program uses high-resolution shock-capturing methods, using HLLE, HLLC, and HLLD flux formulas combined with MINMOD, MC, and reconstructors. The divergence-free magnetic field constraint is controlled using the extended generalized Lagrange multipliers method and flux-constrained transport (Flux-CT) method. Concerning the accuracy of the numerical results, we present three important cases: first, for the self-similar current sheet test, the error with respect to the exact solution is 0.13%; second, about the violation of the divergence-free magnetic field constraint, we use the blast wave test and show the constraint is of order 10−11; and third, related to the magnetic field reconnection, the code reproduces the predicted reconnection rate for the Sweet–Parker model.

Modified magnetohydrodynamics model with wave turbulence: astrophysical applications

Modeling astrophysical flows in the framework of classical magnetohydrodynamics often encounters significant difficulties due to high (up to relativistic) Alfvén wave velocities. Such situations can arise in modeling the magnetosphere of planets and stars and accretion flows in polars, intermediate polars, and near-neutron stars. In a strongly magnetized plasma, wave turbulence can develop, which can significantly affect the energy balance and the forces determining the plasma dynamics. In this paper, a closed system of equations is obtained for modified magnetohydrodynamics with wave turbulence for a wide range of magnetic fields and turbulence energies. The turbulent flow is described as the sum of the mean flow and perturbations induced by relativistic Alfvén waves. Expressions are derived for the turbulence-induced body force, viscosity, and dissipative heating. An analysis of equations in certain limit cases is performed. It is shown that the proposed approach can be used for modeling a broad class of astrophysical plasma flows.

Some sources of plasma inhomogeneities in the solar wind in front of the Earth’s magnetosphere

The origination of various plasma inhomogeneities in the magnetosheath in front of the Earth’s magnetosphere is analyzed within classical magnetohydrodynamics. The effect of directional discontinuities or tangential and rotational discontinuities of the solar wind on plasma is studied. The origination of inhomogeneities of the type of secondary MHD waves in the magnetosheath is shown; the former equalize plasma parameters when restoring the stationary state. The effect of a rotational discontinuity on the bow shock–Earth’s magnetosphere system is of special interest, with distinguishing of plasma inhomogeneities of the plateau type observed in the near-Earth space.

Dynamics of Pantograph–Catenary Arc During the Pantograph Lowering Process

Pantograph–catenary (PC) arc has become an obstacle for the further development of high-speed railway. Understanding on the underlying physical mechanisms of PC arc dynamics is still far away from satisfactory; therefore, researches from both experimental and numerical aspects are urgently required. This paper focused on the dynamic characteristics of PC arc during the pantograph lowering process by numerical simulation method. A PC arc model was established based on the classical magnetohydrodynamics theory, with the temporal evolution of PC arc dynamics considered. The dynamic mesh technique was utilized to take care of the departure process between the pantograph and the catenary. Detailed behaviors of arc plasmas during the pantograph lowering process were presented by the temperature distribution and flow filed. Two interesting vortexes located below the catenary were found. The vortexes rotated in the opposite direction, resulting from the special gas flow motion during the pantograph movement. Furthermore, the gas flow brought about a thermal pinch effect on arc column, which had a significant influence on the next behaviors of arc plasmas. Besides, the effects of input current on the arc characteristics were studied.