Editing Plasma stability (section)

== MHD Instabilities ==
{{More citations needed section|date=September 2023}}
[[Beta (plasma physics)|Beta]] is a ratio of the plasma pressure over the [[magnetic field]] strength.<ref>Wesson, J: "Tokamaks", 3rd edition page 115, Oxford University Press, 2004</ref>
<math display="block">\beta = \frac{p}{p_\text{mag}} = \frac{n k_B T}{(B^2/2\mu_0)}</math>

MHD stability at high beta is crucial for a compact, cost-effective magnetic fusion reactor. Fusion power density varies roughly as <math>\beta^2</math> at constant magnetic field, or as <math>\beta_N^4</math> at constant bootstrap fraction in configurations with externally driven plasma current. (Here <math>\beta_N = \beta / (I / a B)</math> 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 a
variety 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 represent the ultimate operational limit for most configurations. The long-wavelength kink mode and short-wavelength ballooning mode limits are generally well understood and can in principle be avoided.

Intermediate-wavelength modes (n ~ 5&ndash;10 modes encountered in [[tokamak]] edge plasmas, for example) are less well understood due to the computationally intensive nature of the stability calculations. 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 the plasma are accurately measured. This good agreement provides confidence in ideal stability calculations 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, [[Spherical 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, since the onset can occur at beta values well below the ideal limit. The stability of neoclassical tearing modes (NTM) is a key issue for magnetic configurations with a strong [[bootstrap current]]. The NTM is a metastable mode; in certain plasma configurations, a sufficiently large deformation of the bootstrap current produced by a “seed island” can contribute to the growth of the island. The NTM is already an important performance-limiting factor in many tokamak experiments, leading to degraded confinement or disruption. Although the basic mechanism is well established, the capability to predict the onset in present and future devices requires better understanding of the damping mechanisms which determine the threshold island size, and of the [[mode coupling]] by which other instabilities (such as sawteeth in tokamaks) can generate seed islands. [[Resistive Ballooning Mode]], similar to ideal ballooning, but with finite resistivity taken into consideration, provides another example of a resistive instability.