On the merits of heating and current drive for tearing mode stabilization

Abstract

Neoclassical tearing modes (NTMs) are magnetohydrodynamic modes that can limit the performance of high β discharges in a tokamak, leading eventually to a plasma disruption. A NTM is sustained by the perturbation of the ‘bootstrap’ current, which is a consequence of the pressure flattening across a magnetic island. Control and suppression of this mode can be achieved by means of electron cyclotron waves (ECWs) which allow the deposition of highly localized power at the island location. The ECW power replenishes the missing bootstrap current by generating a current perturbation either inductively, through a temperature perturbation (electron cyclotron resonance heating), or non-inductively by direct current drive (electron cyclotron current drive). Although both methods have been applied successfully to experiments showing a predominance of ECRH for medium-sized limiter tokamaks (TEXTOR, T-10) and of ECCD for mid-to-large-sized divertor tokamaks (AUG, DIII-D, JT-60), conditions determining their relative importance are still unclear. We address this problem with a numerical study focused on the contributions of heating and current drive to the temporal evolution of NTMs as described by the modified Rutherford equation. For the effects of both heating as well as current drive, simple analytical expressions have been found in terms of an efficiency fore-factor times a ‘geometrical’ term depending on the power deposition width w dep, location and modulation. When the magnetic island width w equals the width of the deposition profile, w ≈ w dep, both geometric terms are practically identical. Whereas for current drive the geometric term approaches a constant for small island widths and is inversely proportional to (w/w dep)2 for large island widths, the heating term approaches a constant for large island widths and is proportional to (w/w dep) for small island widths. For medium-sized tokamaks (TEXTOR, AUG) the heating and current drive efficiencies are of the same order of magnitude, whereas in a future, large reactor like ITER the current drive efficiency is expected to be significantly larger.

Avoiding Tokamak Disruptions by Applying Static Magnetic Fields That Align Locked Modes with Stabilizing Wave-Driven Currents

“…Currents were either continuously driven [6] or, more efficiently, they were modulated in synch with the spontaneous island rotation [7]. Electron Cyclotron Heating (ECH) was also used for stabilization [8], but is predicted to scale unfavorably to large hot plasmas [9]. Two experiments combined magnetic perturbations -to produce the island-with ECH that stabilized it: in the first one the mode was born locked to a given phase and was stabilized by continuous ECH [10]; the second one controlled island rotation and stabilized the mode by modulated ECH [11].…”

“…In the absence of position control, one can apply ECH only (no current drive) to delay or avoid disruptions in small [19] and mid-size devices [20]. This approach, as mentioned, is predicted to arXiv:1510.08932v1 [physics.plasm-ph] 29 Oct 2015 scale unfavourably to larger, hotter fusion plasmas such as ITER, where the stabilization is expected to be completely governed by current drive [9]. Yet, in order for current drive to be used, it is necessary to gain control of the locking position of the magnetic island, as currents driven at the wrong location, such as the island X-point (the tip of the island), can actually be destabilizing [21].…”

“…The island is caused by a helical "hole" in a pressuredriven ("bootstrap") current [9] and can be modelled with multiple helical filaments offset in the toroidal angle and carrying different currents, according to a sinusoidal distribution [22]. A magnetic dipole is associated with this helical current pattern.…”

Dynamical modelling of neoclassical tearing mode suppression by ECCD

“…This reference case corresponds to Δ CD as obtained conventionally by averaging the power deposition and current drive profiles over a rotation period [4][5][6]. When τ coll is different from zero, the EC driven current takes time to reach a quasi-steady state [8].…”

“…In this parameter space we recognize two limits. On the one hand the regime of very fast rotation (τ NT M /τ rot 100) in which Δ CD may be obtained through an average over a rotation period [3][4][5][6]. On the other hand, the locked mode regime (τ NT M /τ rot 1) in which the island does not rotate.…”