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Stellarator stability theory examines various forms of instability and turbulence that can be present in 3-dimensional stellarator configurations. All bounded magnetically confined plasmas can be expected to be susceptible to some form of plasma instability. In some cases such instabilities can lead to rapid disruptions and strong plasma losses; in other cases, only a low level of saturated turbulence may be present, but this can still significantly enhance losses over what would be expected from purely classical transport. The goal of stellarator stability theory is to understand and develop models for the various instabilities that can exist in stellarator plasmas. Based on this understanding, techniques can then be developed for suppressing such turbulence.
These suppression techniques can take various forms:
- First in the design of the stellarator, the plasma shape is a strong control variable for influencing the linear stability thresholds of certain types of instabilities. Also, existing stellarator experiments will generally have some degree of control over the plasma shape through auxilliary coils that can, for example, shift it inward or outward in horizontal position (vertical field coils) or squeeze/expand it slightly in its minor cross section (quadrupole field coils)
- Next, in the operation of a stellarator plasma profile shapes will determine whether certain types of instabilities can grow. These profiles shapes can often be externally controlled by heating and fueling techniques.
- In the event that an instability cannot be avoided by shape or profile control, it may simply be necessary to avoid it by not operating in a parameter regime where it is unstable. For example, keep the plasma pressure or current below some critical value.
- Finally, during recent years, many instances of enhanced confinement regimes (where the plasma manages to suppress its own turbulence in situ) have been identified in tokamaks and stellarators. This turbulence suppression is generally related to the build-up of sheared flow velocities in the plasma. Such sheared flows can be very effective at "shredding up" the turbulence. The source of these sheared flows and their control is a very active current research area in toroidal plasma physics.
Some of the instabilities that are of particular relevance to stellarators are:
- Ballooning instabilities. These are localized displacements of the plasma column somewhat like a bulge in a bicycle tire or an aneurysm in an artery. They are generally avoided by keeping the plasma pressure below some threshold. We attempt to maximize this threshold through our optimization process. The COBRA code has been developed within our group for very rapid and accurate surveys of ballooning instability in stellarators.
- Mercier, interchange instabilities. These are in the same family of modes as the ballooning instabilities, but with a longer wavelength along the magnetic field (i.e., the aneurysm is less pronounced, more generalized). These instabilities also have a pressure threshold. This pressure limit is sensitive to the plasma shape and structure of the magnetic field.
- Kink instabilities. These are instabilities driven by the plasma current. They generally lead to rapid large scale, long wavelength motions of the plasma column and must generally be avoided by keeping the total plasma current below some critical level.
- Tearing instabilities. These instabilities are also current-driven, but are involve lower level fluctuations internal to the plasma. In stellarators the neoclassical tearing instabilities (driven by the plasma bootstrap current) are of particular interest. These can be avoided by choosing appropriate signs for the bootstrap current and the radial derivative of the rotational transform. For example, a bootstrap current that is in the same direction as that of the equivalent tokamak coupled with a radially increasing rotational transform profile will stabilize neoclassical tearing instabilities. The QPS and NCSX devices satisfy this requirement. They also provide enough flexibility to violate it so that these instabilities can be studied.
- Vertical displacement modes. These are large scale movements of the plasma column vertically up or down and are of particular concern in hybrid stellarators that have siginificant levels of plasma current. However, by appropriate plasma shape optimization, it is possible to stabilize these modes.
- Alfvén instabilities. These are resonant wave-particle instabilities that are driven by energetic particles (neutral beams, RF tails, alpha particles) having velocities close to or a sizeable fraction of the Alfvén velocity. These instabilities have been observed and studied in a number of existing devices (W7-AS, CHS) and can lead to enhanced losses of energetic particles and lowered heating efficiencies. On a more positive note, it has also been suggested that they could be utilized to directly transfer energy from energetic ions to thermal ions without having to go through the intermediate step of collisional slowing-down on electrons. We are developing the STELLGAP code to analyze these instabilities in stellarators, taking into account the strong mode-coupling that can be present in compact devices.