Horizontal ECE measurement of a 2/1 NTM showing phase inversion between radial channels 4 and 8: Note the different phases in the corresponding rate of change of poloidal field, (Mirnov) signal.
ECE contours of electron temperature as a function of normalized minor radius and time, with 2/1 island clearly recognizable: the dashed lines mark the ECE channel locations. The and locations from the motional Stark effect diagnostic are also shown.
Experimental setup for oblique-ECE-assisted alignment and modulation of ECCD in synch and in phase with a rotating NTMs.
(a) ECCD and normalized minor radii and (b) phase difference between oblique ECE signals, exhibiting a phase jump in correspondence of good radial alignment.
Response of the ECE radiometer, in the form of phase difference between the two channels, as a function of the object of the measurement, which is the misalignment , here reconstructed a posteriori by means of the TORAY-GA and ONETWO codes. The system has a sensitivity of : when the alignment is better than that, the system signals it with nonzero phase difference.
(a) The phase difference between ECE signals originating on opposite sides of an island (dotted resonances) is for view (dashed line) perpendicular to the island, as in horizontal ECE: (b) Temperature extremes cross oblique view at distinct times, making . [(c) and (d)] Flow shear is another cause of non-180° phase jumps. [(e)–(h)] Simulated signals corresponding to (a)–(d), not exactly sinusoidal because the island is assumed peaked.
Complete stabilization of a 3/2 NTM by ECCD modulated by oblique ECE: (a) ECCD power, (b) driven current density (spatial peak, averaged over time) and bootstrap current density at , (c) mode amplitude from Mirnov coils at the wall, showing complete stabilization at 2100 ms, and (d) mode rotation frequency from magnetic spectrogram and local fluid rotation frequency from charge exchange recombination spectroscopy, doubled because mode has .
(a) Detail of modulated ECCD in Fig. 7(a), generated by a difference between [(b) and (c)] oblique ECE signals and reasonably well correlated with (d) Mirnov signal.
Comparison of (a) peak- and (b) average-power requirements for (c) complete 3/2 stabilization. Modulated ECCD is 10% more efficient than continuous ECCD in terms of peak power and 30% more efficient in terms of average power.
(a) Scan of modulated ECCD power and corresponding (b) and (c) mode Mirnov amplitudes.
Square root of Mirnov amplitude (proportional to 3/2 island width) in the presence of ECCD, continuous, modulated in the O-point, or in the X-point, as a function of time-averaged EC power. Curves are fit to data. The arrows indicate the 100% stabilization that occurs when the marginal condition is achieved.
Diagnostics of rotating precursors of locked modes and criteria to trigger the control phase: (a) Mirnov coils, (b) frequency counter connected to Mirnov coils, (c) external saddle loops, for locked modes without rotating precursors.
Set of DIII-D coils internal (I-) and external (C-) to the vacuum vessel: The poloidal field sensors used here to detect the rotating precursor of the locked mode are also shown.
Evolution of (a) NBI power, (b) , (c) rotating amplitude and (d) frequency, (e) line-averaged density, (f) ECCD power, (g) I-coil, and (h) C-coil currents:
(a) Sensors: mode amplitude and frequency measured by probes: Actuators: (b) ECCD power and (c) I-coil currents. Plasma response: (d) amplitude and (e) toroidal phase of the mode (in red), slowly rotated by the applied perturbation. The amplitude and toroidal phase of the applied perturbation, measured in a separate “vacuum” shot (126707), are shown for comparison in black.
(a) Phase and (b) radial field amplitude of mode initially locked to the EF, then forced to rotate by RMPs. Vacuum field of #126707 subtracted from #126623.
Radial scan at constant ECCD and fixed RMP: (a) Major radius of plasma, (b) phase, and (c) amplitude of Mirnov. The mode slips more when good radial alignment is achieved and recovers when the ECCD is turned off.
Phase and amplitude of of a 2/1 NTM in #126685 initially locked to the wall, unlocked at , and forced to rotate by an I-coil traveling wave accelerating from 1 to 60 Hz. Vacuum shot with same I-coil currents, #126709, has been subtracted.
(a) phase and (b) amplitude of weak applied RMP (dashed) and of mode (solid line), exhibiting rapid rotations opposite to RMP at .
Explanation of Fig. 19: the mode is locked to the resultant of the static EF and rotating applied RMP: For slow rotations, at any given instant it occupies a minimum of potential. If the RMP is comparable with the EF, e.g., only 20% larger (left) or smaller (right), at a certain time the two nearly cancel out and a new minimum appears in a different location, which the mode rapidly moves to. This explains nonuniform rotation and, in the case on the right, also the change in direction.
NTM stabilization efficiency of two main ECCD mechanisms. is taken at and .
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