Nonlinear Kinetic Ion Response to Small Scale Magnetic Islands in Tokamak Plasmas: Neoclassical Tearing Mode Threshold Physics.

A new drift-kinetic theory of the ion response to magnetic islands in tokamak plasmas is presented. Small islands are considered, with widths w much smaller than the plasma radius r, but comparable to the trapped ion orbit width rho(bi). An expansion in w/r reduces the system dimensions from five down to four. In the absence of an electrostatic potential, the ions follow stream lines that map out a drift-island structure that is identical to the magnetic island, but shifted by an amount similar to few rho(bi). The ion distribution function is flattened across these drift islands, not the magnetic island. For small islands, w similar to rho(bi), the shifted drift islands result in a pressure gradient being maintained across the magnetic island, explaining previous simulation results [E. Poli et al., Phys. Rev. Lett. 88, 075001 (2002)]. To maintain quasineutrality an electrostatic potential forms, which then supports a pressure gradient in the electrons also. This influence on the electron physics is shown to stabilize small magnetic islands of width a few ion banana widths, providing a new threshold mechanism for neoclassical tearing modes-a key result for the performance of future tokamaks, including ITER.