Magnetohydrodynamic States Research Articles

On the evolution of magnetohydrodynamic flow instability in shock-accelerated light bubble

The study investigates the evolution of flow instabilities in a magnetohydrodynamic (MHD) environment involving a shock-accelerated light cylindrical bubble. Numerical simulations were conducted using a cylindrical helium (He) bubble accelerated by a shock wave in nitrogen (N2) gas at various magnetic field strengths. The results highlight the impact of magnetic fields on flow morphology, vorticity generation, and enstrophy. The interaction between incident shock waves and the gas bubble revealed significant differences in flow patterns and interface features when magnetic fields were applied. Key findings include the quantification of shock trajectories and detailed visualizations of the evolving flow structure. The study provides insights into the dynamics of shock–bubble interactions under MHD conditions, contributing to the broader understanding of flow instability mechanisms in such complex environments.

Gas-kinetic scheme for partially ionized plasma in hydrodynamic regime

Most plasmas are only partially ionized. To better understand the dynamics of these plasmas, the behaviors of a mixture of neutral species and plasma in ideal magnetohydrodynamic states are investigated. The current approach is about the construction of coupled kinetic models for the neutral gas, electron, and proton, and the development of the corresponding gas-kinetic scheme (GKS) for the solution in the continuum flow regime. The scheme is validated in the 1D Riemann problem for an enlarged system with the interaction from the Euler waves of the neutral gas and magnetohydrodynamic ones of the plasma. Additionally, the Orszag–Tang vortex problem across different ionized states is tested to examine the influence of neutrals on the MHD wave evolution. These tests demonstrate that the proposed scheme can capture the fundamental features of ideal partially ionized plasma, and a transition in the wave structure from the ideal MHD solution of the fully ionized plasma to the Euler solution of the neutral gas is obtained.

Analysis of Control Problems for Stationary Magnetohydrodynamics Equations under the Mixed Boundary Conditions for a Magnetic Field

The optimal control problems for stationary magnetohydrodynamic equations under the inhomogeneous mixed boundary conditions for a magnetic field and the Dirichlet condition for velocity are considered. The role of controls in the control problems under study is played by normal and tangential components of the magnetic field given on different parts of the boundary and by the exterior current density. Quadratic tracking-type functionals for velocity, magnetic field or pressure are taken as cost functionals. The global solvability of the control problems under consideration is proved, an optimality system is derived and, based on its analysis, a mathematical apparatus for studying the local uniqueness and stability of the optimal solutions is developed. On the basis of the developed apparatus, the local uniqueness of solutions of control problems for specific cost functionals is proved, and stability estimates of optimal solutions are established.

Two‐level stabilized finite volume method for the stationary incompressible magnetohydrodynamic equations

AbstractIn this paper, a two‐level stabilized finite volume method is developed and analyzed for the steady incompressible magnetohydrodynamic (MHD) equations. The linear polynomial space is used to approximate the velocity, pressure and magnetic fields, and two local Gauss integrations are introduced to overcome the restriction of discrete inf‐sup condition. Firstly, the existence and uniqueness of the solution of the discrete problem in the stabilized finite volume method are proved by using the Brouwer's fixed point theorem. ‐stability results of numerical solutions are also presented. Secondly, optimal error estimates of numerical solutions in and ‐norms are established by using the energy method and constructing the corresponding dual problem. Thirdly, the stability and convergence of two‐level stabilized finite volume method for the stationary incompressible MHD equations are provided. Theoretical findings show that the two‐level method has the same accuracy as the one‐level method with the mesh sizes . Finally, some numerical results are provided to identify with the established theoretical findings and show the performances of the considered numerical schemes.

Disruption event characterization and forecasting in tokamaks

Disruption prediction and avoidance is a critical need for next-step tokamaks, such as ITER. Disruption Event Characterization and Forecasting (DECAF) research fully automates analysis of tokamak data to determine chains of events that lead to disruptions and to forecast their evolution allowing sufficient time for mitigation or complete avoidance of the disruption. Disruption event chains related to local rotating or global magnetohydrodynamic (MHD) modes and vertical instability are examined with warnings issued for many off-normal physics events, including density limits, plasma dynamics, confinement transitions, and profile variations. Along with Greenwald density limit evaluation, a local radiative island power balance theory is evaluated and compared to the observation of island growth. Automated decomposition and analysis of rotating tearing modes produce physical event chains leading to disruptions. A total MHD state warning model comprised of 15 separate criteria produces a disruption forecast about 180 ms before a standard locked mode detector warning. Single DECAF event analyses have begun on KSTAR, MAST, and NSTX/-U databases with thousands of shot seconds of device operation using from 0.5 to 1 × 106 tested sample times per device. An initial multi-device database comparison illustrates a highly important result that plasma disruptivity does not need to increase as βN increases. Global MHD instabilities, such as resistive wall modes (RWMs), can give the briefest time period of warning before disruption compared to other physics events. In an NSTX database with unstable RWMs, the mode onset, loss of boundary and current control, and disruption event warnings are found in all cases and vertical displacement events are found in 91% of cases. An initial time-dependent reduced physics model of kinetic RWM stabilization created to forecast the disruption chain predicts instability 84% of the time for experimentally unstable cases with a relatively low false positive rate. Instances of the disruption event chain analysis illustrate dynamics including H–L back transitions for rotating MHD and global RWM triggering events. Disruption warnings are issued with sufficient time before the disruption (on transport timescales) to potentially allow active profile control for disruption avoidance, active mode control, or mitigation.

1.5D non-LTE spectral synthesis of a 3D filament and prominence simulation

Context. Overly idealised representations of solar filaments and prominences in numerical simulations have long limited their morphological comparison against observations. Moreover, it is intrinsically difficult to convert simulation quantities into emergent intensity of characteristic, optically thick line cores and/or spectra that are commonly selected for observational study. Aims. In this paper, we demonstrate how the recently developed Lightweaver framework makes non-‘local thermodynamic equilibrium’ (NLTE) spectral synthesis feasible on a new 3D ab initio magnetohydrodynamic (MHD) filament-prominence simulation, in a post-processing step. Methods. We clarify the need to introduce filament- and prominent-specific Lightweaver boundary conditions that accurately model incident chromospheric radiation, and include a self-consistent and smoothly varying limb-darkening function. Results. Progressing from isothermal and isobaric models to the self-consistently generated stratifications within a fully 3D MHD filament-prominence simulation, we find excellent agreement between our 1.5D NLTE Lightweaver synthesis and a popular hydrogen Hα proxy. We computed additional lines including Ca II 8542 alongside the more optically thick Ca II H&K & Mg II h&k lines, for which no comparable proxy exists, and we explore their formation properties within filament and prominence atmospheres. Conclusions. The versatility of the Lightweaver framework is demonstrated with this extension to 1.5D filament and prominence models, where each vertical column of the instantaneous 3D MHD state is spectrally analysed separately, without accounting for (important) multi-dimensional radiative effects. The general agreement found in the line core contrast of both observations and the Lightweaver-synthesised simulation further validates the current generation of solar filament and prominence models constructed numerically with MPI-AMRVAC.

Magnetohydrodynamic Waves in an Asymmetric Magnetic Slab with Different External Flows

Building on recent studies of the Kelvin–Helmholtz instability (KHI) in the solar atmosphere, we investigate a simple analytical model that can further our understanding of how the presence of bulk flows influences the propagation of magnetohydrodynamic (MHD) waves. Our model builds on a series of recent works on stationary MHD waveguides and looks at a magnetic slab with a density asymmetry, as well as asymmetric background steady flows present in its environment. We obtained approximate solutions to the dispersion relation for the important and applicable limiting cases of a thin or a wide slab, as well as low- and high-β plasmas. We also explored the relation between the angular frequency of trapped MHD waves, the limit for the onset of the KHI, and small parameters describing the flow and density asymmetries. Our analytical investigation is complemented by a numerical analysis for various bulk flow speeds and slab widths. Both these avenues of study reveal that the flow field asymmetry has an important effect on both the cutoff frequencies and the stability of trapped MHD waves in the slab configuration.

Study of general relativistic magnetohydrodynamic accretion flow around black holes

ABSTRACT We present a novel approach to study the global structure of steady, axisymmetric, advective, magnetohydrodynamic (MHD) accretion flow around black holes in full general relativity (GR). Considering ideal MHD conditions and relativistic equation of state (REoS), we solve the governing equations to obtain all possible smooth global accretion solutions. We examine the dynamical and thermodynamical properties of accreting matter in terms of the flow parameters, namely energy (${\cal E}$), angular momentum (${\cal L}$), and local magnetic fields. For a vertically integrated GRMHD flow, we observe that toroidal component (bϕ) of the magnetic fields generally dominates over radial component (br) at the disc equatorial plane. This evidently suggests that toroidal magnetic field indeed plays important role in regulating the disc dynamics. We further notice that the disc remains mostly gas pressure (pgas) dominated (β = pgas/pmag > 1, pmag refers magnetic pressure) except at the near horizon region, where magnetic fields become indispensable (β ∼ 1). We observe that Maxwell stress is developed that eventually yields angular momentum transport inside the disc. Towards this, we calculate the viscosity parameter (α) that appears to be radially varying. In addition, we examine the underlying scaling relation between α and β, which clearly distinguishes two domains coexisted along the radial extent of the disc. Finally, we discuss the utility of the present formalism in the realm of GRMHD simulation studies.

Unsteady MHD Stagnation Point Flow of Al2O3-Cu/H2O Hybrid Nanofluid Past a Convectively Heated Permeable Stretching/Shrinking Sheet with Suction/Injection

The numerical investigation of unsteady magnetohydrodynamic (MHD) stagnation point flow of Al2O3-Cu/H2O hybrid nanofluid past a convectively heated permeable stretching/shrinking sheet with suction/injection effect is underlined. The characteristic of MHD and boundary condition with suction/injection has received a lot of consideration due to its across-the-board application in mechanical and chemical engineering. The governing continuity, momentum and energy equations are transformed into a system of nonlinear ordinary differential equations using similarity transformation, which is then solved using the bvp4c routine. Numerical results are obtained for the skin friction coefficient, local Nusselt number as well as the velocity and temperature profiles for certain values of the governing parameters, namely suction/injection parameter, copper nanoparticle volume fraction parameter and MHD parameter. Results showed that both velocity profile and temperature increase as the suction/injection parameter increases for the first solution and decreases for the second solution. Similarly, when increase the value of MHD parameter M, the velocity and temperature profiles are decreases for both solutions. The magnitude of the reduced skin friction coefficient and the local Nusselt number are notably increased for the first solution with increasing values of the suction/injection and MHD parameters. Finding also revealed that the skin friction coefficient is intensified in conjunction with the local Nussel number by adding up the copper nanoparticle volume fraction. In general, dual solutions are found to exist to a particular extent of the stretching/shrinking sheet.

Improvement in energy channelization behaviour during micro hole formation in Y-SZ ceramic with magnetic field assisted ECSM process

In the present investigation, an energy channelization behavior was improved while machining micro holes in the Yttria–stabilized zirconia (Y-SZ) under magneto hydrodynamic conditions. The integration of magnetic field with electrochemical spark machining (ECSM) process forms the stable and thin gas film on the tool electrode. The subsequent breakdown of this film improves the discharge frequency and increases the discharge current by 18%. The underlying process and material removal mechanisms were demonstrated by using the evidence from discharge signals, gas film images, SEM, and optical images of work material. The stirring action provided by the magnetic field in ECSM process helps to flush out the sludge and stray bubbles from the machining region. In comparison to the ECSM process, the hole depth and aspect ratio were improved by 84.37% and 120%, respectively. Thermal spalling is the leading phenomenon in the material removal process for Y-SZ instead of melting and chemical etching, as in the case of glass substrates. Energy channelization analysis is also carried out to establish the correlations between energy-based parameters and responses. The combination of higher applied energy with small pulse durations is suggested to produce deep holes. The parametric investigation, regression modeling, and optimization for the MFA-ECSM process are also carried out to explore the process behavior.

Liouville theorem of D-solutions to the stationary magnetohydrodynamics system in a slab

In this paper, we study Liouville theorems of D-solutions to the stationary magnetohydrodynamic system in a slab. We will prove trivialness of the velocity and the magnetic field with various boundary conditions. In some boundary conditions, the additional assumption that the horizontal angular component(s) of the velocity or (and) the magnetic field is (are) axially symmetric is needed. More precisely, five types of boundary conditions will be considered: the vertical periodic boundary condition for the velocity and the magnetic field, the Navier-slip boundary condition for the velocity, the perfectly conducting or insulating boundary condition for the magnetic field, the non-slip boundary condition for the velocity, and the perfectly conducting or insulating boundary condition for the magnetic field. One of our innovations is that we do not impose finite Dirichlet integral assumption on the magnetic field compared with previous works.

Fast Dissipation of Colliding Alfvén Waves in a Magnetically Dominated Plasma

Abstract Magnetic energy around compact objects often dominates over plasma rest mass, and its dissipation can power the object’s luminosity. We describe a dissipation mechanism that works faster than magnetic reconnection. The mechanism involves two strong Alfvén waves with anti-aligned magnetic fields B 1 and B 2 that propagate in opposite directions along the background magnetic field B 0 and collide. The collision forms a thin current sheet perpendicular to B 0, which absorbs the incoming waves. The current sheet is sustained by an electric field E breaking the magnetohydrodynamic condition E < B and accelerating particles to high energies. We demonstrate this mechanism with kinetic plasma simulations using a simple setup of two symmetric plane waves with amplitude A = B 1/B 0 = B 2/B 0 propagating in a uniform B 0. The mechanism is activated when A > 1/2. It dissipates a large fraction of the wave energy, f = (2A − 1)/A 2, reaching 100% when A = 1. The plane geometry allows one to see the dissipation process in a one-dimensional simulation. We also perform two-dimensional simulations, enabling spontaneous breaking of the plane symmetry by the tearing instability of the current sheet. At moderate A of main interest, the tearing instability is suppressed. Dissipation transitions to normal, slower, magnetic reconnection at A ≫ 1. The fast dissipation described in this paper may occur in various objects with perturbed magnetic fields, including magnetars, jets from accreting black holes, and pulsar wind nebulae.

An MHD spectral theory approach to Jeans’ magnetized gravitational instability

Abstract In this paper, we revisit the governing equations for linear magnetohydrodynamic (MHD) waves and instabilities existing within a magnetized, plane-parallel, self-gravitating slab. Our approach allows for fully non-uniformly magnetized slabs, which deviate from isothermal conditions, such that the well-known Alfvén and slow continuous spectra enter the description. We generalize modern MHD textbook treatments, by showing how self-gravity enters the MHD wave equation, beyond the frequently adopted Cowling approximation. This clarifies how Jeans’ instability generalizes from hydro to magnetohydrodynamic conditions without assuming the usual Jeans’ swindle approach. Our main contribution lies in reformulating the completely general governing wave equations in a number of mathematically equivalent forms, ranging from a coupled Sturm-Liouville formulation, to a Hamiltonian formulation linked to coupled harmonic oscillators, up to a convenient matrix differential form. The latter allows us to derive analytically the eigenfunctions of a magnetized, self-gravitating thin slab. In addition, as an example we give the exact closed form dispersion relations for the hydrodynamical p- and Jeans-unstable modes, with the latter demonstrating how the Cowling approximation modifies due to a proper treatment of self-gravity. The various reformulations of the MHD wave equation open up new avenues for future MHD spectral studies of instabilities as relevant for cosmic filament formation, which can e.g. use modern formal solution strategies tailored to solve coupled Sturm-Liouville or harmonic oscillator problems.

Magnetohydrodynamic (MHD) stability of wendelstain7-X reactor with reszistive wall (RWMs)

Plasma stability is the biggest challenge facing the nuclear fusion industry. One of the best methods of stability study is magnetohydrodynamic (MHD) equations, which has two linear and nonlinear states. Usually linear stability analysis is used to describe the MHD state, which is obtained by linearizing nonlinear equations. The reactor under study is the W7-X reactor, which is an optimal example of a stellaratoric system. The question raised in this research is how to create suitable conditions for the formation and formation of plasma and heat transfer produced by the melting reaction. Many efforts have been made in this direction, but still the record holder for plasma state maintenance belongs to the international ITER project and around 1000S. However, IPP researchers at the Max Planck Institute in Germany (maker of the W7-X reactor) predicted that by 2020 they would produce a pulse of 30 minutes. The numerical method is used to investigate the stability of the reactor. In this paper, boundary conditions were expressed in terms of resistance wall. With the help of the mathematical Matlab software, magnetic field values ​​were obtained from experimental reports extracted from the Max Planck Institute for various values ​​of β. From the values ​​obtained, it was concluded that the appropriate field value is β = 5 according to the ideal MagnetoHydroDynamic state and the interval defined by the Max Planck Institute.

Modeling the Natural Convection Flow in a Square Porous Enclosure Filled with a Micropolar Nanofluid under Magnetohydrodynamic Conditions

The laminar, natural convective flow of a micropolar nanofluid in the presence of a magnetic field in a square porous enclosure was studied. The micropolar nanofluid is considered to be an electrically conductive fluid. The governing equations of the flow problem are the conservation of mass, energy, and linear momentum, as well as the angular momentum and the induction equations. In the proposed model, the Darcy–Brinkman momentum equations with buoyancy and advective inertia are used. Experimentally obtained forms of the dynamic viscosity, the thermal conductivity, and the electric conductivity are employed. A meshless point collocation method has been applied to numerically solve the flow and transport equations in their vorticity-stream function formulation. The effects of characteristic dimensionless parameters, such as the Rayleigh and Hartmann numbers, for a range of porosity and solid volume fraction of Al2O3 particles in a water-based micropolar nanofluid on the flow and heat transfer in the cavity are investigated. The results indicate that the intensity of the magnetic field significantly affects both the flow and the temperature distributions. Moreover, the addition of nanoparticles deteriorates the heat-transfer efficiency under specific conditions.

Laboratory study of non-ideal effects in magnetically collimated astrophysical outflows

Central outflow’s collimation by magnetic field is an important theoretical mechanism for explaining the astrophysical objects’ morphology formation, and its credibility has been tested in many laser plasma experiments in a dimensionless manner. This article introduces integrated simulation and experiment work based on the present laboratory magnetically collimated jet framework, to explore how non-ideal terms’ strength including radiative cooling and magnetic diffusion from different targets can affect the outflow shape. The interaction between outflow from a target with low atomic number and external field satisfies the ideal magneto-hydrodynamic conditions, and the outflow shape results in diamagnetic cavity and jet; on the other hand, a heavy element target brings strong magnetic diffusion that destroys the collimation structure, together with the stagnation of outflow introduced by radiative cooling, and outflow shape results in weakly collimated hemisphere near the target and a detached magnetized density clump. The detailed dimensionless analysis shows that the large-scale dissipation of jets in young stellar objects can possibly be an analog of the laboratory jet’s magnetic diffusion breakup, also similar structures like the loosely collimated lobes and bright ansaes in planetary nebula can be observed in highly diffusive laboratory outflows. This article shows for the first time that a series of non-relativistic astronomical outflows’ dynamic behaviors can be explained by the non-ideal magneto-hydrodynamic evolution of laboratory plasmas.

On sub-Alfven MHD flows with acceleration in coaxial channels

Magnetohydrodynamic (MHD) flows in coaxial channels of plasma accelerators with a longitudinal magnetic field are considered. Sub-Alfven MHD flows with acceleration transonic to the slow magnetosonic speed are studied. Sub-Alfven MHD flows are related to the case when the plasma flow velocity doesn’t exceed the Alfven speed corresponding to the longitudinal field along the channel. A narrow coaxial nozzle channel with a constant lower bound is considered. The non-stationary and stationary mathematical MHD models are considered in the quasi-one-dimensional approximation. The corresponding MHD problems are solved numerically. Features of the relaxation process and characteristics of the transonic sub-Alfven flow type with acceleration in the channel are studied. The influence of the longitudinal magnetic field on the steady-state plasma flows are researched. The mechanism of energy transformations is described.

High-speed shear-driven dynamos. Part 2. Numerical analysis

This paper aims to numerically verify the large Reynolds number asymptotic theory of magneto-hydrodynamic (MHD) flows proposed in the companion paper Deguchi (J. Fluid Mech., vol. 868, 2019, pp. 176–211). To avoid any complexity associated with the chaotic nature of turbulence and flow geometry, nonlinear steady solutions of the viscous resistive MHD equations in plane Couette flow have been utilised. Two classes of nonlinear MHD states, which convert kinematic energy to magnetic energy effectively, have been determined. The first class of nonlinear states can be obtained when a small spanwise uniform magnetic field is applied to the known hydrodynamic solution branch of plane Couette flow. The nonlinear states are characterised by the hydrodynamic/magnetic roll–streak and the resonant layer at which strong vorticity and current sheets are observed. These flow features, and the induced strong streamwise magnetic field, are fully consistent with the vortex/Alfvén wave interaction theory proposed in the companion paper. When the spanwise uniform magnetic field is switched off, the solutions become purely hydrodynamic. However, the second class of ‘self-sustained shear-driven dynamos’ at the zero external magnetic field limit can be found by homotopy via the forced states subject to a spanwise uniform current field. The discovery of the dynamo states has motivated the corresponding large Reynolds number matched asymptotic analysis in the companion paper. Here, the reduced equations derived by the asymptotic theory have been solved numerically. The asymptotic solution provides remarkably good predictions for the finite Reynolds number dynamo solutions.

Chemical Reaction Effect on Nonlinear Radiative MHD Nanofluid Flow over Cone and Wedge

The awareness of heat and mass transfer in nanofluid flows with magnetohydrodynamic conditions over cone and wedge is very significant for design of heat exchangers, transpiration, fiber coating, etc. With this initiation, we construct a mathematical model to investigate the chemical reaction effects on electrically conducting magnetohydrodynamic nanofluid flow over a cone and a wedge. For this purpose, we also consider a nonlinear thermal radiation, viscous dissipation, Joule heating with non-uniform heat source/sink. The transformed equations are solved by using shooting technique based on RK fourth order method. Effects of pertinent parameters of concern on the common profiles are conversed (in two cases). It is perceived that the momentum, temperature and concentration boundary layers are non-uniform for the flow over a wedge and a cone Key words: MHD, Non-linear Radiation, nanofluid, Chemical Reaction, heat generation.

High-speed shear-driven dynamos. Part 1. Asymptotic analysis

Rational large Reynolds number matched asymptotic expansions of three-dimensional nonlinear magneto-hydrodynamic (MHD) states are the concern of this contribution. The nonlinear MHD states, assumed to be predominantly driven by a unidirectional shear, can be sustained without any linear instability of the base flow and hence are responsible for subcritical transition to turbulence. Two classes of nonlinear MHD states are found. The first class of nonlinear states emerged out of a nice combination of the purely hydrodynamic vortex/wave interaction theory by Hall & Smith (J. Fluid Mech., vol. 227, 1991, pp. 641–666) and the resonant absorption theories on Alfvén waves, developed in the solar physics community (e.g. Sakurai et al. Solar Phys., vol. 133, 1991, pp. 227–245; Goossens et al. Solar Phys., vol. 157, 1995, pp. 75–102). Similar to the hydrodynamic theory, the mechanism of the MHD states can be explained by the successive interaction of the roll, streak and wave fields, which are now defined both for the hydrodynamic and magnetic fields. The derivation of this ‘vortex/Alfvén wave interaction’ state is rather straightforward as the scalings for both of the hydrodynamic and magnetic fields are identical. It turns out that the leading-order magnetic field of the asymptotic states appears only when a small external magnetic field is present. However, it does not mean that purely shear-driven dynamos are not possible. In fact, the second class of ‘self-sustained shear-driven dynamo theory’ shows a magnetic generation that is slightly smaller in size in the absence of any external field. Despite its small size, the magnetic field causes the novel feedback mechanism in the velocity field through resonant absorption, wherein the magnetic wave becomes more strongly amplified than the hydrodynamic counterpart.