Pressure-driven Modes Research Articles

Characteristics of confinement and stability in large helical device edge plasmas

Recent progress in the heating capability in the large helical device [O. Motojima et al., Phys. Plasmas 6, 1843 (1999)] has allowed the highest average β value (4.1%) obtained in the helical devices, and enables exploration of magnetohydrodynamics (MHD) stability in this β region. MHD activities in the periphery are found to become stable spontaneously from the inner region to the outer region when the averaged β value exceeds a threshold, and then a flattening of the electron temperature profile is observed around the resonant surface. Such a flattening can be formed externally by producing an m∕n=1∕1 magnetic island, and the complete stabilization of the m∕n=1∕1 mode is demonstrated by the moderate island width. In addition, attempts to control peripheral plasmas are also performed by using a limiter and a local island divertor utilizing the m∕n=1∕1 island, to improve plasma confinement and, especially, to stabilize pressure-driven modes in the present study. The stabilization of peripheral MHD modes is obtained with both approaches, and this indicates that these are available to the production of higher-β plasmas without edge MHD activities.

Comparison of the efficiency of microparticulate and monolithic capillary columns

A comparison is made between the efficiency of microparticulate capillary columns and silica and polymer-based monolithic capillary columns in the pressure-driven (high-performance liquid chromatography) and electro-driven (capillary electrochromatography) modes. With packed capillary columns similar plate heights are possible as with conventional packed columns. However, a large variation is observed in the plate heights for individual columns. This can only be explained by differences in the quality of the packed bed. The minimum plate height obtained with silica monolithic capillary columns in the HPLC mode is approximately 10 microm, which is comparable to that of columns packed with 5-microm particles. The permeability of wide-pore silica monoliths was found to be much higher than that of comparable microparticulate columns, which leads to much lower pressure drops for the same eluent at the same linear mobile phase velocity. For polymer-based monolithic columns (acrylamide, styrene/divinyl benzene, methacrylate, acrylate) high efficiencies have been found in the CEC mode with minimum plate heights between 2 and 10 microm. However, in the HPLC mode minimum plate heights in the range of 10 to 25 microm have been reported.

Equilibrium and Stability of High-β Plasmas in Wendelstein 7-AS

One of the major goals for Wendelstein 7-AS (W7-AS) was the testing of the theoretical basis for the optimized configuration of Wendelstein 7-X (W7-X), currently under construction in Greifswald, Germany. In the last experimental campaign of W7-AS, volume-averaged β values >3% have been achieved. The underlying experimental changes leading to these results are briefly reviewed. The equilibrium characteristics expected from magnetohydrodynamic (MHD) theory are modeled in a simplified picture and compared with three-dimensional equilibrium calculations. A wide range of parameters has been covered in the experiments with and without net toroidal currents. Experimental data are compared with free-boundary equilibrium calculations and exhibit good agreement. The high-β equilibria usually showed only small MHD activity. The most prominent activities are low-frequency pressure-driven modes connected with low-order rationals also expected from numerical calculations using the CAS3D code, and Alfvén modes driven by energetic particles from the tangential neutral beam injection. Comparison of experimentally measured frequencies and mode structures from soft-X-ray tomography with theoretical predictions also shows the improving understanding of these modes in stellarators. The agreement of experiment and theory gives confidence in the predictions for W7-X.

Kinetic effects on the ideal pressure-driven modes in an L=2 heliotron

The kinetic effects on the ideal ballooning and interchange/Mercier modes are studied in model equilibria for an L=2 heliotron, large helical device (LHD) [A. Iiyoshi et al., Nucl. Fusion 39, 1245 (1999)]. It is shown that the ion finite Larmor radius (FLR) effect stabilizes the modes with high toroidal mode number, n. On the other hand, the finite electron compressibility plays a double role, and stabilizes the low-n modes as the ideal magnetohydrodynamic (MHD) modes, while it destabilizes the high-n modes. It is discussed that the inclusion of the compressibility impacts the stability, and this effect is stronger in LHD than in a comparable tokamak, which is due to the larger magnitude of the local curvature. As a result of the competition between the FLR and the compressibility, it is shown in LHD that the low-n instabilities can become much weaker than that expected by the ideal MHD, while the high-n instabilities are prone to remain unstable near the plasma core region.

A framework for the development and testing of an edge pedestal model: Formulation and initial comparison with DIII-D data

A framework has been formulated for the further development and testing of a predictive edge pedestal model. This framework combines models for the interaction of the various physical phenomena acting in the edge pedestal—transport, neutral fueling penetration, atomic physics cooling, MHD (magnetohydrodynamic) stability limit, edge density limit—to determine the pedestal widths and gradient scale lengths. Predictive models for some of these specific phenomena have been compared with DIII-D [J. L. Luxon, Nucl. Fusion 42, 614 (2002)] measurements. It was found that a neutral penetration model for the density width and a MHD model for the maximum pedestal pressure for stability against ideal pressure-driven surface modes were roughly consistent with experimental observation, but that in both cases some refinements are needed. The major impediments to implementation of a predictive edge pedestal model within the framework of this paper are the lack of knowledge of transport coefficients in the pedestal and the unavailability of a usable characterization of the state-of-the-art MHD stability-limit surface in the space of edge parameters. Efforts to remedy these and other deficiencies and to establish a predictive model for the calculation of density, temperature and pressure widths and gradients in the edge pedestal are suggested.

Recent Progress in High-Beta Studies in the REP.

The recent progress in high-beta reversed-fieldpinch (RFP) studies is reviewed. Experimental efforts to suppress the RPF dynamo modes (core resonant tearing modes) have resulted in remarkable confinement improvement in large RFP experiments. The poloidal beta (≈total beta) value of ˜20% has been achieved with improved confinement. After suppressing the current-driven modes, the role of pressure-driven modes will become important in the RFP dynamics. Theoretical studies of pressure-driven modes have revealed that ideal-mode-stable RFP configurations with βP≈30% exist, and that unstable mode spectra are sensitive to local current profiles as well as to pressure profiles. The role of the Suydam criterion on the stability of ideal modes is discussed briefly. From an experimental point of view, it is essential to investigate the beta limit in the RFP by increasing heating power density under conditions of improved confinement.

Active control of resistive wall modesin the large-aspect-ratio tokamak

The large-aspect-ratio model for current-driven external kinks is applied to study control of non-axisymmetric resistive wall modes in tokamaks. Comparison with toroidal computations indicates that the cylindrical instabilities react in similar ways to feedback as the pressure-driven toroidal modes, when the feedback and sensor coils are placed on the low-field side of the torus. However, higher gain is required in the cylindrical case. The cylindrical model is used to gain insights into design issues concerning a feedback system for ITER, with a double wall and superconducting coils. Good control performance and acceptable coilvoltages are found in an initial value problem, where the initial conditions correspond to expected noise levels, when sensors for the poloidal field are placed inside the first wall. This can be accomplished with a PI (proportional plus integral) controller from the voltages of the sensor loops to the voltage over the active coils. The two-wall structure of ITER makes control somewhat more demanding than for tokamaks with a single wall. Adequate control can be achieved also when poloidal sensors are placed outside a single wall, but this requires additional derivative action (PID) and the resulting voltages are significantly higher.

Resistive–ideal transition of pressure-driven instabilities in current-carrying plasmas beyond the Suydam criterion

The linear magnetohydrodynamics stability of local and global resistive pressure-driven instabilities is examined computationally in a cylinder. Both instabilities are resistive from beta values of zero up to several times the Suydam limit. Both transition to ideal modes at higher beta values. No sudden change in growth rate occurs at the Suydam limit. The global pressure-driven modes, of tearing parity, will likely be important in high beta plasmas, such as obtained in the reversed field pinch.

Ballooning instabilities in a Heliotron J plasma

Ideal magnetohydrodynamic stability analysis of local pressure-driven modes in an L=1 heliotron, Heliotron J [M. Wakatani et al., Nucl. Fusion 40, 569 (2000)], is investigated by means of three-dimensional (3D) ballooning formalism and the Mercier criterion. In 3D systems such as heliotrons, the ballooning modes are separated into two categories: One is tokamak-like ballooning modes which are localized only in the poloidal direction, and the other is modes inherent to 3D systems which are localized on the specific flux tubes. The tokamak-like ballooning modes change to the Mercier modes in the limit that the mode is sufficiently extended along the field line, but the nonaxisymmetric ballooning mode does not so. The L=1 Heliotron J equilibrium investigated here has weak global shear and the dominant Fourier amplitudes of magnetic-field strength is rather different from the conventional helical systems with L=2 helical coils. Since the weak global shear causes the reduction of integrated local shear along the field lines easily, which combines with strongly modulated destabilizing effects on the flux surface, the nonaxisymmetric ballooning modes localized on the specific flux tubes can become unstable. On the other hand, the Mercier modes are suppressed due to the deep magnetic well. The results obtained from the model equilibrium of L=2 Large Helical Device (LHD), for which several reports have already published [N. Nakajima, Phys. Plasmas 3, 4556 (1996), for example], are also shown and compared with the results of Heliotron J. The LHD equilibrium employed here has a magnetic hill region at the outer radius, and this tends to make the Mercier modes unstable. It is found that this difference of the Mercier stability property in two equilibria is concerned in the local ballooning stability, and the notable difference of local dispersion relations appears. It is also found from the comparison of two systems that the nonaxisymmetric ballooning modes have a similar property to the tokamak-like ballooning modes, in the sense of the s̄-ᾱ diagram where s̄ and ᾱ are shear and pressure gradient parameter.

Strong "quantum" chaos in the global ballooning mode spectrum of three-dimensional plasmas.

The spectrum of ideal magnetohydrodynamic (MHD) pressure-driven (ballooning) modes in strongly nonaxisymmetric toroidal systems is difficult to analyze numerically owing to the singular nature of ideal MHD caused by lack of an inherent scale length. In this paper, ideal MHD is regularized by using a k-space cutoff, making the ray tracing for the WKB ballooning formalism a chaotic Hamiltonian billiard problem. The minimum width of the toroidal Fourier spectrum needed for resolving toroidally localized ballooning modes with a global eigenvalue code is estimated from the Weyl formula. This phase-space-volume estimation method is applied to two stellarator cases.

Dispersive phenomena in electromigration separation methods.

A review on dispersive effects and on peak broadening in electromigration separation methods (capillary electrophoresis and electrochromatography) is presented, mainly covering papers published between the beginning of 1997 and the beginning of 2000. Most attention is drawn to work dealing with nonlinear effects that cause anomalous electromigration dispersion in electrolyte systems with two or multiple coions. Further, topics cover the comparison of electroosmotic and pressure-driven modes in electrochromatography, dispersive effects due to nonhomogeneous velocity fields in packed electrochromatography columns, to nonuniform electroosmotic flow, to sorption of analytes (mainly proteins) at the column wall or the stationary phase, and due to the influence of the nonideal column geometry like coiling or irregularities in shape.

Feedback stabilization of nonaxisymmetric resistive wall modes in tokamaks. I. Electromagnetic model

Active feedback stabilization of pressure-driven modes in tokamaks is studied computationally in toroidal geometry. The stability problem is formulated in terms of open-loop transfer functions for fluxes in sensor coils resulting from currents in feedback coils. The transfer functions are computed by an extended version of the MARS stability code [A. Bondeson et al., Phys. Fluids B 4, 1889 (1992)] and can be accurately modeled by low order rational functions. In the present paper stability is analyzed for a system with an ideal amplifier (current control). It is shown that feedback with modest gain, and a single coil array poloidally, gives substantial stabilization for a range of coil shapes. Optimum design uses sensors for the poloidal field, located inside the resistive wall, in combination with rather wide feedback coils outside the wall. Typically, the feedback does not strongly modify the plasma-generated magnetic field perturbation. A future companion paper [C. M. Fransson et al., Phys. Plasmas (accepted for publication)] will apply control theory to study the limitations arising for finite time-constant of the amplifier-feedback coil circuit.

Active feedback stabilization of toroidal external modes in tokamaks

Active feedback stabilization of pressure-driven modes in tokamaks is investigated by toroidal computations. Typically, the feedback does not strongly modify the plasma-generated magnetic field perturbation. Feedback with modest gain and a single coil array poloidally stabilizes substantially for a range of coil shapes. Optimum design uses narrow sensor coils not too far from the plasma and rather wide feedback coils, which may be outside the resistive wall. Complex gain, which makes the mode rotate, can decrease the gain required for stabilization, but real gain is more robust.

Recent innovations in enantiomer separation by electrochromatography utilizing modified cyclodextrins as stationary phases.

Enantiomer separation by electrochromatography employing modified cyclodextrins as stationary phases is performed in two ways. (i) Polysiloxane-linked permethylated beta-cyclodextrin (Chirasil-Dex 1) or related selectors are coated and immobilized onto the inner surface of a capillary column. Enantiomer separation is performed in the open tube and the method is referred to as open-tubular capillary electrochromatography (o-CEC). (ii) Silica-linked native beta-cyclodextrin, permethylated beta-cyclodextrin (Chira-Dex 2) or hydroxypropyl-beta-cyclodextrin are filled into a capillary column and the bed is secured by two frits. Enantiomer separation is performed in a packed column and the method is referred to as packed capillary electrochromatography (p-CEC). In a unified instrumental approach, method (i) as well as method (ii) can be operated both in the electro- and pressure-driven modes (o-CEC vs. open-tubular liquid chromatography (o-LC) and p-CEC vs. p-LC). It is demonstrated that the electro-driven variant affords higher efficiencies at comparable elution times. Employing a single open-tubular column coated with Chirasil-Dex 1, a unified enantioselective approach can be realized in which the same selectand is separated using all existing chromatographic modes for enantiomers, i.e., gas chromatography (GC), super-critical fluid chromatography (SFC), o-LC and o-CEC. As the chiral selector is utilized as a stationary phase, an additional chiral selector may be added to the mobile phase. In the resulting dual chiral recognition systems, enhancement of enantioselectivity (matched case) or compensation of enantioselectivity (mismatched case) may be observed. The overall enantioselectivity is dependent on the sense of enantioselectivity of the selectors chosen and their influence on the electrophoretic and electroosmotic migration of the enantiomers of a selectand.

Global mode analysis of ideal magnetohydrodynamic modes in a heliotron/torsatron system: I. Mercier-unstable equilibria

By means of a global mode analysis of ideal magnetohydrodynamic (MHD) modes for Mercier-unstable equilibria in a planar axis L=2/M=10 heliotron/torsatron system with an inherently large Shafranov shift, the conjecture for global mode in Mercier-unstable equilibria from local mode analysis [N. Nakajima, Phys. Plasmas 3, 4556 (1996)] has been confirmed and the properties of pressure-driven modes inherent to such three-dimensional systems have been clarified. The Mercier-unstable equilibria are categorized into toroidicity-dominant and helicity-dominant Mercier-unstable equilibria. In the toroidicity-dominant Mercier-unstable equilibria, the pressure-driven modes change from interchange modes for low toroidal mode numbers n<M, to tokamak-like ballooning modes for moderate toroidal mode numbers n∼M, and finally to ballooning modes purely inherent to three-dimensional systems for fairly high toroidal mode numbers n≫M. In the helicity-dominant Mercier-unstable equilibria, the pressure-driven modes change from interchange modes for n<M or n∼M, directly to ballooning modes purely inherent to three-dimensional systems for n≫M.

Collisionless nonideal ballooning modes

The nonzero inertia of the electron is shown to destabilize pressure-driven ballooning modes in collisionless tokamak plasmas that are stable in the ideal magnetohydrodynamic (MHD) approximation. The effect of the electron mass is characterized by the collisionless electron skin depth de=c/ωpe, where ωpe=4πne2/me is the electron plasma frequency. The growth rate of electron inertia ballooning modes increases with the magnitude of de, and also with the magnitude of the ratio β of the plasma thermal pressure to the pressure in the confining magnetic field.

Shear optimization experiments with current profile control on JET

A record performance on JET has been obtained with shear optimization scenarios. A neutron yield of in deuterium discharges, and a global energy confinement improvement above the ITER-89 L-mode scaling with in L-mode and in H-mode have been achieved. The tailoring of plasma current, density and heating power waveforms and current profile control with lower hybrid current drive and ICRF phasing have been essential. Internal energy, particle and momentum transport barriers develop spontaneously upon heating above a threshold power of about 15 MW with neutral beams and ICRH into a low-density target plasma, with a wide central region of slightly negative or flat magnetic shear with q > 1 everywhere. An additional H-mode transition can also raise the pressure in the region between internal and edge transport barriers. The ion heat conductivity falls to the neoclassical level in the improved core confinement region. Pressure profile control through power deposition feedback control makes it possible to work close to the marginal stability boundary for pressure-driven MHD modes. First experiments in deuterium/tritium plasmas, with up to 75% tritium target concentration, have established internal transport barriers already with heating powers at the lowest threshold of pure deuterium plasmas, resulting in a fusion power output of .

The stability of advanced operational regimes on the Tokamak Fusion Test Reactor

The performance of the Tokamak Fusion Test Reactor [D. Meade and the TFTR Group, in Plasma Physics and Controlled Nuclear Fusion Research, Washington, D.C., 1990 (International Atomic Energy Agency, Vienna, 1991), Vol. I, pp. 9–24], as defined by the maximum fusion power production, has been limited, not by confinement, but by stability to pressure-driven modes. Two classes of current profile modification have been investigated to overcome this limit. A new technique has been developed to increase the internal inductance of low-q (q≈4), high-current (Ip>2MA) plasmas. As was the case at higher edge q, the disruptive β limit has been found to increase roughly linearly with the internal inductance, li. Plasmas with hollow current profiles, i.e., reversed shear, are also predicted and experimentally observed to have increased stability in the negative shear region to ballooning and kink modes. However, performance of these plasmas is still limited by pressure-driven modes in the normal shear region.

Analytical solutions for the growth rates of localized pressure-driven modes in the screw-pinch configuration

The growth rate spectrum of the ideal pressure-driven localized modes in a general screw pinch configuration is obtained in an explicit analytical from under the condition of the Suydam criterion violation. The suppression effect of the magnetic shear near the singular surface is exponential and depends strongly upon the relative values of two small parameters: μ = m/[(krs)2 + m2] and ε = (P' - P's), where m(k) is a poloidal (axial) wavenumber and P's is the Suydam marginally stable pressure gradient. The result is applied to partially relaxed states of reversed field pinch.

Effects of diamagnetic drift and compressibility on linear resistive magnetohydrodynamic stability of stellarators

To study diamagnetic and compressibility effects for stellarators, toroidally averaged equations describing resistive pressure-driven modes are developed. Linear stability results are given for cylindrical geometry and toroidal geometry. When toroidal coupling is included, both the analytical theory and numerical calculations show that diamagnetic effects can be destabilizing when they are small. However, for parameters appropriate to the Advanced Toroidal Facility (ATF) experimental device [J. F. Lyon et al., Fusion Technol. 10, 179 (1986)] the diamagnetic effects are large and stabilizing. The linear results also show that for the specific cases reported here compressibility effects tend to cancel toroidal effects. Cylindrical calculations which include diamagnetic effects may then be adequate for the study of the experimental data.