The sensitivity of tokamak plasmas to very small deviations from the axisymmetry of the magnetic field.

The structure of the magnetic field perturbations due to non-axisymmetric field-aligned currents in the tokamak scrape-off layer (SOL) are analytically calculated near the X-point. Part I [I. Joseph, et al., submitted to Phys. Plasmas (2008)] demonstrated that biasing divertor target plates in a toroidally asymmetric fashion can generate an appreciable toroidally asymmetric parallel current density in the SOL along the separatrix. Here, the magnetic field perturbation caused by a SOL current channel of finite width and step-wise constant amplitude at the target plate is derived. Flux expansion amplifies the magnetic perturbation near the X-point, while phase interference causes the SOL amplitude to be reduced at large toroidal mode number. Far enough from the current channel, the magnetic field can be approximated as arising from a surface current near the separatrix with differing amplitudes in the SOL and the divertor leg. The perturbation spectrum and resonant components of this field are computed analytically asymptotically close to the separatrix in magnetic flux coordinates. The size of the stochastic layer due to the applied perturbation that would result without self-consistent plasma shielding is also estimated. If enough resonant field is generated, control of the edge pressure gradient may allow stabilization of edge localized modes.

The tokamak is the principal tool in controlled fusion research. This book acts as an introduction to the subject and a basic reference for theory, definitions, equations, and experimental results. The fourth edition has been completely revised, describing their development of tokamaks to the point of producing significant fusion power.

A potential technique for suppressing edge localized magnetohydrodynamic instabilities (ELMs) is theoretically analyzed. Recent experiments have shown that externally generated resonant magnetic perturbations (RMPs) can stabilize ELMs by modifying the density profile [T.E. Evans, et al., Nature Phys. 2, 419 (2006); Y. Liang, et al., Phys. Rev. Lett. 98, 265004 (2007)]. Driving toroidally asymmetric current internally, through the scrape-off layer (SOL) plasma itself, can also generate RMPs that are close to the required threshold for ELM control. The limiting ion saturation current densities can be achieved by producing potential differences on the order of the electron temperature. Although the threshold is uncertain in future devices, if driven coherently though the SOL, the upper limit for the resulting field would exceed the present experimental threshold. This analysis provides the tools required for estimating the magnitude of the coherent SOL current and RMP generated via toroidally asymmetric biasing of the target. Flux expansion increases the RMP near the X-point, while phase interference due to the shearing of field lines near the X-point reduces the amplitude of the effective SOL perturbation and makes the result sensitive to both toroidal mode number n and the radial coherence width of the biasing region. If the limiting current density decays rapidly enough radially, both the width and the amplitude of the current density drawn from the target will be reduced. The RMP can still exceed the present threshold at low n if the radial location and width of the biasing region are optimally chosen.