Tearing Mode Stability Research Articles

Sawtooth Pacing by Real-Time Auxiliary Power Control in a Tokamak Plasma

In the standard scenario of tokamak plasma operation, sawtooth crashes are the main perturbations that can trigger performance-degrading, and potentially disruption-generating, neoclassical tearing modes. This Letter demonstrates sawtooth pacing by real-time control of the auxiliary power. It is shown that the sawtooth crash takes place in a reproducible manner shortly after the removal of that power, and this can be used to precisely prescribe, i.e., pace, the individual sawteeth. In combination with preemptive stabilization of the neoclassical tearing modes, sawtooth pacing provides a new sawtooth control paradigm for improved performance in burning plasmas.

The impact of 3D fields on tearing mode stability of H-modes

New processes have been discovered in the interaction of 3D fields with tearing mode stability at low torque and modest β on DIII-D and NSTX. These are thought to arise from the plasma response at the tearing resonant surface, which theoretically is expected to depend strongly on plasma rotation and underlying intrinsic tearing stability. This leads to sensitivities additional to those previously identified at low density where the plasma rotation is more readily stopped, or at high βN where ideal MHD responses amplify the fields (where βN is the plasma β divided by the ratio of plasma current to minor radius multiplied by toroidal field). It is found that the threshold size for 3D fields to induce modes tends to zero as the natural tearing βN limit is approached. 3D field sensitivity is further enhanced at low rotation, with magnetic probing detecting an increased response to applied fields in such regimes. Modelling with the MARS-F code confirms the interpretation with the usual plasma screening response breaking down in low rotation plasmas and a tearing response developing, opening the door to additional sensitivities to β and the current profile. Typical field thresholds to induce modes in torque-free βN ∼ 1.5 H-modes are well below those in ohmic plasmas or plasmas near the ideal βN limit. The strong interaction with the tearing mode βN limit is identified through rotation shear, which is decreased by the 3D field, leading to decreased tearing stability. Thus both locked and rotating mode field thresholds can be considered in terms of a torque balance, with sufficient braking leading to destabilization of a mode. On this basis new measurements of the principal parameter scalings for error field threshold have been obtained in torque-free H-modes leading to new predictions for error field sensitivity in ITER. The scalings have similar exponents to ohmic plasmas, but with seven times lower threshold at the ITER baseline βN value of 1.8, and a linear dependence on proximity to the tearing mode βN limit (∼2.2 at zero torque). This reinforces the need to optimize error field correction strategies in ITER, and implement sources to drive plasma rotation.

Progress in the Development of the ITER ECE Diagnostic

This paper explains the present status of the ITER electron cyclotron emission (ECE) diagnostic and gives an outlook on the upcoming technical and design activity. The open questions of calibration and stability of ECE systems, as well as proposals for the calibration, the design of the front end, and the transmission line are reviewed. The possible role of ECE in the neoclassical tearing mode detection and stabilization by electron cyclotron heating is also discussed. Because integration of the ITER ECE diagnostic within the tokamak requires proper definition of interfaces with many different components located both in-vessel and ex-vessel, a special attention is paid to address the associated issues.

Interaction of turbulence with magnetic islands: effect on bootstrap current

A finite radial temperature gradient has been observed to be maintained within magnetic islands in gyro-kinetic turbulence simulations despite the fast motion along the field, and is related to the trapped particles which do not move along the field around the island. Recent calculations of the interaction of drift-wave turbulence with magnetic islands have shown that turbulence can exist within the separatrix, which in turn allows only the partial flattening of electron temperature profiles. Here we calculate, using a minimal drift-kinetic model, the effect on the bootstrap current in a tokamak. Consequences for the stability of the neoclassical tearing mode are discussed.

Real-Time Diagnostics and Their Applications at ASDEX Upgrade

For applications of advanced plasma control schemes, many computers that execute complex algorithms need to communicate with low latency so that result data are promptly available for operating adequate actuators that can directly influence the plasma behavior. ASDEX Upgrade has completed the commissioning phase of its real-time diagnostic framework serving that purpose. Several applications were successfully tested, and progress toward a full feedback neoclassical tearing mode stabilization loop is evident. The new real-time diagnostics comprise several new diagnostics capable of acquiring raw data (up to 1 MHz, up to 60 channels), processing the raw data (calibrate, transform, evaluate, etc.) and transmitting the results over suitable networks to other computers, all in real time. Projects for machine safety (divertor cooling and hot spot detection), physics studies [regulation of density peaking by application of electron cyclotron resonance heating (ECRH)], and real-time state monitors (ECRH deposition calculation) have demonstrated the capabilities of the new diagnostics and the control framework. The control system can now operate its actuators in line with decisions based on algorithms with rather high complexity. Adding new control algorithms has become a distributed effort with manageable overhead.

Real-time control of tearing modes using a line-of-sight electron cyclotron emission diagnostic

The stability and performance of tokamak plasmas are limited by instabilities such as neoclassical tearing modes. This paper reports on an experimental proof of principle of a feedback control approach for real-time, autonomous suppression and stabilization of tearing modes in a tokamak. The system combines an electron cyclotron emission diagnostic for sensing of the tearing modes in the same sight line with a steerable electron cyclotron resonance heating and current drive (ECRH/ECCD) antenna. A methodology for fast detection of q = m/n = 2/1 tearing modes and retrieval of their location, rotation frequency and phase is presented. Set-points to establish alignment of the ECRH/ECCD deposition location with the centre of the tearing mode are generated in real time and forwarded in closed loop to the steerable launcher and as a modulation pulse train to the gyrotron. Experimental results demonstrate the capability of the control system to track externally perturbed tearing modes in real time.

Suppression of MHD instabilities by ion Bernstein wave (IBW) heating in the HT-7 tokamak

In the HT-7 tokamak, the m = 2/n = 1 tearing mode can be effectively suppressed by the ion Bernstein wave (IBW) when the location of power deposition is near the q = 2 rational surface. Off-axis electron heating and electron density broadening have been observed. In the meantime, the particle confinement is improved with an increase in electron density and a drop in Dα emission. The induced large electron density gradients and electron pressure gradients can be spatially correlated with the IBW deposition profile via theoretical calculation. It is suggested that off-axis IBW heating modified the electron pressure profile and the current density profile can be redistributed, thus resulting in the suppression of the magnetohydrodynamics (MHD) instability. It provides an integrated way for both the stabilization of tearing modes and controlling pressure profiles.

Modelling the effect of cross-field diffusion on tearing mode stability

A non-linear theory of tearing modes in a magnetized plasma which retains the effect of cross-field diffusion on the ion polarization current is presented. This ion polarization current is predicted to influence the tearing mode evolution when its amplitude is small, corresponding to a magnetic island with a width that is comparable to the ion Larmor radius. It is therefore likely to be most relevant for understanding whether tearing modes can drive magnetic turbulence, and for understanding the threshold physics of neoclassical tearing modes, of particular relevance to tokamaks. There are two opposing contributions to the ion polarization current: one from a narrow layer in the vicinity of the island separatrix and one in the opposite direction from outside this layer. These contributions are comparable, so the net effect of the ion polarization current on tearing mode stability requires a quantitative prediction of both. The region outside the layer is relatively well understood. The separatrix layer, on the other hand, must treat a range of complex physics mechanisms, including finite Larmor radius effects and the influence of cross-field diffusion. This paper treats both together for the first time. The cross-field diffusion is found to have the following influences on the separatrix region: (i) the density distribution is smoothed across the separatrix; (ii) density is no longer a flux surface function and (iii) the distribution function is not entirely Maxwellian. The net effect of including cross-field diffusion is a substantial reduction of the contribution of the ion polarization current from the separatrix layer region.

Application of the Bayesian analysis to the modified Rutherford equation for NTM stabilization

The determination of the free parameters present in the modified Rutherford equation (MRE), which is routinely used for studying the physics of neoclassical tearing mode (NTM) stabilization, is addressed by making use of the Bayesian probability theory. The evaluation of the free coefficients is particularly sensitive to the assumptions used in the modelled equation, to the correlation of various physical parameters and to the uncertainties of the experimental measurements. A probabilistic method was applied for the consistent evaluation of the coefficients and their uncertainties using a large database of discharges and by considering the correlations and the uncertainties of the multiple physical quantities present in the MRE. The estimated values and uncertainties of the coefficients are related to the precise determination of the minimum amount of electron cyclotron current drive power necessary to stabilize NTMs in the International Thermonuclear Experimental Reactor.

Islands in the stream: The effect of plasma flow on tearing stability

Reducing plasma flow clearly decreases the stability of tearing modes in multiple regimes (sawtooth, hybrid) in both high- and low-aspect-ratio tokamaks (DIII-D [J. L. Luxon, Nucl. Fusion 42, 614 (2002)], Joint European Torus [M. Keilhacker and the JET Team, Plasma Phys. Controlled Fusion 41, 301 (1999)], National Spherical Torus Experiment [M. Ono, S. M. Kaye, Y.-K. M. Peng, Nucl. Fusion 40, 557 (2000)], each with distinct means of lessening rotation). Further, reducing flow makes pre-existing “saturated” islands larger at the same beta (β). Thus lower plasma flow impairs high-beta operation owing both to the destabilization and to the impact of tearing-mode islands. Experimental results suggest that flow shear (not flow) at the tearing rational surface is classically stabilizing, making the effective tearing stability index Δ′ of the total current density profile more negative (more stable). In this picture, with profiles and all else the same, the minimum metastable beta at which neoclassical tearing modes (NTMs) can destabilize is proportional to −Δ′ and hence lower flow and flow shear lead to possible destabilization (depending on seeding) at lower beta. Similarly, if destabilized, the saturated NTM island width is proportional to −β/Δ′ and thus increases as flow and flow shear are reduced. A working model gives a significant level of stabilizing shear if the plasma toroidal angular flow shear −dΩϕ/dr at a given rational surface is of order of the inverse of the product of the local values of the parallel magnetic shear length Ls and the Alfvén time τA. Experimental data are fitted for the effect of this normalization of flow shear in a simple empirical model for both onset and saturation of tearing modes. Most theoretical literature is on the consequence of flow shear on tearing stability at zero beta; tokamaks at high beta have large magnetic Prandtl number (an issue for the sign of the flow effect) and very large Lundquist number. It is in this regime that theory will be compared with experimentally based empirical models. The consequence for future tokamaks with low rotation may be lower tearing stability than now expected.

Calculating electron cyclotron current drive stabilization of resistive tearing modes in a nonlinear magnetohydrodynamic model

A model which incorporates the effects of electron cyclotron current drive (ECCD) into the magnetohydrodynamic equations is implemented in the NIMROD code [C. R. Sovinec et al., J. Comput. Phys. 195, 355 (2004)] and used to investigate the effect of ECCD injection on the stability, growth, and dynamical behavior of magnetic islands associated with resistive tearing modes. In addition to qualitatively and quantitatively agreeing with numerical results obtained from the inclusion of localized ECCD deposition in static equilibrium solvers [A. Pletzer and F. W. Perkins, Phys. Plasmas 6, 1589 (1999)], predictions from the model further elaborate the role which rational surface motion plays in these results. The complete suppression of the (2,1) resistive tearing mode by ECCD is demonstrated and the relevant stabilization mechanism is determined. Consequences of the shifting of the mode rational surface in response to the injected current are explored, and the characteristic short-time responses of resistive tearing modes to spatial ECCD alignments which are stabilizing are also noted. We discuss the relevance of this work to the development of more comprehensive predictive models for ECCD-based mitigation and control of neoclassical tearing modes.

DIII-D research in support of ITER

DIII-D research is providing key information for the design and operation of ITER. Investigations of axisymmetric stability and of edge-localized mode (ELM) suppression with resonant magnetic perturbations have helped provide the physics basis for new axisymmetric and non-axisymmetric control coils in ITER. Discharges that simulate ITER operating scenarios in conventional H-mode, advanced inductive, hybrid and steady state regimes have achieved normalized performance consistent with ITER's goals for fusion performance. Stationary discharges with high βN and 90% non-inductive current that project to Q = 5 in ITER have been sustained for a current relaxation time (∼2.5 s), and high beta wall-stabilized discharges with fully non-inductive current drive have been sustained for more than one second. Detailed issues of plasma control have been addressed, including the development of a new large-bore startup scenario for ITER. DIII-D research also contributes to the basis for reliable operation in ITER, through active control of the chief performance-limiting instabilities. Simultaneous stabilization of neoclassical tearing modes (by localized current drive) and resistive wall modes (by magnetic feedback) has allowed stable operation at high beta and low rotation. In research aimed at improving the lifetime of material surfaces near the plasma, recent experiments have investigated several approaches to mitigation of disruptions, including injection of low-Z gas and low-Z pellets, and have shown the conditions that minimize core impurity accumulation during radiative divertor operation. Investigation of carbon erosion, transport and co-deposition with hydrogenic species, and methods for the removal of co-deposits, will contribute to the physics basis for initial operation of ITER with a carbon divertor. A broad research programme provides the physics basis for predicting the performance of ITER. Recent key results include the discovery that the L–H power threshold is reduced with low neutral beam torque, and the development of a successful model for prediction of the H-mode pedestal height in DIII-D. Research areas with the potential to improve ITER's performance include the demonstration of ELM-free ‘quiescent H-mode’ discharges with both co- and counter-neutral beam injection, and validation of the predicted torque generated by static, non-axisymmetric magnetic fields. New diagnostics provide detailed benchmarking of turbulent transport codes and direct measurements of the anomalous transport of fast ions by Alfvén instabilities. Successful comparison of experiment and modelling for off-axis neutral beam current drive provides the basis for more flexible current profile control in advanced scenarios.

Consequences of finite transport on the effectiveness of ECCD for neoclassical tearing mode stabilization in ITER

One of the main aims of the ITER electron cyclotron resonance heating (ECRH) system, in particular of the Upper Port Launcher, is the control of magnetohydrodynamics instabilities. This control typically requires non-inductively driven currents with a high degree of localization, i.e. with a very narrow profile. A numerical analysis of the effect of the radial diffusion of the EC driven current carrying electrons has been performed in order to estimate the effectiveness of electron cyclotron current drive (ECCD) for neoclassical tearing mode (NTM) stabilization. In particular, Fokker–Planck calculations including radial diffusion for the case of the ITER ECRH Upper Port Launcher are presented. These show a significant decrease in the local current density when radial diffusion at a rate of only 1 m2 s−1 is included and consequently a broadening of the profile with a drop in the predicted efficiency for NTM control. Furthermore, it is shown that a simple formula combining the effect of the radial diffusion and the width of the EC power deposition profile reproduces quite accurately the maximum EC driven current density, which is the more relevant number in determining the NTM suppression figure of merit, for typical ITER parameters.

Progress of high power 170 GHz gyrotron in JAEA

Recent progress on the high power gyrotron development in JAEA is presented. The gyrotron is featured to have a triode-type magnetron injection gun, a cylindrical resonator working at 170 GHz with TE31,8 mode, a water-cooled diamond window and a depressed collector. After the demonstration of the ITER basic performance, the gyrotron has been operated for 3 years, and recorded ∼200 GJ of total output energy. Next, a gyrotron which oscillates in higher order resonator mode, TE31,12, is designed and fabricated to study the long pulse oscillation at greater than 1 MW. In parallel, feasibility studies of a CW-power modulation for neoclassical tearing mode stabilization, a dual frequency gyrotron and a rapid frequency control are carried out. It is shown that these gyrotrons will be available with current technology.

On the merits of heating and current drive for tearing mode stabilization

Neoclassical tearing modes (NTMs) are magnetohydrodynamic modes that can limit the performance of high β discharges in a tokamak, leading eventually to a plasma disruption. A NTM is sustained by the perturbation of the ‘bootstrap’ current, which is a consequence of the pressure flattening across a magnetic island. Control and suppression of this mode can be achieved by means of electron cyclotron waves (ECWs) which allow the deposition of highly localized power at the island location. The ECW power replenishes the missing bootstrap current by generating a current perturbation either inductively, through a temperature perturbation (electron cyclotron resonance heating), or non-inductively by direct current drive (electron cyclotron current drive). Although both methods have been applied successfully to experiments showing a predominance of ECRH for medium-sized limiter tokamaks (TEXTOR, T-10) and of ECCD for mid-to-large-sized divertor tokamaks (AUG, DIII-D, JT-60), conditions determining their relative importance are still unclear. We address this problem with a numerical study focused on the contributions of heating and current drive to the temporal evolution of NTMs as described by the modified Rutherford equation. For the effects of both heating as well as current drive, simple analytical expressions have been found in terms of an efficiency fore-factor times a ‘geometrical’ term depending on the power deposition width wdep, location and modulation. When the magnetic island width w equals the width of the deposition profile, w ≈ wdep, both geometric terms are practically identical. Whereas for current drive the geometric term approaches a constant for small island widths and is inversely proportional to (w/wdep)2 for large island widths, the heating term approaches a constant for large island widths and is proportional to (w/wdep) for small island widths. For medium-sized tokamaks (TEXTOR, AUG) the heating and current drive efficiencies are of the same order of magnitude, whereas in a future, large reactor like ITER the current drive efficiency is expected to be significantly larger.

Relaxed MHD states of a multiple region plasma

We calculate the stability of a multiple relaxation region MHD (MRXMHD) plasma, or stepped-Beltrami plasma, using both variational and tearing mode treatments. The configuration studied is a periodic cylinder. In the variational treatment, the problem reduces to an eigenvalue problem for the interface displacements. For the tearing mode treatment, analytic expressions for the tearing mode stability parameter Δ′, being the jump in the logarithmic derivative in the helical flux across the resonant surface, are found. The stability of these treatments is compared for m = 1 displacements of an illustrative reverse field pinch-like configuration, comprising two distinct plasma regions. For pressureless configurations, we find the marginal stability conclusions of each treatment to be identical, confirming the analytical results in the literature. The tearing mode treatment also resolves ideal MHD unstable solutions for which Δ′ → ∞: these correspond to displacement of a resonant interface. Wall stabilization scans resolve the internal and external ideal kink. Scans with increasing pressure are also performed: these indicate that both variational and tearing mode treatments have the same stability trends with β, and show destabilization in configurations with increasing core pressure. Combined, our results suggest that variational stability of MRXMHD configurations is sufficient for both ideal and tearing (Δ′ < 0) stability. Such configurations, and their stability properties, are of emerging importance in the quest to find mathematically rigorous solutions of ideal MHD force balance in 3D geometry.

Prospects for stabilization of neoclassical tearing modes by electron cyclotron current drive in ITER

The system planned for electron cyclotron current drive (ECCD) in ITER can mitigate the deleterious effects of neoclassical tearing modes (NTMs) provided that either adequate alignment of the ECCD to the rational surface is maintained or too large a misalignment is corrected on a time scale shorter than the deleterious plasma response to ‘large’ islands. Resistive neoclassical tearing modes will be the principal limit on stability and performance in the ITER standard scenario as the drag from rotating island induced eddy current in the resistive wall (particularly from the m/n = 2/1 mode) can slow the plasma rotation, produce locking to the wall and cause loss of high-confinement H-mode and disruption. Continuous wave (cw) ECCD at the island rational surface is successful in stabilization and/or prevention of NTMs in ASDEX Upgrade, DIII-D and JT-60U. Modulating the ECCD so that it is absorbed only on the rotating island O-point is proving successful in recovering effectiveness in ASDEX Upgrade when the ECCD is configured for wider deposition as expected in ITER. The models for the effect of misalignment on ECCD effectiveness are applied to ITER. Tolerances for misalignment are presented to establish criteria for both the alignment (by moving mirrors in ITER) in the presence of an island, and for the accuracy of real-time ITER MHD equilibrium reconstruction in the absence of an island, i.e. alignment to the mode or to the rational surface in the absence of the mode. The narrower ECCD with front steering makes precise alignment more necessary for the most effective stabilization even though the ECCD is still relatively broad, with current density deposition (full width half maximum) almost twice the marginal island width. This places strict requirements on ECCD alignment with the expected ECCD effectiveness dropping to zero for misalignments as small as 1.7 cm. The system response time for growing islands and slowing rotation without and with ECCD (at different misalignments) are provided for the plasma system controller to be developed. An alignment resolution error of no more than 1 cm and a realignment rate of at least 1 cm s−1 are required for a moderate cw ECCD power so as to avoid locking. Finally, a case study in ITER of prompt dynamic alignment and suppression is presented.

Finalization of the conceptual design of the remote steering ECH launcher for ITER

The design of a remote steering (RS) variant of the electron cyclotron heating (ECH) upper port launcher (UPL) for neo-classical tearing mode (NTM) stabilization in ITER is being finalised. The RS variant is the fall-back option for the reference design, which is a front steering (FS) UPL. This paper presents the changes made in the design of the RS UPL with respect to the previous baseline (the October 2005 baseline) design. The changes are motivated by a demand to improve the reliability of the launching system by solving a number of pressing issues. To accomplish this, a reduction in the steering range of the launcher was proposed. This reduction yields more tolerable head loads on the focusing elements for a given performance. Modifications of the launcher layout allow for an increase of the toroidal injection angle, which improves the NTM stabilization efficiency. A mode converter can reduce the stray radiation in the vicinity of the steering mechanism down to tolerable levels. Abandoning the concept of the mini-duct leads to a reduction of stray radiation concerns and allows for the implementation of improved alignment facilities of the individual steerable mirror units. The work shows that a launcher based on the RS principle is feasible. This launcher can be made reliable, flexible and easily accessible for maintenance purposes accepting the consequent limitations in the achievable steering range inside the ITER plasma.

Development of High Power Gyrotron and Power Modulation Technique using the JT-60U ECRF System

Electron cyclotron range of frequency system of the JT-60U finished operation at the end of August 2008, and improvements toward JT-60SA have been started. In the last two years stable gyrotron oscillation at an output power of 1.5 MW for 1 s was demonstrated, for the first time, using the 110 GHz gyrotron. It was verified that the heat load on the cavity was at an acceptable level with continuous oscillations at 1.5 MW. The absorption power of the collector was also at an acceptable level for the longer pulse oscillation of 5 s. A power modulation technique based on anode voltage modulation was also developed in order to study the effects of modulated Electron Cyclotron Current Drive (ECCD) on Neoclassical Tearing Mode (NTM) stabilization. Modulation frequencies of up to 7 kHz were achieved at output power of 0.8 MW exceeding the previous limit of 3 kHz. Modulated ECCD experiments in synchronization with the NTM were successfully performed with a modulation frequency of around 5 kHz. Development of an accurate synchronization system played an essential role in the experiments that needed a maintained phase between the magnetic probe signal and modulated ECCD in real time. The results provide significant information for further developments that will enhance the overall performance of ECRF systems in the near future.

Linear tearing mode stability equations for a low collisionality toroidal plasma

Tearing mode stability is normally analysed using MHD or two-fluid Braginskii plasma models. However for present, or future, large hot tokamaks like JET or ITER the collisionality is such as to place them in the banana regime. Here we develop a linear stability theory for the resonant layer physics appropriate to such a regime. The outcome is a set of ‘fluid’ equations whose coefficients encapsulate all neoclassical physics: the neoclassical Ohm's law, enhanced ion inertia, cross-field transport of particles, heat and momentum all play a role. While earlier treatments have also addressed this type of neoclassical physics we differ in incorporating the more physically relevant ‘semi-collisional fluid’ regime previously considered in cylindrical geometry; semi-collisional effects tend to screen the resonant surface from the perturbed magnetic field, preventing reconnection. Furthermore we also include thermal physics, which may modify the results. While this electron description is of wide relevance and validity, the fluid treatment of the ions requires the ion banana orbit width to be less than the semi-collisional electron layer. This limits the application of the present theory to low magnetic shear—however, this is highly relevant to the sawtooth instability—or to colder ions. The outcome of the calculation is a set of one-dimensional radial differential equations of rather high order. However, various simplifications that reduce the computational task of solving these are discussed. In the collisional regime, when the set reduces to a single second-order differential equation, the theory extends previous work by Hahm et al (1988 Phys. Fluids 31 3709) to include diamagnetic-type effects arising from plasma gradients, both in Ohm's law and the ion inertia term of the vorticity equation. The more relevant semi-collisional regime pertaining to JET or ITER, is described by a pair of second-order differential equations, extending the cylindrical equations of Drake et al (1983 Phys. Fluids 26 2509) to toroidal geometry.