In plasma physics, plasma stability concerns the stability properties of a plasma in equilibrium and its behavior under small perturbations. The stability of the system determines if the perturbations will grow, oscillate, or be damped out. It is an important consideration in topics such as nuclear fusion and astrophysical plasma. In many cases, a plasma can be treated as a fluid and analyzed with the theory of magnetohydrodynamics (MHD). MHD stability is necessary for stable operation of magnetic confinement fusion devices and places certain operational limits. The beta limit, for example, sets the maximum achievable plasma beta in tokamaks. On the other hand, small-scale plasma instabilities (typically described by kinetic theory), such as the drift wave instability, are widely under the current theory thought to be the driving mechanism of turbulent transport in tokamaks, which leads to high rate of particle and energy transport across the confining magnetic fields. Plasma instabilities described by kinetic theory can contain aspects such as finite Larmor radius (FLR) effects and resonant wave-particle interactions, which is not captured in fluid models such as MHD.
Plasma instabilities Plasma instabilities can be divided into two general groups:
hydrodynamic instabilities kinetic instabilities. Plasma instabilities are also categorized into different modes (e.g. with reference to a particle beam):
List of plasma instabilities
MHD Instabilities
Beta is a ratio of the plasma pressure over the magnetic field strength.
β = p p mag = n k B T ( B 2 / 2 μ 0 ) {\displaystyle \beta ={\frac {p}{p_{\text{mag}}}}={\frac {nk_{B}T}{(B^{2}/2\mu _{0})}}}
MHD stability at high beta is crucial for a compact, cost-effective magnetic fusion reactor. Fusion power density varies roughly as β 2 {\displaystyle \beta ^{2}} at constant magnetic field, or as β N 4 {\displaystyle \beta _{N}^{4}} at constant bootstrap fraction in configurations with externally driven plasma current. (Here β N = β / ( I / a B ) {\displaystyle \beta _{N}=\beta /(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 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 ~ 5–10 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.
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