Plasma stability

An important field of plasma physics is the stability of the plasma. It usually only makes sense to analyze the stability of a plasma once it has been established that the plasma is in equilibrium. "Equilibrium" asks whether there are net forces that will accelerate any part of the plasma. If there are not, then "stability" asks whether a small perturbation will grow, oscillate, or be damped out.

In many cases a plasma can be treated as a fluid and its stability analyzed with magnetohydrodynamics (MHD). MHD theory is the simplest representation of a plasma, so MHD stability is a necessity for stable devices to be used for nuclear fusion, specifically magnetic fusion energy. There are, however, other types of instabilities, such as velocity-space instabilities in magnetic mirrors and systems with beams. There are also rare cases of systems, e.g. the Field-Reversed Configuration, predicted by MHD to be unstable, but which are observed to be stable, probably due to kinetic effects.

MHD Instabilities

Beta is a measure of plasma pressure normalized to the magnetic field strength. (See magnetohydrodynamics for a full definition.) MHD stability at high beta is crucial for a compact, cost-effective magnetic fusion reactor. Fusion power density varies roughly as β² at constant magnetic field, or as β_N⁴ at constant bootstrap fraction in configurations with externally driven plasma current. (Here β_N = β /(I/aB) is the normalized beta.) In many cases MHD stability represents the primary limitation on beta and thus on fusion power density. MHD stability is also closely tied to issues of creation and sustainment of certain magnetic configurations, energy confinement, and steady-state operation. Critical issues include understanding and extending the stability limits through the use of avariety of plasma configurations, and developing active means for reliable operation near those limits. Accurate predictive capabilities are needed, which will require the addition of new physics to existing MHD models. Although a wide range of magnetic configurations exist, the underlying MHD physics is common to all. Understanding of MHD stability gained in one configuration can benefit others, by verifying analytic theories, providing benchmarks for predictive MHD stability codes, and advancing the development of active control techniques.

The most fundamental and critical stability issue for magnetic fusion is simply that MHD instabilities often limit performance at high beta. In most cases the important instabilities are long wavelength, global modes, because of their ability to cause severe degradation of energy confinement or termination of the plasma. Some important examples that are common to many magnetic configurations are ideal kink modes, resistive wall modes, and neoclassical tearing modes. A possible consequence of violating stability boundaries is a disruption, a sudden loss of thermal energy often followed by termination of the discharge. The key issue thus includes understanding the nature of the beta limit in the various configurations, including the associated thermal and magnetic stresses, and finding ways to avoid the limits or mitigate the consequences. A wide range of approaches to preventing such instabilities is under investigation, including optimization of the configuration of the plasma and its confinement device, control of the internal structure of the plasma, and active control of the MHD instabilities.

Ideal Instabilities

Ideal MHD instabilities driven by current or pressure gradients representthe ultimate operational limit for most configurations. The long-wavelength kink mode and short-wavelengthballooning mode limits are generally well understood and can in principle be avoided.Intermediate-wavelength modes (n ~ 5–10 modes encountered in tokamak edge plasmas, forexample) are less well understood due to the computationally intensive nature of the stabilitycalculations. The extensive beta limit database for tokamaks is consistent with ideal MHD stability limits, yielding agreement to within about 10% in beta for cases where the internal profiles of theplasma are accurately measured. This good agreement provides confidence in ideal stabilitycalculations for other configurations and in the design of prototype fusion reactors.

Resistive Wall Modes

Resistive wall modes (RWM) develop in plasmas that require the presence of a perfectly conducting wall for stability. RWM stability is a key issue for many magnetic configurations. Moderate beta values are possible without a nearby wall in the tokamak, stellarator, and other configurations, but a nearby conducting wall can significantly improve ideal kink mode stability in most configurations, including the tokamak, ST, reversed field pinch (RFP), spheromak, and possibly the FRC. In the advanced tokamak and ST, wall stabilization is critical for operation with a large bootstrap fraction. The spheromak requires wall stabilization to avoid the low-m,n tilt and shift modes, and possibly bending modes. However, in the presence of a non-ideal wall, the slowly growing RWM is unstable. The resistive wall mode has been a long-standing issue for the RFP, and has more recently been observed in tokamak experiments. Progress in understanding the physics of the RWM and developing the means to stabilize it could be directly applicable to all magnetic configurations. A closely related issue is to understand plasma rotation, its sources and sinks, and its role in stabilizing the RWM.

Resistive instabilities

Resistive instabilities are an issue for all magnetic configurations, sincethe onset can occur at beta values well below the ideal limit. The stability of neoclassical tearingmodes (NTM) is a key issue for magnetic configurations with a strong bootstrap current. Theneoclassical tearing mode (NTM) is a metastable mode; in certain plasma configurations, asufficiently large deformation of the bootstrap current produced by a “seed island” can contributeto the growth of the island. The NTM is already an important performance-limiting factor in manytokamak experiments, leading to degraded confinement or disruption. Although the basicmechanism is well established, the capability to predict the onset in present and future devicesrequires better understanding of the damping mechanisms which determine the threshold islandsize, and of the mode coupling by which other instabilities (such as sawteeth in tokamaks) cangenerate seed islands.

Opportunities for Improving MHD Stability

Configuration

The configuration of the plasma and its confinement device represent anopportunity to improve MHD stability in a robust way. The benefits of discharge shaping and lowaspect ratio for ideal MHD stability have been clearly demonstrated in tokamaks and STs, and willcontinue to be investigated in experiments such as DIII-D, Alcator C-Mod, NSTX, and MAST. Newstellarator experiments such as NCSX (proposed) will test the prediction that addition ofappropriately designed helical coils can stabilize ideal kink modes at high beta, and lower-beta testsof ballooning stability are possible in HSX. The new ST experiments provide an opportunity totest predictions that a low aspect ratio yields improved stability to tearing modes, includingneoclassical, through a large stabilizing “Glasser effect” term associated with a large Pfirsch-Schlütercurrent. Neoclassical tearing modes can be avoided by minimizing the bootstrap current inquasi-helical and quasi-omnigenous stellarator configurations. Neoclassical tearing modes are alsostabilized with the appropriate relative signs of the bootstrap current and the magnetic shear; thisprediction is supported by the absence of NTMs in central negative shear regions of tokamaks.Stellarator configurations such as the proposed NCSX, a quasi-axisymmetric stellarator design,can be created with negative magnetic shear and positive bootstrap current to achieve stability to theNTM. Kink mode stabilization by a resistive wall has been demonstrated in RFPs and tokamaks,and will be investigated in other configurations including STs (NSTX) and spheromaks (SSPX).A new proposal to stabilize resistive wall modes by a flowing liquid lithium wall needs furtherevaluation.

Internal Structure

Control of the internal structure of the plasma allows more activeavoidance of MHD instabilities. Maintaining the proper current density profile, for example, canhelp to maintain stability to tearing modes. Open-loop optimization of the pressure and currentdensity profiles with external heating and current drive sources is routinely used in many devices.Improved diagnostic measurements along with localized heating and current drive sources, nowbecoming available, will allow active feedback control of the internal profiles in the near future.Such work is beginning or planned in most of the large tokamaks (JET, JT–60U, DIII–D,
C–Mod, and ASDEX–U) using RF heating and current drive. Real-time analysis of profile datasuch as MSE current profile measurements and real-time identification of stability boundaries areessential components of profile control. Strong plasma rotation can stabilize resistive wall modes,as demonstrated in tokamak experiments, and rotational shear is also predicted to stabilize resistivemodes. Opportunities to test these predictions are provided by configurations such as the ST,spheromak, and FRC, which have a large natural diamagnetic rotation, as well as tokamaks withrotation driven by neutral beam injection. The Electric Tokamak experiment is intended to have avery large driven rotation, approaching Alfvénic regimes where ideal stability may also beinfluenced. Maintaining sufficient plasma rotation, and the possible role of the RWM in dampingthe rotation, are important issues that can be investigated in these experiments.

Feedback Control

Active feedback control of MHD instabilities should allow operationbeyond the “passive” stability limits. Localized rf current drive at the rational surface is predictedto reduce or eliminate neoclassical tearing mode islands. Experiments have begun in ASDEX–Uand COMPASS-D with promising results, and are planned for next year in DIII–D. Routine useof such a technique in generalized plasma conditions will require real-time identification of theunstable mode and its radial location. If the plasma rotation needed to stabilize the resistive wallmode cannot be maintained, feedback stabilization with external coils will be required. Feedbackexperiments have begun in DIII–D and HBT-EP, and feedback control should be explored for theRFP and other configurations. Physics understanding of these active control techniques will bedirectly applicable between configurations.

Disruption Mitigation

The techniques discussed above for improving MHD stability are theprincipal means of avoiding disruptions. However, in the event that these techniques do notprevent an instability, the effects of a disruption can be mitigated by various techniques.Experiments inJT–60U have demonstrated reduction of electromagnetic stresses through operation at a neutralpoint for vertical stability. Pre-emptive removal of the plasma energy by injection of a large gaspuff or an impurity pellet has been demonstrated in tokamak experiments, and ongoingexperiments in C–Mod, JT–60U, ASDEX–U, and DIII–D will improve the understanding andpredictive capability. Cryogenic liquid jets of helium are another proposed technique, which maybe required for larger devices. Mitigation techniques developed for tokamaks will be directlyapplicable to other configurations.

References