Control of tearing modes in tokamak plasmas by means of a bifurcation behavior

Summary form only given. Tearing modes (with low mode numbers) are known to affect tokamak performances, as it has recently been observed during TFTR Supershots. As a result, understanding their stability properties is quite a challenging issue. The evolution and saturation of the associated magnetic islands seem in reasonable agreement with the predictions of the so-called neoclassical /spl nabla/p-driven tearing mode model (instability driven by the bootstrap current). However, the latter does not predict any threshold condition (to be overcome by a mode before it can grow and saturate). This is in contradiction with experiment, since any mode should be unstable in the absence of a threshold condition, while only few are indeed observed (m/n=3/2, 4/3 and 5/4), indicating the lack of a stabilizing contribution in the analysis. Two mechanisms have recently been proposed that could remove this discrepancy: 1) the destabilizing bootstrap current contribution is found to be reduced when longitudinal and transverse diffusivities are properly taken into account, preventing electron pressure to equilibrate upon perturbed magnetic surfaces, so that the required (to effectively drive the instability) pressure flattening inside the island does not occur for small perturbations. 2) ion polarization drift effects (including both inertia and finite Larmor radius) provide a stabilizing contribution, potentially dominant for island width of the order of the ion Larmor radius (but rapidly decreasing with growing islands). These mechanisms provide the previously missing threshold condition: an island can grow if only its width w overcomes a critical value w/sub crit/ controlled by a single parameter C. In addition, the dependence of w/sub crit/ with respect to C exhibits a bifurcation behavior for C less than a bifurcation value C/sub bif/ (associated with the maximum threshold w/sub max/) the threshold w/sub crit/ is infinity.