Currents driven by rf (radio frequency) waves in the interior of magnetic islands can stabilize deleterious tearing modes in tokamaks. Present analyses of stabilization assume that the local electron acceleration is unaffected by the presence of the island. However, the power deposition and electron acceleration are sensitive to the perturbation of the temperature. The nonlinear feedback on the power deposition in the island increases the temperature perturbation, and can lead to a bifurcation of the solution to the steady-state heat diffusion equation. The combination of the nonlinearly enhanced temperature perturbation with the rf current drive sensitivity to the temperature leads to an rf current condensation effect, which can increase the efficiency of rf current drive stabilization and reduce its sensitivity to radial misalignment of the ray trajectories. The threshold for the effect is in a regime that has been encountered in experiments, and will likely be encountered in ITER.
PACS numbers:Introduction: A study of the root causes of disruptions in the JET tokamak found that neoclassical tearing modes (NTMs) were the single most common cause [1,2]. Theoretical calculations in the early 1980's showed the feasibility of using rf current drive to stabilize tearing modes [3,4]. The recognition in the late 1990's that bootstrap currents were driving NTMs in hot, collisionless tokamak plasmas [5][6][7][8], led to a resurgence of theoretical work in this area [9][10][11][12][13], to experimental demonstrations of stabilization [14][15][16][17][18][19][20], and to continuing intensive attention [21][22][23][24][25][26][27][28][29][30][31][32][33][34][35][36][37][38][39][40]. A variety of rf waves are used to drive current [41], but, for stabilizing the NTM, the most studied methods are electron cyclotron current drive (ECCD) [42] and lower hybrid current drive (LHCD) [43]. ITER is designed with an NTM ECCD stabilization capability, with continued effort to model and improve this capability [25,29,30,44]. We identify here an rf current condensation effect, previously overlooked, which can significantly facilitate island stabilization.Calculations of rf stabilization of magnetic islands assume, at present, that the local acceleration of electrons is unaffected by the presence of the island. However, the local deposition is sensitive to small changes in the temperature, and these changes can be significantly affected by the presence of an island. The effect on the local deposition becomes significant when the fractional temperature perturbation exceeds about 5% for electron cyclotron waves and 2.5% for lower hybrid waves. Temperature perturbations as high as 20% have been measured in islands in rf stabilization experiments [45].In the conventional picture of rf current drive stabilization of a rotating island, a geometric effect associated with the equilibration of the rf driven current density within the flux surfaces of the island leads to a higher current density near the center of the island than near its peripher...