Scalable Implicit / IMEX Resistive MHD with Stabilized Finite Element Methods and Fully-coupled Newton-Krylov-AMG Solution Methods.
Abstract not provided.
Shadid, John N.↗
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Results for “MHD stability”
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Stability of the Halley Cometo-Sheath with Resistivity and Plasma Motion
The MHD stability of the cometary inner shealth determined by the balance between the inward Lorentz body force and the outward ion-neutral drag force is investigated by numerically solving the wave equations which include resistivity, plasma motion and plasma pressure with the help of two-point boundary value method.
Comets Cometosheath MHD Stability↗
Nonlinear stability of the dayside cometary ionopause
The MHD stability of the cometary ionopause is investigated by nonlinear analysis, describing that stability in terms of the finite perturbation amplitude of both Kelvin-Helmholtz and Rayleigh-Taylor modes. The evolution of the unstable modes is examined, determining the conditions under which finite amplitude effects are expected to stabilize a growing wave disturbance. The analysis is applied to the ionopause at Comet Halley and Comet Giacobini-Zinner, showing that the theoretical prediction concerning the stability of this interface based on an earlier linear analysis remains valid in both cases despite the nonlinear stabilization effects.
Ershkovich, A. I.↗
Tokamak elongation – how much is too much? Part 2. Numerical results
We report the analytic theory presented in Paper I is converted into a form convenient for numerical analysis. A fast and accurate code has been written using this numerical formulation. The results are presented by first defining a reference set of physical parameters based on experimental data from high performance discharges. Scaling relations of maximum achievable elongation (κ max ) versus inverse aspect ratio (ε) are obtained numerically for various values of poloidal beta (β p ), wall radius (b/a) and feedback capability parameter (γ τ w ) in ranges near the reference values. It is also shown that each value of κ max occurs at a corresponding value of optimized triangularity (δ), whose scaling is also determined as a function of ε. The results show that the theoretical predictions of κ max are slightly higher than experimental observations for high performance discharges, as measured by high average pressure. The theoretical δ values are noticeably lower. We suggest that the explanation is associated with the observation that high performance involves not only n = 0 MHD stability, but also n ≥ 1 MHD modes described by β N in the Troyon limit and transport as characterized by τ E . Operation away from the n = 0 MHD optimum may still lead to higher performance if there are more than compensatory gains in β N and τ E . Unfortunately, while the empirical scaling of β N and τ E with the elongation (κ) has been determined, the dependence on δ has still not been quantified. This information is needed in order to perform more accurate overall optimizations in future experimental designs.
70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
Development of a neural network model for peeling–ballooning stability analysis in the KSTAR tokamak pedestals
The neural network model, MISHKA-NN is developed to mitigate the computational burden associated with the linear ideal magnetohydrodynamic (MHD) stability analysis of the pedestal based on the peeling–ballooning (P–B) model. By utilizing both 1D plasma profiles (current density, pressure gradient, and safety factor) and 0D parameters (plasma geometry, total current, and toroidal mode number), the model predicts linear growth rate of edge-localized ideal MHD instability in a given equilibrium state. By enabling the prediction of each instability within a second, the model reduces the time required for plotting a pedestal P–B stability diagram (j - α diagram) from approximately 100 CPU hours to a few CPU minutes. Notably, even with the utilization of parametric pressure and current profiles and plasma boundary shapes for the training dataset, the model shows a satisfactory level of performance in benchmarking the j - α diagram for the reconstructed equilibrium from a KSTAR tokamak experiment. We anticipate the model to serve as a versatile alternative to 2D linear MHD stability codes, alleviating numerical costs.
70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
AToM: Advanced Tokamak Modeling Environment
Stability constraints play an important role in integrated modeling. The global plasma stability and macro-instabilities such as internal kink modes, neoclassical tearing modes, and edge localized perturbations limit the plasma performance and can result in large-scale transient events and plasma disruptions. These macro-instabilities can be also beneficial to the plasma performance. For example, the peeling models often lead to the edge localized modes (ELMs). However, the formation of stationary edge harmonic oscillations (EHOs) due to nonlinear interaction of peeling modes can result in a transition to the Quiescent H-mode (QH-mode) without ELMs. The profiles predicted with transport models need to be refined using the MHD stability constraints. This is important especially for transient and nonlinear stages of discharges such as ramp-up access to hybrid and steady state operation, and L- to H-mode transition as well as transition to the QH-mode. Several stability and MHD codes are already included in the OMFIT framework. These codes include BALOO, ELITE, GATO, M3DC1, MARS, and NIMROD. However, the verifications of stability constraints are currently mostly excluded from transport modeling workflows. The only exception is the EPED module which includes the ELITE predictions to limit the pedestal height. Here, we improved the OMFIT workflow to include stability calculations. Including the stability conditions to the integrated modeling workflow improved the robustness of the predictive modeling discharges. Being implemented in the workflow, the stability conditions can be also used for the stability analysis of experimental data. This improved the physics understanding of various discharge scenarios and can be used in experiment planning.
70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
Multi-region relaxed magnetohydrodynamic stability of a current sheet
It is shown that the resistive MHD stability of a slab force-free current sheet can be calculated using the variational principle of multi-region relaxed magnetohydrodynamics (MRxMHD) and that the corresponding stability boundary is in exact agreement with linear tearing mode theory.
70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
Stability of the Halley cometosheath with resistivity and plasma motion
The MHD stability of the cometary inner sheath determined by the balance between the inward Lorentz body force and the outward ion-neutral drag force is investigated by numerically solving the wave equations which include resistivity, plasma motion and plasma pressure with the help of two-point boundary value method. The eigenvalues and the eigenfunctions are obtained numerically by treating the cometary inner sheath as a layer of finite thickness, bounded by the contact surface, that is, the diamagnetic cavity boundary. To gain insight into the problem, certain limiting cases of the wave equations are also discussed. The diamagnetic cavity boundary and the adjacent layer of about 100-km thickness of Comet Halley is found to be unstable. The effects of finite plasma pressure, dissociative recombination, mass loading due to photoionization, resistivity, and plasma motion are found to be stabilizing but are unable to quench the instability completely. Motion of the Halley ionopause has been confirmed by observations.
Srivastava, Krishna M.↗
Isotope dependence of the type I ELMy H-mode pedestal in JET-ILW hydrogen and deuterium plasmas
The pedestal structure, edge transport and linear MHD stability have been analyzed in a series of JET with the ITER-like wall hydrogen (H) and deuterium (D) type I ELMy H-mode plasmas. The pedestal pressure is typically higher in D than in H at the same input power and gas rate, with the difference mainly due to lower density in H than in D (Maggi et al (JET Contributors) 2018 Plasma Phys. Control. Fusion 60 014045). A power balance analysis of the pedestal has shown that higher inter-ELM separatrix loss power is required in H than in D to maintain a similar pedestal top pressure. This is qualitatively consistent with a set of interpretative EDGE2D-EIRENE simulations for H and D plasmas, showing that higher edge particle and heat transport coefficients are needed in H than in D to match the experimental profiles. It has also been concluded that the difference in neutral penetration between H and D leads only to minor changes in the upstream density profiles and with trends opposite to experimental observations. This implies that neutral penetration has a minor role in setting the difference between H and D pedestals, but higher ELM and/or inter-ELM transport are likely to be the main players. The interpretative EDGE2D-EIRENE simulations, with simultaneous upstream and outer divertor target profile constraints, have indicated higher separatrix electron temperature in H than in D for a pair of discharges at low fueling gas rate and similar stored energy (which required higher input power in H than in D at the same gas rate). The isotope dependence of linear MHD pedestal stability has been found to be small, but if a higher separatrix temperature is considered in H than in D, this could lead to destabilization of peeling-ballooning modes and shrinking of the stability boundary, qualitatively consistent with the reduced pedestal confinement in H.
08 HYDROGEN↗
Nonlinear stability of Halley comethosheath with transverse plasma motion
Weakly nonlinear Magneto Hydrodynamic (MHD) stability of the Halley cometosheath determined by the balance between the outward ion-neutral drag force and the inward Lorentz force is investigated including the transverse plasma motion as observed in the flanks with the help of the method of multiple scales. The eigenvalues and the eigenfunctions are obtained for the linear problem and the time evolution of the amplitude is obtained using the solvability condition for the solution of the second order problem. The diamagnetic cavity boundary and the adjacent layer of about 100 km thickness is found unstable for the travelling waves of certain wave numbers. Halley ionopause has been observed to have strong ripples with a wavelength of several hundred kilometers. It is found that nonlinear effects have stabilizing effect.
Srivastava, Krishna M.↗
Magnetotail dynamics under isobaric constraints
Using linear theory and nonlinear MHD simulations, we investigate the resistive and ideal MHD stability of two-dimensional plasma configurations under the isobaric constraint dP/dt = 0, which in ideal MHD is equivalent to conserving the pressure function P = P(A), where A denotes the magnetic flux. This constraint is satisfied for incompressible modes, such as Alfven waves, and for systems undergoing energy losses. The linear stability analysis leads to a Schroedinger equation, which can be investigated by standard quantum mechanics procedures. We present an application to a typical stretched magnetotail configuration. For a one-dimensional sheet equilibrium characteristic properties of tearing instability are rediscovered. However, the maximum growth rate scales with the 1/7 power of the resistivity, which implies much faster growth than for the standard tearing mode (assuming that the resistivity is small). The same basic eigen-mode is found also for weakly two-dimensional equilibria, even in the ideal MHD limit. In this case the growth rate scales with the 1/4 power of the normal magnetic field. The results of the linear stability analysis are confirmed qualitatively by nonlinear dynamic MHD simulations. These results suggest the interesting possibility that substorm onset, or the thinning in the late growth phase, is caused by the release of a thermodynamic constraint without the (immediate) necessity of releasing the ideal MHD constraint. In the nonlinear regime the resistive and ideal developments differ in that the ideal mode does not lead to neutral line formation without the further release of the ideal MHD constraint; instead a thin current sheet forms. The isobaric constraint is critically discussed. Under perhaps more realistic adiabatic conditions the ideal mode appears to be stable but could be driven by external perturbations and thus generate the thin current sheet in the late growth phase, before a nonideal instability sets in.
Birn, Joachim↗
Real-time multi-EC-actuator MHD control on TCV
Real-time control of multiple plasma actuators is a requirement in advanced tokamaks; for example for burn control, plasma current profile control and MHD stabilization - EC wave absorption is ideally suited especially for the latter. For example, on ITER 24 EC sources can be switched between 54 inputs at the torus. In the torus, 5 launchers direct the power to various locations across the plasma profile via 11 steerable mirrors. For optimal usage of the available power, the aiming and polarization of the beams must be adapted to the plasma configuration and the needs of the scenario. Since the EC system performs many competing tasks, present day systems should demonstrate the ability of an EC plant to deal with several targets in parallel and/or to switch smoothly between goals to attain overall satisfaction. Recently TCV has taken a first step towards such a demonstration. Several EC launchers are used simultaneously to regulate the sawtooth period and to preempt m/n = 3/2 NTMs, by controlling the power levels. In parallel, a second algorithm stabilizes any NTM that saturates [1]. These and real-time MHD control experiments on ELMs [2] are presented.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
Magnetohydrodynamic modeling of the solar eruption on 2010 April 8
The structure of the coronal magnetic field prior to eruptive processes and the conditions for the onset of eruption are important issues that can be addressed through studying the magnetohydrodynamic (MHD) stability and evolution of nonlinear force-free field (NLFFF) models. This paper uses data-constrained NLFFF models of a solar active region (AR) that erupted on 2010 April 8 as initial conditions in MHD simulations. These models, constructed with the techniques of flux rope insertion and magnetofrictional relaxation (MFR), include a stable, an approximately marginally stable, and an unstable configuration. The simulations confirm previous related results of MFR runs, particularly that stable flux rope equilibria represent key features of the observed pre-eruption coronal structure very well, and that there is a limiting value of the axial flux in the rope for the existence of stable NLFFF equilibria. The specific limiting value is located within a tighter range, due to the sharper discrimination between stability and instability by the MHD description. The MHD treatment of the eruptive configuration yields a very good agreement with a number of observed features, like the strongly inclined initial rise path and the close temporal association between the coronal mass ejection and the onset of flare reconnection. Minor differences occur in the velocity of flare ribbon expansion and in the further evolution of the inclination; these can be eliminated through refined simulations. We suggest that the slingshot effect of horizontally bent flux in the source region of eruptions can contribute significantly to the inclination of the rise direction. Finally, we demonstrate that the onset criterion, formulated in terms of a threshold value for the axial flux in the rope, corresponds very well to the threshold of the torus instability in the considered AR.
79 ASTRONOMY AND ASTROPHYSICS↗
Numerical study of coronal plasma jet formation
A new scenario for solar flare eruption in the coronal holes is analyzed by using MHD stability concepts for a spheromak configuration. The stability properties of a spheromak partially embedded into a conducting surface are studied using three dimensional MHD simulations. In agreement with the analytical theory, a large degree of line-tying stabilizes the spheromak's tilt instability, while the elongation has a destabilizing effect. High-resolution nonlinear simulations also demonstrate current sheet formation at the upper surface of the spheromak, where the tilted magnetic field of the spheromak reconnects with the background magnetic field. The calculated stability threshold and the observed magnetic reconnection support a model of coronal jet eruptions where a dome-like magnetic structure grows through flux emergence on the solar surface, tilts, reconnects, and erupts. Countering the effect from elongation, line-tying strongly stabilizes a spheromak growing from a flux-emergence process, suggesting that to accelerate the onset of eruptive coronal jets, there must be magnetic reconnection at the bottom of the spheromak to detach the structure from the solar surface.
70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
Low- n stability and plasma response to RMP in various STEP scenarios
The low-n (n is the toroidal mode number) magnetohydrodynamic (MHD) stability and plasma response are numerically investigated for various scenarios designed for STEP, that are relevant for the H-mode pedestal analysis. Control of the edge-localized modes (ELMs) with externally applied resonant magnetic perturbations (RMPs) is considered. Optimization of the ELM control coil current configuration, based on the computed plasma MHD response and well-established figures of merit validated on present-day experiments, finds reasonable robustness of a fixed coil phasing (for a given n-number) to control ELMs in all five STEP plasmas considered. Based on certain semi-empirical criteria, the required coil current to achieve ELM suppression is estimated to be about 10–20 kAt with the n = 1 or 2 RMP configuration and about 100–200 kAt for the n = 4 RMP. Systematic linear stability calculations are used to map out stability windows for the low-n kink-peeling modes, in terms of the ideal-wall location and variation of the edge safety factor q 95 with respect to the target design. The kink-peeling stability boundary is found to be generally sensitive to the q 95 variation, which has implications for achieving the quiescent H-mode regime in STEP. Full toroidal quasilinear initial-value simulations for these STEP plasmas find that generation of the edge-harmonic oscillations (EHOs) depends sensitively on the plasma scenario, the initial linear stability of the kink-peeling modes, the initial plasma toroidal flow and q 95 . In general, it is easier (more robust) to access the EHO-regime for two of the cases considered with smaller plasma volume and higher on-axis safety factor. Finally, quasilinear simulations find robust density pumpout due to applied RMPs in these STEP plasmas, but the effect on the plasma toroidal flow varies among different cases.
EHO↗
Plasma rotation and diamagnetic drift effects on the resistive wall modes in the negative triangularity tokamaks
Abstract It was found previously that the negative triangularity (NT) configuration is more MHD-unstable for low n modes than the positive triangularity (PT) case, although the situation is reversed for intermediate n modes and the NT configuration becomes more stable for intermediate n modes ( n = 3 − 10 ) (Zheng et al 2021 Nucl. Fusion 61 116014). Here, n is the toroidal mode number. In this work, we extend the studies to include the rotation effects, as well as the diamagnetic drift effects, to see how the resistive wall modes (RWMs) in the NT configuration are affected as compared with the PT configuration. This is particularly motivated by noting that the wall interface with the plasma is quite different between the NT and PT configurations. It affects the plasma rotation and diamagnetic drift effects on the low n RWM. We consider the DIII-D-NT-experiment equilibrium reconstructed by the EFIT code. Based on the equilibrium g-file, the extended equilibria are constructed with the VMEC code by varying the beta values while keeping the pressure and poloidal current flux profiles basically unchanged. The bootstrap current contribution to the equilibria is taken into account with the Sauter formula. The MHD stability is then computed using the AEGIS code with the rotation and diamagnetic drift effects taken into account. We found that, although the NT configuration is less stable for n = 1 MHD modes, the rotation and diamagnetic drift stabilization effects on RWMs are more effective in the NT configuration than in the PT one. Note that even in the PT case, the stabilization of RWMs by the rotation and kinetic effects is critical. Because the low-n RWMs in the regular NT case are more unstable, the rotation and diamagnetic drift stabilization effects found in this research are important for the NT tokamak concept.
70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
The stability of solar coronal loops with realistic photospheric boundary conditions
Finite-length effects are the primary influence for the MHD stability of coronal loops. This paper gives a new physical description of the photospheric boundary conditions, and the first complete and uniformly convergent initial-perturbation set. A general energy-principle (or variational) stability analysis is then developed. The results of this calculation show that large classes of cylindrical-symmetry perturbations, those with separable contributions to the energy integral, are completely stable. Comparisons are also made with other more restrictive formulations of this problem.
Van Hoven, G.↗
Landau resonant modification of multiple kink mode contributions to 3D tokamak equilibria
Detailed measurements of the plasma's response to applied magnetic perturbations provide experimental evidence that the form of three-dimensional (3D) tokamak equilibria, with toroidal mode number n = 1, is determined by multiple stable kink modes at high-pressure. For pressures greater than the ideal magnetohydrodynamic (MHD) stability limit, as calculated without a stabilizing wall, the 3D structure transitions in a way that is qualitatively predicted by an extended MHD model that includes kinetic wave-particle interactions. These changes in poloidal mode structure are correlated with the proximity of rotation profiles to thermal ion bounce and the precession drift frequencies suggesting that these kinetic resonances are modifying the relative amplitudes of the stable modes. These results imply that each kink may eventually be independently controlled.
70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗