Fusion Science and Technology / Volume 59 / Number 3 / April 2011 / Pages 499-518
Lecture / Fourth ITER International Summer School (IISS2010)
The models describing macroscopic magnetic perturbations that evolve slowly compared to the Alfvén velocity are reviewed. The perturbations of interest include tearing modes, resistive interchange and ballooning modes, internal kink modes, resistive wall modes, and resonant magnetic perturbations. Two important features that distinguish the various models are their descriptions of parallel dynamics and of ion gyration. The evolution of macroscopic modes is generally characterized by resonances that result in the development of small scales. For processes involving magnetic reconnection, for example, all scales from the ion down to the electron Larmor radius are generated nonlinearly. The magnetohydrodynamic model assumes that the gradient lengths are always greater than the ion Larmor radius and thus is unable to properly describe the resonances. The drift models rely on a much more detailed description of the motion that enables them to capture many of the features of the short-scale phenomena, but they remain limited by their local description of the effects of gyration, and by their inability to describe the effects of wave-particle interactions in the parallel dynamics. These limitations are remedied by the gyrokinetic model, which provides a consistent, first-principles description of all the dynamics below the ion cyclotron frequency, but this model is computationally costly and its range of practical applicability remains to be established. Lastly, the gyrofluid models constitute a family of closures based on the moments of the gyrokinetic equations. These models offer an attractive compromise between fidelity and computational cost but have only recently begun to be applied to macroscopic evolution.