Page 2 - Detection and prediction of a beam-driven mode in field-reversed configuration plasma with recurrent neural networks

Nucl. Fusion 60 (2020) 126025
C. Scott et al
Figure1. OneFRCshotdemonstratingstaircaseinstability(top) and one which does not (bottom). The plotted signal is the excluded flux radius at the midplane of the C-2U device. Canny edge detector output visualized as red lines.
gradient at the midplane. And while the pressure at the mid- plane drops during the burst, the pressure near the fast ion mir- ror points upticks, consistent with fast ions being transported outward axially from the midplane. The mode has the cyc- lic character of a limit cycle in which the free energy source builds slowly in time until a critical point is reached and that energy is released in a burst. The release relies on a resonance between the plasma diamagnetic frequency and the precession frequency of the fast ion orbits. During the bursting phase of this cycle, magnetic oscillations detectable at the plasma edge appear with an initial frequency of 100-200 kHz and down chirp to 50 kHz in 50 us. The magnetic oscillations have tor- oidal mode number n = 2, as do perturbations observed with bolometric measurements. Because the instability relies on a resonance between the fast ions and the plasma diamagnetic rotation, it can be avoided by tuning the NB energy up or down out of the resonance zone.
The goals of the present work are to identify the parameter regions in which this onset occurs to assist future physical interpretation, and to provide fast and accurate prediction of the mode with a view to future real-time control of the mode. The C-2U experiment has numerous diagnostics [5] including magnetic sensors, interferometry, Thomson scattering, spec- troscopy, bolometry, reflectometry, neutral particle analyzers, and fusion product detectors.
Previous work has applied artificial neural network (ANN) models to the prediction of other plasma instability phenom- ena, such as the “disruption’ of the tokamak plasma [1], fol- lowed by many similar works such as [6, 7]. In this work [1] a neural network was trained and was able to predict
a class of disruptive instability in plasma shots. Another type of tokamak-specific plasma instability phenomenona are edge-localized modes (ELMs): burst-like modes which tend to limit the pressure gradient at the plasma boundary. ELMs have been successfully predicted using a variety of methods includ- ing deep neural networks [8]. The underlying plasma physics of tokamaks and FRCs, and therefore the cause of the instabil- ity, may be distinct. However, both phenomena are similar in that they are difficult to anticipate. Therefore it is highly desir- able to adopt the ANN instability prediction method to the FRC system, to build a detector for the onset of staircase mode. To our knowledge, the attempt of ANN prediction of an FRC plasma is a first attempt.
2. Dataset creation and preprocessing
First, we select several hundred shots during which all probe measurements of interest are present, and the measurement of excluded flux radius at midplane is well-behaved. We select shots by 1) running the edge detection described below on all shots to find staircase instances; 2) dividing all the shots into those where at least one staircase event occurs, and those where none occur; and 3) selecting uniformly at random an equal number from each group.
We take several measurements during each shot, including:
• 14 channels of magnetic data from Mirnov probes, distrib- uted axially and azimuthally around the edge of the plasma, including two planes perpendicular to the main axis of the C-2U device;
• 19 channels of bolometer data, which measure the total radiated power on the wall (particles and photons);
• secondary electron emission (SEE) detectors, which meas- ure neutral beam shine through and can be used to infer beam trapping efficiency or plasma density;
• pre-shot magnetic field;
• neutron detectors;
• electron temperature;
• CO2 interferometers;
• the excluded flux radius at the midplane, R∆φ, which is an estimate of the of the separatrix radius derived from mag- netic diagnostics.
We also use as inputs to the neural network(s) several moments of these diagnostics, such as the spatial Fourier trans- form of the azimuthal magnetic probe measurements, and the axial gradient of the excluded flux radius at fixed locations along the central axis. These moments are an effective way to assert the existence of physical relationships between data streams that would otherwise be considered independent by the ANN; supplying the network with precalculated functions of the input data also aid our interpretation of the trained net- work later. For example, if the model largely ignores a par- ticular signal, but pays attention to that signal’s instantaneous slope, we can infer that the slope may be more relevant to predicting staircase. Also, practically, the moments improve
2