Magnetohydrodynamic Stability Research Articles

Nature of ideal MHD instabilities as described by multi-region relaxed MHD

In this work, the stepped pressure equilibrium code (SPEC) (Hudson et al 2012 Phys. Plasmas 19 112502), which computes the equilibria of the multi-region relaxed magnetohydrodynamic energy principle (MRxMHD), has been upgraded to determine the MRxMHD stability in toroidal geometry. A theoretical formalism for SPEC is obtained by relating the second variation of the MRxMHD energy functional to the Hessian matrix, enabling the prediction of magnetohydrodynamic (MHD) linear instabilities. Negative eigenvalues of this matrix imply instability. Further, we demonstrate our method on simplified test scenarios in both tokamak and stellarator magnetic topologies, with a systematic comparison study between the marginal stability prediction of the SPEC with the ideal MHD stability code packages CAS3D and MISHKA-1.

Predicted optimization of β N limit for steady-state scenario with double transport barriers in HL-2M tokamak

The equilibria of the HL-2M tokamak, designed for steady-state operation with reversed magnetic shear and double transport barriers, are calculated using TOQ code, and the linear ideal magnetohydrodynamic (MHD) stability of the equilibria is investigated using GATO code. To improve the beta () limit, the MHD stability of the equilibria with different heights of internal transport barrier (ITB) and edge transport barrier (ETB) is simulated. The simulation results indicate that the ITB drives low globalized modes while the ETB drives high edge localized modes, and thus a moderate barrier height ratio is beneficial to MHD stability. By adjusting the heights of both barriers with different plasma shapes, as well as different locations and widths of ITBs, optimal equilibria with improved MHD stability are achieved, which always have a moderate barrier height ratio unless the ITB is extremely wide or very close to the edge. In ideal-wall conditions, when the ITB is wide enough or very close to the edge, limits could exceed six, or even reach seven in some special cases. Increasing elongation and triangularity, broadening the ITB, as well as moving the ITB to a large minor radius, can contribute to the optimization of the limit, especially when combined with the stabilizing effect from an ideal wall.

Pedestal analysis of MAST ELMy regimes

Mega Ampere Spherical Tokamak (MAST) pedestal data has been analysed, where a pedestal database of 892 shots was obtained, using the upgraded MAST Thomson scattering (TS) diagnostic. Various edge localised mode (ELM) types are discussed, where characteristics and trends of MAST pedestals are shown. The data from the upgraded TS diagnostic confirms pedestal characteristics found in earlier analysis, using previous TS systems. Using the database, calculations of the bootstrap current are obtained using the different analytical formulae (Sauter and Redl), and comparisons are performed. The upgraded MAST TS system now spans the full plasma mid-plane, such that direct comparisons between inboard and outboard pedestals can be obtained, and asymmetries in the density pedestal width were found. To increase confidence in spherical tokamak pedestal predictions, the assumptions of Europed have been validated from the MAST pedestal data, and a value for the kinetic ballooning mode constraint () has been obtained. The first spherical tokamak pedestal predictions were performed in Europed and compared to experimental values. Using C = 0.145 the temperature pedestal height was predicted to within 10% of the experimental value. In addition type II ELMs on MAST are analysed, and stability analysis and parameter scans have been performed using ESSIVE. Similar magneto-hydrodynamic (MHD) stability properties are observed for type I and type II ELMs, originating from the mixed ELM regimes; it is therefore difficult to distinguish these ELMs using the ideal MHD codes.

Healing plasma current ramp-up by nitrogen seeding in the full tungsten environment of WEST

Achieving a successful plasma current ramp-up in a full tungsten tokamak can be challenging due to the large core radiation (and resulting low core temperature) that can be faced with this heavy metallic impurity if its relative concentration is too high. Nitrogen injection during the plasma current ramp-up of WEST discharges greatly improves the core temperature and magnetohydrodynamic (MHD) stability. Experimental measurements and integrated simulations with the RAPTOR code, complemented with the QuaLiKiz neural network for computing turbulent transport, allow a detailed understanding of the mechanisms at play. Increased edge radiation during this transient phase is shown to improve confinement properties, driving higher core temperature and better MHD stability. This also leads to increased operation margins with respect to tungsten contamination.

Advances in prediction of tokamak experiments with theory-based models

The successful validation of theory-based models of transport, magnetohydrodynamic stability, heating and current drive, with tokamak measurements over the last 20 years, has laid the foundation for a new era where these models can be routinely used in a ‘predict first’ approach to design and predict the outcomes of experiments on tokamaks today. The capability to predict the plasma confinement and core profiles with a quantified uncertainty, based on a multi-machine, international, database of experience, will provide confidence that a proposed discharge will remain within the operational limits of the tokamak. Developing this predictive capability for the first generation of burning plasma devices, beginning with ITER, and progressing to tokamak demonstration reactors, is a critical mission of fusion energy research. Major advances have been made implementing this predict first methodology on today’s tokamaks. An overview of several of these recent advances will be presented, providing the integrated modeling foundations of the experimental successes. The first steps to include boundary plasmas, and tokamak control systems, have been made. A commitment to predicting experiments as part of the planning process is needed in order to collect predictive accuracy data and evolve the models and software into a robust whole discharge pulse design simulator.

Numerical study on predicting MHD stability of HL-2A tokamak pedestal structure

HL-2A tokamak achieved the first ELMy H-mode discharge operation in 2009 under divertor configuration, and many experimental and simulation researches have been carried out to investigate the pedestal magnetohydrodynamic (MHD) instability. However, there are still few studies on the effect of pedestal structure on MHD stability. Therefore, based on HL-2A experimental parameters, equilibria with different pedestal structures are generated by using TOQ code, and the MHD stability of the equilibria is simulated by using the BOUT++ three-field module. The linear simulations show that reducing the pedestal height, increasing the pedestal width, reducing the pedestal current density and reducing the ion density in the pedestal can improve the MHD stability of pedestal. Using the theory of dispersion relation, the simulation results are explained. Under the premise of MHD stability, the maximum pedestal heights corresponding to different pedestal widths are found, and the data are fitted to obtain an empirical formula that can predict pedestal height, and on this basis, considering the kinetic ballooning mode theory, pedestal height and width are predicted simultaneously. The effect of the pedestal structure on the MHD mode structure is investigated, it is found that the pedestal height can affect the radial width of the mode. Nonlinear simulations show that the pre-growth of instability is affected mainly by a single dominant mode, and the growth of the dominant mode to a certain size will cause the collapse of the pedestal and the eruption of the edge localized mode (ELM). The variation of ELM size after ELM eruption is synchronized with the evolution of the dominant mode. Generally, equilibria with larger linear growth rates have larger ELM sizes and a wider range of pedestal collapse in nonlinear simulations. In this work, the scanning of the pedestal data focuses mainly on the width and height of the pedestal, and other parameters such as small radius, toroidal magnetic field, plasma current, and the pedestal safety factor values will be changed in the future based on the work in this paper, with the aim of enriching the HL-2A pedestal database and predicting the pedestal structure more accurately. Finally these results will be integrated under the HL-2A integrated platform, which in turn will provide a reference for HL-2A tokamak H-mode experiments and integrated simulations.

Ideal magnetohydrodynamic stability in stellarators with subsonic equilibrium flow

The effect of a subsonic flow, inherent to most stellarators because of a radial electric field, on their ideal magnetohydrodynamic (MHD) stability properties is studied employing the quasi-Lagrangian picture developed by Frieman and Rotenberg (1960 Rev. Mod. Phys. 32 898). The Mach number of the perpendicular E × B flow in stellarators is of order 0.01 and, therefore, admits the usage of a subsonic approximation in form of a static equilibrium. A mathematical formulation of the weak form of the stability equation with flow has been implemented in the ideal-MHD stability code CAS3D. This formulation uses magnetic coordinates and does not involve any derivatives across magnetic surfaces. In addition to the expected Doppler shift of frequencies, properties of the spectrum of the ideal MHD force operator, which are already known for tokamaks, but now also shown in the stellarator case, are: firstly, the appearance of unstable flow-induced continua stemming from the coupling of sound and Alfvén continuum branches with equal mode numbers; and, secondly, the existence of flow-induced, global, stable modes near extrema of sound continuum branches, the extrema, in turn, being generated by the influence of a sheared flow on the static sound continua.

Stabilization of kink/peeling modes by coupled rotation and ion diamagnetic drift effects in quiescent H-mode plasmas in DIII-D and JT-60U

Magnetohydrodynamic stability at the edge pedestal in several quiescent H-mode (QH-mode) plasmas in DIII-D and JT-60U experiments was analyzed by considering plasma rotation and ion diamagnetic drift effects. It was identified that a kink/peeling mode, which is a prime candidate for a trigger of edge harmonic oscillation in QH-mode, is stabilized by plasma rotation when considering the ion diamagnetic drift simultaneously in both experiments. The stabilizing effect by rotation becomes more effective in case using the rotation profile of the main ion species evaluated by assuming radial force balance. In addition, when inverting the rotation direction, it was found that the kink/peeling mode is more stabilized when considering the rotation of the main ion species, though the mode is less stabilized by the rotation of impurity ion species. The result implies that the kink/peeling mode stability in QH-mode plasmas is sensitive to how the rotation profile is evaluated, but it is shown that a qualitative trend stabilizing the kink/peeling mode by rotation can be reproduced with the poloidal rotation profile of an impurity predicted numerically based on the neoclassical theory.

A brief history of negative triangularity tokamak plasmas

This review is devoted to tokamak plasmas with a cross sectional shape featuring negative triangularity, which appear to hold great promise as a candidate reactor configuration owing to their improved confinement. A brief historical perspective of its role in the worldwide magnetic fusion program is offered before reviewing theoretical predictions and experimental results on both magneto-hydrodynamic stability and turbulent transport. The material covers more prominently the confined plasma region, while limited work in the published literature is devoted to the scrape-off layer and plasma-wall interactions. A discussion on the suitability of this plasma shape in future reactors concludes the paper.

Kinetic equilibrium reconstruction and the impact on stability analysis of KSTAR plasmas

High fidelity kinetic plasma equilibrium reconstructions are an essential requirement for accurate stability and disruption prediction analyses to support continuous operation of high beta tokamak plasmas. The present kinetic equilibrium reconstructions of plasmas in the KSTAR device include plasma density and temperature profiles from Thomson scattering and ion temperature from charge exchange spectroscopy diagnostics, and allowance for fast particle pressure. In addition, up to 25 channels of motional Stark effect diagnostic data are used to constrain the magnetic field pitch angle profile in the plasma to produce a reliable computation of the safety factor, q, profile. H-mode plasmas exhibit clear pedestal characteristics in the reconstructed pressure profile compared to internal transport barrier or L-mode plasmas. The plasma configuration and vertical position of inner strike points are validated by CCD and infrared camera images. Ideal and resistive magnetohydrodynamic (MHD) stability analyses using the DCON and resistive DCON codes utilize these kinetic equilibrium reconstructions to compare to experimental plasma stability. Equilibria with sufficiently low convergence error can provide reliable computation of ideal and resistive MHD stability analysis.

Interpretation of the hydrogen isotope effect on the density limit in JET-ILW L-mode plasmas using EDGE2D-EIRENE

Experiments in JET with the Be/W ITER-like wall show that in pure hydrogen low-confinement mode (L-mode) plasmas the density limit is approximately 20% higher than their corresponding deuterium plasmas. The maximum achievable density in L-mode plasmas is limited by the magnetohydrodynamic stability of the m/n = 2/1 tearing mode. Studies with the edge fluid-neutral Monte-Carlo code package EDGE2D-EIRENE show that the density of hydrogen atoms inside the separatrix is two times lower than for deuterium in plasma conditions preceding the density limit. The difference between the isotopes is caused by the non-linear process at density limit onset which leads to more efficient dissociation and ionization of hydrogen molecules and atoms in hydrogen than in deuterium plasmas at the high-field X-point region at electron temperatures lower than 2 eV. The m/n = 2/1 island size is estimated to be 30% smaller islands for hydrogen than for deuterium cases for equal fuelling conditions and radial transport assumptions.

Stellarator optimization for good magnetic surfaces at the same time as quasisymmetry

A method is demonstrated to optimize a stellarator's geometry to eliminate magnetic islands and achieve other desired physics properties at the same time. For many physics quantities that have been used in stellarator optimization, including quasisymmetry, neoclassical transport, and magnetohydrodynamic stability, it is convenient to use a magnetic equilibrium representation that assures the existence of magnetic surfaces. However, this representation hides the possible presence of magnetic islands, which are typically undesirable. To include both surface-based objectives and island widths in a single optimization, two fixed-boundary equilibrium calculations are run at each iteration of the optimization: one that enforces the existence of magnetic surfaces (the Variational Moments Equilibrium Code) [S. P. Hirshman and J. C. Whitson, Phys. Fluids 26, 3553 (1983)] and one that does not (the Stepped Pressure Equilibrium Code) [Hudson et al., Phys. Plasmas 19, 112502 (2012)]. By penalizing the island residues in the objective function, the two magnetic field representations are brought into agreement during the optimization. An example is presented in which, particularly on the surface where quasisymmetry was targeted, quasisymmetry is achieved more accurately than in previously published examples.

Magnetohydrodynamic stability of magnetars in the ultrastrong field regime I: the core

ABSTRACT We study magnetohydrodynamic stability of neutron star core matter composed of neutrons, protons, and leptons threaded by a magnetar-strength magnetic field 1014–1017 G, where quantum electrodynamical effects and Landau quantization of fermions are important. Stability is determined using the Friedman–Schutz formalism for the canonical energy of fluid perturbations, which we calculate for a magnetizable fluid with H ≠ B. Using this and the Euler–Heisenberg–Fermi–Dirac Lagrangian for a strongly magnetized fluid of Landau-quantized charged fermions, we calculate the local stability criteria for a neutron star core with a spherical axisymmetric geometry threaded by a toroidal field, accounting for magnetic and composition gradient buoyancy. We find that, for sufficiently strong fields B ≳ 1015 G, the magnetized fluid is unstable to a magnetosonic-type instability with growth times of the order of 10−3 s. The instability is triggered by sharp changes in the second-order field derivative of the Euler–Heisenberg–Fermi–Dirac Lagrangian that occur where additional Landau levels start being populated. These sharp changes are divergent at zero temperature, but are finite for non-zero temperature, so realistic neutron star core temperatures 5 × 107 K < T < 5 × 108 K are used. We conjecture that this mechanism could promote the formation of magnetic domains as predicted by Blandford and Hernquist and Suh and Mathews.

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.

Prominence formation by levitation-condensation at extreme resolutions

Context. Prominences in the solar atmosphere represent an intriguing and delicate balance of forces and thermodynamics in an evolving magnetic topology. How this relatively cool material comes to reside at coronal heights, and what drives its evolution prior to, during, and after its appearance, remains an area full of open questions. Aims. We here set forth to identify the physical processes driving the formation and evolution of prominence condensations within 2.5D magnetic flux ropes. We deliberately focus on the levitation-condensation scenario, where a coronal flux rope forms and eventually demonstrates in situ condensations, revisiting it at extreme resolutions down to order 6 km in scale. Methods. We perform grid-adaptive numerical simulations in a 2.5D translationally invariant setup, where we can study the distribution of all metrics involved in advanced magnetohydrodynamic stability theory for nested flux rope equilibria. We quantify in particular convective continuum instability (CCI), thermal instability (TI), baroclinicity, and mass-slipping metrics within a series of numerical simulations of prominences formed via levitation-condensation. Results. Overall, we find that the formation and evolution of prominence condensations happens in a clearly defined sequence regardless of resolution, with background field strength between 3 and 10 Gauss. The CCI governs the slow evolution of plasma prior to the formation of distinct condensations found to be driven by the TI. Evolution of the condensations towards the topological dips of the magnetic flux rope is a consequence of these condensations initially forming out of pressure balance with their surroundings. From the baroclinicity distributions, smaller-scale rotational motions are inferred within forming and evolving condensations. Upon the complete condensation of a prominence ‘monolith’, the slow descent of this plasma towards lower heights appears consistent with the mass-slippage mechanism driven by episodes of both local current diffusion and magnetic reconnection.

Solutions of BVPs arising in hydrodynamic and magnetohydro-dynamic stability theory using polynomial and non-polynomial splines

This paper describes the exceptionally precise results of 6th-order and 8th-order nonlinear boundary-value problems(BVPs). Cubic-Nonpolynomial spline(CNPS) and Cubic-polynomial spline(CNPS) are utilized to solve such types of BVPs. We develop the class of numerical techniques for a particular selection of the factors that are associated with nonpolynomial and polynomial splines. Using the developed class of numerical techniques, the problem is reduced to a new system that consists of 2nd-order BVPs only. The end conditions associated with the BVPs are determined. For each problem, the results obtained by CNPS and CPS is compared with the exact solution. The absolute error(AE) for every iteration is calculated. To show that the suitable responses established by using CNPS and CPS have a higher level of preciseness, the absolute errors of the CNPS and CPS have been compared with different techniques such as DTM, ADM, Parametric septic splines, Variational-iteration method(VIM), Daftardar Jafari strategy, MDM, Cubic B-Spline, Homotopy method(HM), Quintic and Sextic B-spline and observed to be more accurate. Graphs that describe the graphical comparison of CNPS and CPS at n=10 are also included in this paper.

Galatea trap: magnetohydrodynamic stability of plasma surrounding current-carrying conductors

Ideal magnetohydrodynamic (MHD) properties depending on the plasma pressure are considered for axisymmetric equilibrium magnetoplasma configurations in the Galatea trap with three ring current-carrying conductors embedded in plasma. The study of ideal MHD modes with different toroidal wave numbers takes into account the plasma compressibility with an adiabatic index of 5/3 in the perturbed potential energy functional in the framework of the energy principle. The stability calculations are performed in the presence of a vacuum layer between the plasma and the vacuum chamber. The limiting pressure values corresponding to stable multiply connected plasma configurations without an assumption of nested magnetic surfaces are estimated.

Исследование МГД-стабильности алюминиевого электролизера при различных условиях проведения технологического процесса

Mathematical simulation of industrial aluminium electrolytic cell operation allows us to predict and indicate the causes of magnetohydrodynamic (MHD) instability and bath level skewing, as well as investigate other features of the aluminium electrolysis process. In order to analyse the MHD stability of the electrolytic cell, we adapted a three-dimensional mathematical model that uses a multi-phase approach to describing the media (aluminium, electrolyte and gas) and treats the hydrodynamic, electromagnetic, thermal and electrochemical processes in the bath as interrelated. Our test calculations confirmed that the model is adequate and that the numerical solution proposed converges with sufficient accuracy. The paper describes our numerical investigation results concerning MHD stability of a multi-anode electrolytic cell when its thermal conditions and working space shape configuration change; our simulation included the metal-electrolyte phase interfaces and took into account the MHD instability developing when replacing burnt-out anodes. We estimated how various initial crust configurations affect the MHD stability. We investigated how the process parameters affect the working space shape in the bath, which is a dynamic object, same as the metal-electrolyte interface and the reverse oxidation zone surface. We specifically studied the way changes in potential affect the MHD stable shape of the working space in the bath. We show that varying the potential between any given pair of anodes can change the shape of the working space, that is, crust melts as potential increases, while lowering potential leads to further accretion. As this happens, we note that there is an increase in the vibration magnitudes of the liquid metal and the lower reverse oxidation zone boundary, but these variations are still within the range acceptable in terms of MHD stability of the electrolysis process

Magnetic well and Mercier stability of stellarators near the magnetic axis

We have recently demonstrated that by expanding in small distance from the magnetic axis compared with the major radius, stellarator shapes with low neoclassical transport can be generated efficiently. To extend the utility of this new design approach, here we evaluate measures of magnetohydrodynamic interchange stability within the same expansion. In particular, we evaluate the magnetic well, Mercier's criterion, and resistive interchange stability near a magnetic axis of arbitrary shape. In contrast to previous work on interchange stability near the magnetic axis, which used an expansion of the flux coordinates, here we use the ‘inverse expansion’ in which the flux coordinates are the independent variables. Reduced expressions are presented for the magnetic well and stability criterion in the case of quasisymmetry. The analytic results are shown to agree with calculations from the VMEC equilibrium code. Finally, we show that near the axis, Glasser, Greene and Johnson's stability criterion for resistive modes approximately coincides with Mercier's ideal condition.

Advancing the physics basis for quasi-helically symmetric stellarators

A new optimized quasi-helically symmetric configuration is described that has the desirable properties of improved energetic particle confinement, reduced turbulent transport by three-dimensional shaping and non-resonant divertor capabilities. The configuration presented in this paper is explicitly optimized for quasi-helical symmetry, energetic particle confinement, neoclassical confinement and stability near the axis. Post optimization, the configuration was evaluated for its performance with regard to energetic particle transport, ideal magnetohydrodynamic stability at various values of plasma pressure and ion temperature gradient instability induced turbulent transport. The effects of discrete coils on various confinement figures of merit, including energetic particle confinement, are determined by generating single-filament coils for the configuration. Preliminary divertor analysis shows that coils can be created that do not interfere with expansion of the vessel volume near the regions of outgoing heat flux, thus demonstrating the possibility of operating a non-resonant divertor.