Magnetohydrodynamic Instabilities Research Articles

Design, Construction, and Operation of the Compact Toroidal Hybrid

The Compact Toroidal Hybrid (CTH) is a low-aspect-ratio (), low-beta (%) torsatron with a major radius of . CTH is operable as a pure stellarator, but most research on this device is conducted with hybrid discharges in which a toroidal plasma current is driven in order to study magnetohydrodynamic instabilities and disruptions in current-carrying stellarator plasmas. The vacuum helical field of CTH is produced by a continuously wound helical coil with poloidal and toroidal periodicities of and , respectively. The maximum on-axis toroid al magnetic field is . The helical coil encloses a circular vacuum vessel of major radius = 0.75 m with a circular cross section of minor radius 0.29 m. A toroidal plasma current up to 80 kA is produced with an ohmic heating (OH) transformer. The average plasma radius is typically 0.20 m. Five independently controllable magnet coil sets produce the base stellarator magnetic field configuration. With 15-kW electro.n cyclotron heating at the fundamental frequency, densities of and electron temperatures of 20 eV are achieved. With the addition of OH, densities reach with temperatures of . Ten motor/generator power supplies provide up to 10 MW of power to energize the magnet set providing the equilibrium field, and a capacitor bank provides the pulsed current for the OH system. Design considerations, constraints, and construction techniques of the CTH magnet coils, vacuum vessel, and support structure are discussed, and an operational overview is given.

Role of a continuous MHD dynamo in the formation of 3D equilibria in fusion plasmas

Stationary 3D equilibria can form in fusion plasmas via saturation of magnetohydrodynamic (MHD) instabilities or stimulated by external 3D fields. In these cases the current profile is anomalously broad due to magnetic flux pumping produced by the MHD modes. Flux pumping plays an important role in hybrid tokamak plasmas, maintaining the minimum safety factor above unity and thus removing sawteeth. It also enables steady-state hybrid operation, by redistributing non-inductive current driven near the center by electron cyclotron waves. A validated flux pumping model is not yet available, but it would be necessary to extrapolate hybrid operation to future devices. In this work flux pumping physics is investigated for helical core equilibria stimulated by external 3D fields in DIII-D hybrid plasmas. We show that flux pumping can be produced in a continuous way by an MHD dynamo emf. The same effect maintains helical equilibria in reversed-field pinch (RFP) plasmas. The effective MHD dynamo loop voltage is calculated for experimental 3D equilibrium reconstructions, by balancing Ohm’s law over helical flux surfaces, and is consistent with the expected current redistribution. Similar results are also obtained with more sophisticated nonlinear MHD simulations. The same modelling approach is applied to helical RFP states forming spontaneously in RFX-mod as the plasma current is raised above 0.8–1 MA. This comparison allows to identify the underlying physics common to tokamak and RFP: a helical core displacement modulates parallel current density along flux tubes, which requires a helical electrostatic potential to build up, giving rise to a helical MHD dynamo flow.

Multiple MHD instabilities in high-βN toroidal plasmas with reversed magnetic shear

The toroidal magnetohydrodynamic (MHD) code MARS-F (Liu et al 2000 Phys. Plasmas 7 3681) is applied to numerically investigate multiple MHD instabilities in high-βN (βN is the beta normalized) toroidal plasmas with reversed magnetic shear, and with different radial separations between the two q = 2 rational surfaces. A resistive wall is also taken into account. In the small regime, it is found that a finite βN leads to multiple branches of the double tearing mode (DTM). The beta normalized has a stabilizing effect on the most unstable branch. There exists a critical value βNc, above which the real frequency of the most unstable mode becomes finite due to the favorable average curvature effect (Glasser et al 1975 Phys. Fluids 18 875). Moreover, the critical value βNc decreases with increasing plasma resistivity In the large regime, on the other hand, finite beta normalized can help to transform the two DTM branches into an external kink mode (EKM). Increasing βN can also couple two single tearing modes, forming a DTM. In the intermediate regime, interestingly, a new branch with EKM structure appears, which successively couples with the other two branches as increases, recovering the EKM found in the large limit. Characteristics of the eigenmode structures in different regimes are compared and analyzed in detail. Furthermore, the properties of the high-βN MHD instabilities, with higher toroidal mode number n, are also investigated. It is found that, in the small limit, the growth rate always first increases and then decreases with n, forming a broad n spectrum. The critical value decreases with n. In the large limit, however, the growth rate of the n = 2 mode is strongly reduced with increasing βN.

Analysis of anisotropic effects on energy induced by lower hybrid wave heating on EAST

It has been pointed out that plasma anisotropy has a significant impact on the characteristics of magnetohydrodynamic equilibrium and instability. Recently, anisotropic pressure effects induced by 4.6 GHz lower hybrid wave (LHW) heating on the Experimental Advanced Superconducting Tokamak (EAST) has been investigated. The mechanism is due to the high-energy electrons generated by LHW Landau damping effects in the direction parallel to the magnetic field line.

Reduced fluid simulation of runaway electron generation in the presence of resistive kink modes

A reduced fluid simulation is developed to study the formation of runaway current profiles in the framework of a reduced magnetohydrodynamic (MHD) model. In our simulation,three-dimensional dynamics of runaway electrons in real space is treated in terms of the equation for fluid electron density with source terms representing Dreicer and secondary generation mechanisms. The excitation of MHD instabilities, non-diffusive transport due to magnetic field fluctuation and dynamical changes of the runaway generation rate due to MHD activity are incorporated. The results of an m/n = 1/1 single-helicity simulation for resistive kink instability are illustrated, where m and n are the poloidal and toroidal mode numbers, respectively. It is found that: (1) profile relaxation due to resistive kink instability affects net runaway generation through modification of the internal inductance; and (2) inductive voltage spike can be a direct channel to enhance Dreicer seed electrons with background electric fields exceeding the critical threshold of runaway generation.

Numerical Study of the Buoyancy Effect on Magnetohydrodynamic Three-Dimensional LiPb Flow in a Rectangular Duct

In this paper, the effect of transverse magnetic field on a laminar liquid lead lithium flow in an insulating rectangular duct is numerically solved with three-dimensional (3D) simulations. Cases with and without buoyancy force are examined. The stability of the buoyant flow is studied for different values of the Hartmann number from 0 to 120. We focus on the combined influence of the Hartmann number and buoyancy on flow field, flow structure in the vicinity of walls and its stability. Velocity and temperature distributions are presented for different magnetic field strengths. It is shown that the magnetic field damps the velocity and leads to flow stabilization in the core fluid and generates magnetohydrodynamic (MHD) boundary layers at the walls, which become the main source of instabilities. The buoyant force is responsible of the generation of vortices and enhances the velocities in the core region. It can act together with the MHD forces to intensify the flow near the Hartmann layers. Two critical Hartmann numbers (Hac1 = 63, Hac2 = 120) are found. Hac1 is corresponding to the separation of two MHD regimes: the first one is characterized by a core flow maximum velocity, whereas the second regime is featured by a maximum layer velocity and a pronounced buoyancy effect. Hac2 is a threshold value of electromagnetic force indicating the onset of MHD instability through the generation of small vortices close to the side layers.

Simulating Magnetohydrodynamic Instabilities with Conservative Perturbed MHD Model Using Discontinuous Galerkin Method

AbstractIn magnetically confined plasma research, the understandings of small and large perturbations at equilibrium are both critical for plasma controlling and steady state operation. Numerical simulations using original MHD model can hardly give clear picture for small perturbations, while non-conservative perturbed MHD model may break conservation law, and give unphysical results when perturbations grow large after long-time computation. In this paper, we present a nonlinear conservative perturbed MHD model by splitting primary variables in original MHD equations into equilibrium part and perturbed part, and apply an approach in the framework of discontinuous Galerkin (DG) spatial discretization for numerical solutions. This enables high resolution of very small perturbations, and also gives satisfactory non-smooth solutions for large perturbations, which are both broadly concerned in magnetically confined plasma research. Numerical examples demonstrate satisfactory performance of the proposed model clearly. For small perturbations, the results have higher resolution comparing with the original MHD model; for large perturbations, the non-smooth solutions match well with existing references, confirming reliability of the model for instability investigations in magnetically confined plasma numerical research.

Ideal and resistive magnetohydrodynamic instabilities in cylindrical geometry with a sheared flow along the axis

The problem of the linear stability of internal magnetohydrodynamic modes in a cylindrical plasma with a sheared longitudinal flow is addressed. A Newcomb-like equation describing the perturbation is derived and exactly solved for a class of analytic profiles for rotational transform, equilibrium flow and pressure. A dispersion relation for ideal modes is then derived and analysed for different limits of the poloidal mode number (viz. m = 1, and ). In the resistive case, a simple and exact expression for the tearing stability index is derived using the same class of equilibrium profiles. It is found that a small flow shear has a destabilising effect, while if the flow shear is dominant over the magnetic shear the tearing mode is stabilised. Implications on the stability of the m = 1 resistive mode are also discussed.

General-relativistic Large-eddy Simulations of Binary Neutron Star Mergers

Abstract The flow inside remnants of binary neutron star (NS) mergers is expected to be turbulent, because of magnetohydrodynamics instability activated at scales too small to be resolved in simulations. To study the large-scale impact of these instabilities, we develop a new formalism, based on the large-eddy simulation technique, for the modeling of subgrid-scale turbulent transport in general relativity. We apply it, for the first time, to the simulation of the late-inspiral and merger of two NSs. We find that turbulence can significantly affect the structure and survival time of the merger remnant, as well as its gravitational-wave (GW) and neutrino emissions. The former will be relevant for GW observation of merging NSs. The latter will affect the composition of the outflow driven by the merger and might influence its nucleosynthetic yields. The accretion rate after black hole formation is also affected. Nevertheless, we find that, for the most likely values of the turbulence mixing efficiency, these effects are relatively small and the GW signal will be affected only weakly by the turbulence. Thus, our simulations provide a first validation of all existing post-merger GW models.

Multiple secondary islands formation in nonlinear evolution of double tearing mode simulations

A new numerical code solving the conservative perturbed resistive magnetohydrodynamic (MHD) model is developed. Numerical tests of the ideal Kelvin-Helmholtz instability and the resistive double tearing mode (DTM) show its capability in solving linear and nonlinear MHD instabilities. The nonlinear DTM evolution in 2D geometry is numerically investigated with low guiding field Bz0, short half-distance y0 between the equilibrium current sheets, and small resistivity η. The interaction of islands on the two initial current sheets may generate an unstable flow driven current sheet with a high length-to-thickness aspect ratio (α), and multiple secondary islands can form. In general, the length-to-thickness aspect ratio α and the number of secondary islands increase with decreasing guide field Bz0, decreasing half-distance y0, and increasing Lundquist number of the flow driven current sheet SL although the dependence may be non-monotonic. The reconnection rate dependence on SL, Bz0, and y0 is also investigated.

Rayleigh-Taylor and Parker instabilities in MHD fluids

We present a brief survey of recent mathematical results on the stability and instability of magnetohydrodynamic flows in the presence of a gravitational field, which include the incompressible magnetic Rayleigh-Taylor instability, and the Parker instability (i.e., the magnetic buoyancy instability) in compressible magnetohydrodynamics. In particular, the stabilizing effect of some factors (e.g., steady magnetic fields, boundary conditions, domains) are analyzed. In addition, the mathematical results on the Rayleigh-Taylor instability problem in viscoelastic flows are discussed.

Metal pad roll instability in liquid metal batteries

The increasing deployment of renewable energies requires three fundamental change to the electric grid: more transmission lines, a flexibilization of the demand and grid scale energy storage. Liquid metal batteries (LMBs) are considered these days as a promising means of stationary energy storage. Built as a stable density stratification of two liquid metals separated by a liquid salt, LMBs have three main advantages: a low price, a long life-time and extremely high current densities. In order to be cheap, LMBs have to be built large. However, battery currents of the order of kilo-amperes may lead to magnetohydrodynamic (MHD) instabilities, which – in the worst case – may short-circuit the thin electrolyte layer. The metal pad roll instability, as known from aluminium reduction cells, is considered as one of the most dangerous phenomena for LMBs. We develop a numerical model, combining fluid- and electrodynamics with the volume-of-fluid method, to simulate this instability in cylindrical LMBs. We explain the instability mechanism similar to that in aluminium reduction cells and give some first results, including growth rates and oscillation periods of the instability

Quasi-static and dynamic magnetic tension forces in arched, line-tied magnetic flux ropes

Solar eruptions are often driven by magnetohydrodynamic instabilities such as the torus and kink instabilities that act on line-tied magnetic flux ropes. Recent laboratory experiments designed to study these eruptive instabilities have demonstrated the key role of both dynamic (Myers et al 2015 Nature 528 526) and quasi-static (Myers et al 2016 Phys. Plasmas 23 112102) magnetic tension forces in contributing to the equilibrium and stability of line-tied magnetic flux ropes. In this paper, we synthesize these laboratory results and explore the relationship between the dynamic and quasi-static tension forces. While the quasi-static tension force is found to contribute to the flux rope equilibrium in a number of regimes, the dynamic tension force is substantial mostly in the so-called failed torus regime where magnetic self-organization events prevent the flux rope from erupting.

The Effect of “Wave Breakers” on the Magnetohydrodynamic Instability in Aluminum Reduction Cells

We report the results of the experiments on the suppression of the MHD instability in a model of the aluminum reduction cells (Pedchenko et al. in EPL 88:24001, 2009). The idea behind the study is to introduce obstacles in the liquid metal to suppress the propagation of the rolling-pad instability wave. As a result, in some configurations with obstacles, we detect lowering of the wave amplitude, reduction of its propagation speed, and rise of the main parameters’ thresholds, responsible for the instability onset.

Multi-phase hybrid simulation of energetic particle driven magnetohydrodynamic instabilities in tokamak plasmas

Magnetohydrodynamic (MHD) instabilities driven by energetic particles in tokamak plasmas and the energetic particle distribution formed with the instabilities, neutral beam injection, and collisions are investigated with hybrid simulations for energetic particles and an MHD fluid. The multi-phase simulation, which is a combination of classical simulation and hybrid simulation, is applied to examine the distribution formation process in the collisional slowing-down time scale of energetic ions for various beam deposition power () and slowing-down time (). The physical parameters other than and are similar to those of a Tokamak Fusion Test Reactor (TFTR) experiment (Wong et al 1991 Phys. Rev. Lett. 66 1874). For = 10 MW and = 100 ms, which is similar to the TFTR experiment, the bursts of toroidal Alfvén eigenmodes take place with a time interval 2 ms, which is close to that observed in the experiment. The maximum radial velocity amplitude (vr) of the dominant TAE at the bursts in the simulation is where vA is the Alfvén velocity at the plasma center. For = 5 MW and = 20 ms, the amplitude of the dominant TAE is kept at a constant level . The intermittency of TAE rises with increasing and increasing (= decreasing collision frequency). With increasing volume-averaged classical energetic ion pressure, which is well proportional to , the energetic ion confinement degrades monotonically due to the transport by the instabilities. The volume-averaged energetic ion pressure depends only on the volume-averaged classical energetic ion pressure, not independently on or . The energetic ion pressure profile resiliency, where the increase in energetic ion pressure profile is saturated, is found for the cases with the highest where the TAE bursts take place.

The Influence of Neutral Beam Injection on the Heating and Current Drive with Electron Cyclotron Wave on EAST**supported by the National Magnetic Confinement Fusion Science Program of China (Nos. 2013GB101001 and 2014DFG61950) and National Natural Science Foundation of China (Nos. 11405212 and 11175211)

Both neutral beam injection (NBI) and electron cyclotron resonance heating (ECRH) have been applied on the Experimental Advanced Superconducting Tokamak (EAST) in the 2015 campaign. In order to achieve more effective heating and current drive, the effects of NBI on the heating and current drive with electron cyclotron wave (ECW) are analyzed utilizing the code TORAY and experimental data in the shot #54411 and #54417. According to the experimental and simulated results, for the heating with ECW, NBI can improve the heating efficiency and move the power deposition place towards the inside of the plasma. On the other hand, for the electron cyclotron current drive (ECCD), NBI can also improve the efficiency of ECCD and move the place of ECCD inward. These results will be valuable for the center heating, the achievement of fully non-inductive current drive operation and the suppression of magnetohydrodynamic (MHD) instabilities with ECW on EAST or ITER with many auxiliary heating methods.

Parametric instabilities in shallow water magnetohydrodynamics of astrophysical plasma in external magnetic field

This article deals with magnetohydrodynamic (MHD) flows of a thin rotating layer of astrophysical plasma in external magnetic field. We use the shallow water approximation to describe thin rotating plasma layer with a free surface in a vertical external magnetic field. The MHD shallow water equations with external vertical magnetic field are revised by supplementing them with the equations that are consequences of the magnetic field divergence-free conditions and reveal the existence of third component of the magnetic field in such approximation providing its relation with the horizontal magnetic field. It is shown that the presence of a vertical magnetic field significantly changes the dynamics of the wave processes in astrophysical plasma compared to the neutral fluid and plasma layer in a toroidal magnetic field. The equations for the nonlinear wave packets interactions are derived using the asymptotic multiscale method. The equations for three magneto-Poincare waves interactions, for three magnetostrophic waves interactions, for the interactions of two magneto-Poincare waves and for one magnetostrophic wave and two magnetostrophic wave and one magneto-Poincare wave interactions are obtained. The existence of parametric decay and parametric amplifications is predicted. We found following four types of parametric decay instabilities: magneto-Poincare wave decays into two magneto-Poincare waves, magnetostrophic wave decays into two magnetostrophic waves, magneto-Poincare wave decays into one magneto-Poincare wave and one magnetostrophic wave, magnetostrophic wave decays into one magnetostrophic wave and one magneto-Poincare wave. Following mechanisms of parametric amplifications are found: parametric amplification of magneto-Poincare waves, parametric amplification of magnetostrophic waves, magneto-Poincare wave amplification in magnetostrophic wave presence and magnetostrophic wave amplification in magneto-Poincare wave presence. The instabilities growth rates are obtained respectively.

Scaled laboratory experiments explain the kink behaviour of the Crab Nebula jet.

The remarkable discovery by the Chandra X-ray observatory that the Crab nebula's jet periodically changes direction provides a challenge to our understanding of astrophysical jet dynamics. It has been suggested that this phenomenon may be the consequence of magnetic fields and magnetohydrodynamic instabilities, but experimental demonstration in a controlled laboratory environment has remained elusive. Here we report experiments that use high-power lasers to create a plasma jet that can be directly compared with the Crab jet through well-defined physical scaling laws. The jet generates its own embedded toroidal magnetic fields; as it moves, plasma instabilities result in multiple deflections of the propagation direction, mimicking the kink behaviour of the Crab jet. The experiment is modelled with three-dimensional numerical simulations that show exactly how the instability develops and results in changes of direction of the jet.

FADING CORONAL STRUCTURE AND THE ONSET OF TURBULENCE IN THE YOUNG SOLAR WIND

ABSTRACT Above the top of the solar corona, the young, slow solar wind transitions from low-β, magnetically structured flow dominated by radial structures to high-β, less structured flow dominated by hydrodynamics. This transition, long inferred via theory, is readily apparent in the sky region close to 10° from the Sun in processed, background-subtracted solar wind images. We present image sequences collected by the inner Heliospheric Imager instrument on board the Solar-Terrestrial Relations Observatory (STEREO/HI1) in 2008 December, covering apparent distances from approximately 4° to 24° from the center of the Sun and spanning this transition in the large-scale morphology of the wind. We describe the observation and novel techniques to extract evolving image structure from the images, and we use those data and techniques to present and quantify the clear textural shift in the apparent structure of the corona and solar wind in this altitude range. We demonstrate that the change in apparent texture is due both to anomalous fading of the radial striae that characterize the corona and to anomalous relative brightening of locally dense puffs of solar wind that we term “flocculae.” We show that these phenomena are inconsistent with smooth radial flow, but consistent with the onset of hydrodynamic or magnetohydrodynamic instabilities leading to a turbulent cascade in the young solar wind.

Power Amplifiers Based on SiC Technology for MHD Mode Control in Fusion Experiments

The effective control of magnetohydrodynamic instabilities in fusion experiments by means of actively controlled coils calls for challenging dynamic requirements to the relevant power supply (PS) systems. The first part of this paper gives an overview on typical requirements and technological solutions adopted in some present fusion experiments. Then, the advantages of SiC devices with respect to the Si ones are described in this paper, including lower switching losses, higher switching speed, higher operating junction temperature, and higher voltage capability. As an application example, this paper reports on the case of the PS system for resistive wall mode control in the JT-60SA satellite tokamak, where analyses showed the difficulty of satisfying the demanding requirements in terms of high current bandwidth (3 kHz) and short latency ( $ ) with a simple H-bridge topology adopting standard IGBT. On the contrary, the use of Si–SiC IGBT with the same topology can allow meeting the specifications, as demonstrated by the development and test of such a power amplifier, rated for $300~A_{{\mathrm{pk}}}$ and 240 V.