Neoclassical Tearing Modes

Transformer action is not the only source of toroidal plasma current in a tokamak plasma. In fact, there is an additional, non-inductive component of the toroidal plasma current, known as the bootstrap current [3,67,68], that is driven by radial gradients in the plasma pressure. (See Section 2.20.) The flattening of the pressure profile inside the magnetic separatrix of a magnetic island chain gives rise to a helical hole in the bootstrap current that has a destabilizing effect on the chain [8]. A tearing mode that is driven unstable by this mechanism, rather than the usual free energy sources for a tearing mode (i.e., global current and pressure gradients), is known as a neoclassical tearing mode. (See Chapter 12.) Neoclassical tearing modes were originally identified experimentally on the TFTR tokamak [10], and are regarded as the main obstacle to obtaining $\beta$ values in tokamak plasmas that are adequate for the achievement of thermonuclear fusion [7,37,52]. However, a magnetic island chain can only locally flatten the plasma pressure when its radial width exceeds a certain threshold value that depends on the local ratio of the parallel and perpendicular energy diffusivities [19]. This observation leads to the conclusion that neoclassical tearing modes are actually meta-stable. In other words, some sort of seed perturbation must be applied to the relevant rational magnetic flux-surface in order to trigger a neoclassical tearing mode. In practice, the seed perturbation usually takes the form of a transient magnetic perturbation that is resonant at the rational surface [31]. Such perturbations arise naturally in tokamak plasmas as a consequence of plasma instabilities such as internal kink modes and edge localized modes [64]. Neoclassical tearing modes can be stabilized by driving a parallel (to the magnetic field) current in the vicinity of the rational surface by means of electron cyclotron waves injected into the plasma; the idea is to fill in the helical hole in the bootstrap current profile [30,38,46,49,69,70]. (See Chapter 12.)