Magnetohydrodynamic Stability Research Articles

Trapped particle stability for the kinetic stabilizer

A kinetically stabilized axially symmetric tandem mirror (KSTM) uses the momentum flux of low-energy, unconfined particles that sample only the outer end-regions of the mirror plugs, where large favourable field-line curvature exists. The window of operation is determined for achieving magnetohydrodynamic (MHD) stability with tolerable energy drain from the kinetic stabilizer. Then MHD stable systems are analysed for stability of the trapped particle mode. This mode is characterized by the detachment of the central-cell plasma from the kinetic-stabilizer region without inducing field-line bending. Stability of the trapped particle mode is sensitive to the electron connection between the stabilizer and the end plug. It is found that the stability condition for the trapped particle mode is more constraining than the stability condition for the MHD mode, and it is challenging to satisfy the required power constraint. Furthermore, a severe power drain may arise from the necessary connection of low-energy electrons in the kinetic stabilizer to the central region.

Hydrodynamic stability of selfgravitating streaming magnetized fluid cylinder

The magnetohydrodynamic stability criterion of self-gravitating streaming fluid cylinder under the combined effect of capillary, inertia, pressure gradient and electromagnetic forces has been derived. The results are discussed analytically and some data are verified numerically for different parameters of the problem. The magnetic field is stabilizing, but the streaming is destabilizing while the self-gravitating and capillary forces are stabilizing or destabilizing according to restrictions. The stable and unstable domains are identified and moreover the influences of the magnetic field and capillary forces on the self-gravitating instability of the model have been examined. The including of the electromagnetic force together with both the capillary and self-gravitating forces improve the instability of the model. However, the self-gravitating instability will never be suppressed whatever are the effects of the capillary and MHD forces stabilizing effects.

Real-time control of the safety factor profile diagnosed by magneto-hydrodynamic activity on the Tore Supra tokamak

Real-time control is essential for many aspects of tokamak operation. A key parameter to control is the current profile, since both confinement properties and magneto-hydrodynamic (MHD) activity depend on it in quite a sensitive way. The long pulse capability of the Tore Supra tokamak has allowed a unique type of experiment, where successive stationary states of the safety factor profile, defined by their MHD activity, are established and controlled in real time. Multiple target stationary states could be requested and reached during the main heating phase of a single plasma discharge. Experiments have been carried out featuring (i) control of the presence/absence of sawteeth with varying plasma parameters, (ii) obtaining and sustaining a ‘hot core’ plasma regime without MHD activity and (iii) recovery from a voluntarily triggered deleterious MHD regime. During these experiments, the influence of fast ions on MHD stability could be observed and characterized, as well as indications of an enhanced ‘hot core’ confinement in electron heat transport during quiescent MHD states.

Mechanisms of plasma rotation effects on the stability of type-I edge-localized mode in tokamaks

Mechanisms of plasma rotation effects on edge magnetohydrodynamic (MHD) stability are investigated numerically by introducing energies that are distinguished by physics. By comparing them, it is found that an edge-localized MHD mode is destabilized by the difference between the eigenmode frequency and the equilibrium toroidal rotation frequency, which is induced by rotation shear. In addition, this destabilizing effect is found to be effective in the shorter wavelength region. The effect of poloidal rotation on the edge MHD stability is also investigated. Under the assumption that the change in equilibrium by poloidal rotation is negligible, it is identified numerically that poloidal rotation can have both stabilizing and destabilizing effects on the edge MHD stability, which depends on the direction of poloidal rotation. A numerical analysis demonstrates that these effects of plasma rotation in both the toroidal and poloidal directions can play important roles in type-I edge-localized mode phenomena in JT-60U H-mode plasmas.

Magnetohydrodynamic properties of nominally axisymmetric systems with 3D helical core

Magnetohydrodynamic equilibrium states with a three-dimensional helical core are computed to model the MAST spherical tokamak and the RFX-mod reversed field pinch. The boundary is fixed as axisymmetric. The MAST equilibrium state has the appearance of an internal kink mode and is obtained under conditions of weak reversed central shear. The RFX-mod equilibrium state has seven-fold periodicity. An ideal magnetohydrodynamic stability analysis reveals that the reversal of the core magnetic shear can stabilize a periodicity-breaking mode that is dominantly m/n = 1/8 strongly coupled to a m/n = 2/15 component, as long as the central rotational transform does not exceed the value of 8.

Lessons from the RFP on Magnetic Feedback Control of Plasma Stability

This lecture was given at the 4th ITER International Summer School in May 2010 to describe the broad research program on feedback control of magnetohydrodynamic (MHD) stability performed by the reversed field pinch (RFP) community and its implication for magnetic confinement fusion. The lecture provides a bird’s-eye view on RFP feedback control results obtained with active coils, and on their implications for ITER and tokamaks in general. A number of selected key examples are presented with the aim of highlighting the more innovative and broadly applicable results. RFPs provide a significant contribution to the effort of the broader fusion community on active control of MHD stability, and to fusion science in general.

Stability of localized modes in rotating tokamak plasmas

The ideal magnetohydrodynamic stability is investigated of localized interchange modes in a large-aspect ratio tokamak plasma. The resulting stability criterion includes the effects of toroidal rotation and rotation shear and contains various well-known limiting cases. The analysis allows for a general adiabatic index, resulting in a stabilizing contribution from the convective effect. A further stabilizing effect from rotation exists when the angular frequency squared decreases radially more rapidly than the density. Flow shear, however, also decreases the stabilizing effect of magnetic shear through the Kelvin–Helmholtz mechanism. Numerical simulations reveal the merits and limitations of the performed local analysis.

A magnetospheric energy principle extended to include neutral atmosphere

The problem of ideal magnetohydrodynamic stability of plasmas in a magnetosphere-atmosphere system, in which the unperturbed magnetic field is assumed to be perpendicular to the plasma-atmosphere interface (ionospheric surface), is investigated by means of an extended magnetospheric energy principle. The derivation of the principle and conditions under which it applies to a real terrestrial magnetosphere is given. In the principle, the atmosphere is considered to be a very heavy and compressible gas with finite pressure. A thin ionospheric layer is taken into account as boundary conditions, but energetics within it are neglected. The solid-earth surface is assumed to be a perfectly conducting wall for perturbations. For a perturbation that satisfies either rigid or horizontally free boundary conditions at the plasma-atmosphere interface, the self-adjointness of the force operator is satisfied and an extended magnetospheric energy principle can be developed on the basis of the extended energy principle for fusion plasmas. These two boundary conditions are shown to be realized in the magnetosphere when the ionospheric conductivity is either very large or very small. Whereas in fusion plasmas the perturbed magnetic energy in the vacuum makes a stabilizing contribution to the potential energy, in the magnetosphere the perturbed magnetic energy in the atmosphere makes no such stabilizing contribution. This is due to the difference of the assumed field configurations of the magnetospheric and fusion plasmas. The ionospheric surface makes a destabilizing negative contribution to the potential energy owing to a horizontal plasma displacement on the spherical ionospheric surface. The method is applied to magnetospheric ballooning and interchange instabilities. The existence of a new type of magnetospheric interchange instability is shown and its structure in the magnetosphere-atmosphere system is clarified. Possible consequences of the instabilities and their relevance to magnetospheric physics are discussed.

Conceptual design of the power supply system for the in-vessel saddle coils for MHD control in ASDEX Upgrade

In the frame of an ASDEX Upgrade enhancement, a system of active in-vessel coils (of two types, dubbed “A” and “B”) and conducting wall for MagnetoHydroDynamic (MHD) stabilization is being designed and implemented. The conceptual design of the power supply (PS) system has been worked out and extensive analyses have been performed to verify that the identified basic modules, based on a cascade topology with two IGBT (Isolated Gate Bipolar Transistor) H-bridges in series for the A units and one H-bridge for the B ones, were able to fulfil all the requirements, well within semiconductors safety operating limits. The paper summarizes the work which led to the definition of the PS requirements, describes the topologies of the selected basic units and of the overall scheme, discusses the design choices and reports the results of the numerical simulations carried out to check the overall performance.

Ion-Cyclotron Resonance Heating Experiment in the Quadruple Minimum-B Field on GAMMA 10

In the GAMMA 10 tandem mirror, Magneto Hydro Dynamic (MHD) stabilization is kept with quadruple minimum-B anchor configuration. In the previous heating experiments, Ion-Cyclotron Range of Frequency (ICRF) antenna installed in the central cell was used for the anchor heating. Fast Alfvén wave excited in the central cell is partly converted to the slow wave in the nonaxisymmetric transition region between the central and the anchor cells, and heats ions in the minimum-B well. In order to produce higher performance plasmas in the central cell, the ion heating should be enhanced in the anchor cell. In this study, an experiment is carried out in the anchor cell to heat ions by ICRF waves without mode conversion. A bar-type antenna is installed in the anchor cell. Applied frequency is adjusted to ion-cyclotron resonance frequency in the minimum-B well. By the additional ion heating with the bar-type antenna, remarkable increase in the diamagnetic signal has been observed in the anchor cell. It is confirmed that the additional heating by the bar-type antenna can also keep MHD stabilization.

Magnetohydrodynamic stability comparison theorems revisited

Magnetohydrodynamic (MHD) stability comparison theorems are presented for several different plasma models, each one corresponding to a different level of collisionality: a collisional fluid model (ideal MHD), a collisionless kinetic model (kinetic MHD), and two intermediate collisionality hybrid models (Vlasov-fluid and kinetic MHD-fluid). Of particular interest is the re-examination of the often quoted statement that ideal MHD makes the most conservative predictions with respect to stability boundaries for ideal modes. Some of the models have already been investigated in the literature and we clarify and generalize these results. Other models are essentially new and for them we derive new comparison theorems. Three main conclusions can be drawn: (1) it is crucial to distinguish between ergodic and closed field line systems; (2) in the case of ergodic systems, ideal MHD does indeed make conservative predictions compared to the other models; (3) in closed line systems undergoing perturbations that maintain the closed line symmetry this is no longer true. Specifically, when the ions are collisionless and their gyroradius is finite, as in the Vlasov-fluid model, there is no compressibility stabilization. The Vlasov-fluid model is more unstable than ideal MHD. The reason for this is related to the wave-particle resonance associated with the perpendicular precession drift motion of the particles (i.e., the E×B drift and magnetic drifts), combined with the absence of any truly toroidally trapped particles. The overall conclusion is that to determine macroscopic stability boundaries for ideal modes for any magnetic geometry using a simple conservative approach, one should analyze the ideal MHD energy principle for incompressible displacements.

Magnetohydrodynamic stability of an oscillating fluid cylinder

The magnetohydrodynamic stability of an oscillating streaming fluid cylinder pervaded by longitudinal magnetic fields has been discussed. The problem is formulated, the basic equations are solved, upon appropriate boundary conditions the non-singular solutions are identified. Moreover, a second-order integro-differential equation in the amplitude of the deflection of perturbation, of Mathieu equation type is derived. The magnetic fields interior and exterior to the fluid have strong stabilizing influences for all perturbation modes. The capillary force is destabilizing only in the small axisymmetric domain while it is stabilizing in all the other domains of perturbation modes. The oscillating streaming of the fluid has a strong stabilizing tendency. The destabilizing character of the model due to the capillary force could be reduced and suppressed, then the stability sets in.

Dependence of pedestal performance on the characteristics of the H-mode pedestal**http://iopscience.iop.org/0029-5515/50/6

Given the small level of residual transport within the edge pedestal of H-mode tokamak plasmas, even low levels of additional transport within this region (e.g. due to ripple losses of thermal ions or edge ergodization) can have a significant effect on pedestal performance. Such additional transport will affect the shape of the plasma profiles within the pedestal. In this paper, the dependence of the sustainable level of pedestal pressure gradient and toroidal edge current density on the pedestal plasma profile shapes is systematically studied by means of ideal linear magnetohydrodynamic stability analysis. It is concluded that the further inside the separatrix the maximum pressure gradient is reached, the larger the level of pressure gradient that the plasma can sustain is. It is also found that the further inside the separatrix the pressure gradient maximum is located, the wider the eigenfunctions of the unstable modes are and the smaller the toroidal mode number of the most unstable mode is.

The rotating wall machine: A device to study ideal and resistive magnetohydrodynamic stability under variable boundary conditions

The rotating wall machine, a basic plasma physics experimental facility, has been constructed to study the role of electromagnetic boundary conditions on current-driven ideal and resistive magnetohydrodynamic instabilities, including differentially rotating conducting walls. The device, a screw pinch magnetic geometry with line-tied ends, is described. The plasma is generated by an array of 19 plasma guns that not only produce high density plasmas but can also be independently biased to allow spatial and temporal control of the current profile. The design and mechanical performance of the rotating wall as well as diagnostic capabilities and internal probes are discussed. Measurements from typical quiescent discharges show the plasma to be high β (≤p>2μ(0)/B(z)(2)), flowing, and well collimated. Internal probe measurements show that the plasma current profile can be controlled by the plasma gun array.

Analysis of high β regimes for DEMO

Stability limit calculations are presented for a range of tokamak power plant equilibria. The current drive requirements to sustain the optimised equilibrium profiles are confirmed by a transport code and the plasma shape is obtained from free-boundary equilibrium calculations. A pressure pedestal is included according to empirical scaling and ballooning mode stability limits. A terative optimisation of the profiles is undertaken to improve the baseline profiles in order to achieve the highest possible plasma performance and most favourable magnetohydrodynamic stability within conservative assumptions in order to increase confidence in the availability and control of the plasma. This results in a fully noninductive baseline operating scenario for a tokamak power plant design which has a broad low-shear q-profile which is meant to complement previous advanced tokamak design studies.

Activities on Integrated Simulations in LHD

One of the purposes of fusion simulations is to develop a code that could predict the entire temporal behavior of experimentally observed macroscopic physics quantities under continuous external control, which will be used to create the path to helical-type reactor by combining knowledge of reactor design. In this paper an integrated simulation code system for three-dimensional toroidal helical plasmas in the Large Helical Device (LHD) is reported. This code has been developed under the domestic and international research collaborations among universities and institutes. After explaining the structure of the code system, including the transport simulation code TASK3D and the magnetohydrodynamic (MHD) equilibrium and stability code MHD3D, we present typical simulation results: evolution of the rotational transform, MHD stability beta limit, and recent progress in the TASK3D code.

Study of MHD Stability in LHD

This paper reviews progress in the study of pressure-driven interchange stability in the Large Helical Device (LHD) for 10 years. When the plasma approaches the boundary of ideal interchange mode, a strong magnetohydrodynamic (MHD) mode appears, leading to a distortion of pressure profile, although no major disruption is caused. The experiments for investigating magnetic shear effects in the magnetic hill configuration indicate that the reduction of magnetic shear leads to a minor collapse due to an excitation of low-order MHD mode. In the high-beta regime of more than 4%, MHD modes excited in the periphery with magnetic hill are observed to dominate, and it was found that the amplitude depends on the magnetic Reynolds number as well as the pressure gradient, which is qualitatively consistent with the prediction of resistive interchange mode. Also, experiments and theory for finding parameter dependence of the onset of the mode indicate that the onset is related to both the magnetic Reynolds number and the stability index of resistive interchange mode.

Measurements of Rotational Transform with Motional Stark Effect Spectroscopy

Radial profiles of the rotational transform are measured with the motional Stark effect spectroscopy in the Large Helical Device. They are derived from the radial profiles of the polarization angle of the σ and π components in the Hα line emitted from high-energy hydrogen atoms of beams with four sets of linear polarizers, spectrometers, and charge-coupled device detectors. Changes in the rotational transform due to the neutral beam current drive (NBCD) and the electron cyclotron current drive are measured. When NBCD is in the direction counter to the equivalent plasma current, the central rotational transform increases because of the inductive current while the edge rotational transform decreases, as is expected. Therefore, the magnetic shear becomes weak with NBCD in the counterdirection, whereas it becomes strong with NBCD in the codirection. NBCD that drives toroidal current, typically <10% of the equivalent toroidal current determined by the external current in the helical coils, can change the rotational transform and magnetic shear significantly enough to change magnetohydrodynamic stability.

MHD stability analysis for advanced tokamak modes in the KSTAR device

The Korea Superconducting Tokamak Advanced Research (KSTAR) device aims to demonstrating the steady-state operation of high-performance advanced tokamak (AT) modes. In order to meet this research goal it is critical to have a good magnetohydrodynamic (MHD) stability, so that KSTAR adopted a strong plasma shape and a conducting wall close to plasma for such stability. An early calculation during the KSTAR design phase had shown that a target AT mode stable up to β N above 5 can be then obtained. A recent work by Katsuro-Hopkins et al. [O. Katsuro-Hopkins, S.A. Sabbagh, J.M. Bialek, H.K. Park, J.G. Bak, J. Chung, et al., Equilibrium and global MHD stability study of KSTAR high beta plasmas under passive and active mode control, Nucl. Fusion 50(2010) 025019] showed, however, that the maximum β N value can be substantially lower than 5, unlike the earlier result. In this work, we present a more detailed study on the MHD stability limit of the KSTAR target AT mode and try to clarify the discrepancy observed in the previous two works. It is shown that in the reverse-shear plasma the target mode with β N above 5 can be obtained if the pressure profile is relatively peaked, but the maximum β N value is substantially reduced below 5 if the pressure profile becomes broader. This result suggests the importance of a proper control of the pressure profile to get the high-beta AT mode in KSTAR.

Effects of line-tying on magnetohydrodynamic instabilities and current sheet formation

An overview of some recent progress on magnetohydrodynamic stability and current sheet formation in a line-tied system is given. Key results on the linear stability of the ideal internal kink mode and resistive tearing mode are summarized. For nonlinear problems, a counterexample to the recent demonstration of current sheet formation by Low and Janse [Astrophys. J. 696, 821 (2009)] is presented, and the governing equations for quasistatic evolution of a boundary driven, line-tied magnetic field are derived. Some open questions and possible strategies to resolve them are discussed.