H. van den Brand

Integrated modelling of island growth, stabilization and mode locking : consequences for NTM control on ITER

Full suppression of neoclassical tearing modes (NTMs) using electron cyclotron current drive (ECCD) should be reached before mode locking (stop of rotation) makes suppression impossible. For an ITER scenario 2 plasma, the similar time scales for locking and island growth necessitate the combined modelling of the growth of the mode and its slow down due to wall induced drag. Using such a model, the maximum allowed latency between the seeding of the mode and the start of ECCD deposition and maximum deviation in the radial position are determined. The maximum allowed latency is determined for two limiting models for island growth; the polarization model with W-marg = 2 cm, representing the worst case, and the transport model with W-marg = 6 cm, representing the best case. NTMs with seed island widths up to 9.5 cm and 12 cm for the 2/1 and the 3/2 NTM, respectively, are suppressible. The maximum allowed latency is 1.05 s and 2.95 s for the 2/1 and 3/2 NTM, respectively, for the worst case model. Radial misalignment should not exceed 7-10 mm for the 2/1 NTM and 5-16 mm for the 3/2 NTM depending on the model for island growth. As long as the alignment suffices, it does not reduce the maximum allowed latency. Mode locking has serious implications for any real-time NTM control system on ITER that aims to suppress NTMs by ECCD.

Evaluating neoclassical tearing mode detection with ECE for control on ITER

Neoclassical tearing mode (NTM) control on ITER requires detection of the mode location to be accurate and with low latency. This paper presents a systematic way to evaluate mode detection algorithms for ITER using numerical simulations of electron cyclotron emission (ECE), taking into account the radial asymmetry in the temperature perturbation by a rotating magnetic island. Simulated ECE is detected using a synthetic radiometer, in the ITER equatorial port plug, and processed by two detection algorithms for the 2/1 and 3/2 NTMs for a burning H-mode ITER plasma. One of the algorithms also incorporates simulated Mirnov data. The video bandwidth is set at 2 kHz. This allows for intermediate frequency bandwidths of BIF = 400 MHz and BIF = 300 MHz for the two algorithms, respectively. The intermediate frequency bandwidth provides a trade-off between radial accuracy (low bandwidth) and low noise/latency (large bandwidth). 2/1 and 3/2 NTMs, seeded with widths up to 9 and 11 cm, are detectable with the required accuracy within 250 ms. With appropriate settings for the radiometer, the NTM detection using ECE is accurate and with low latency. The algorithm that incorporates both ECE and Mirnov data showed the lowest detection latencies.

Estimation of the thermal diffusion coefficient in fusion plasmas taking frequency measurement uncertainties into account

In this paper, the estimation of the thermal diffusivity from perturbative experiments in fusion plasmas is discussed. The measurements used to estimate the thermal diffusivity suffer from stochastic noise. Accurate estimation of the thermal diffusivity should take this into account. It will be shown that formulas found in the literature often result in a thermal diffusivity that has a bias (a difference between the estimated value and the actual value that remains even if more measurements are added) or have an unnecessarily large uncertainty. This will be shown by modeling a plasma using only diffusion as heat transport mechanism and measurement noise based on ASDEX Upgrade measurements. The Fourier coefficients of a temperature perturbation will exhibit noise from the circular complex normal distribution (CCND). Based on Fourier coefficients distributed according to a CCND, it is shown that the resulting probability density function of the thermal diffusivity is an inverse non-central chi-squared distribution. The thermal diffusivity that is found by sampling this distribution will always be biased, and averaging of multiple estimated diffusivities will not necessarily improve the estimation. Confidence bounds are constructed to illustrate the uncertainty in the diffusivity using several formulas that are equivalent in the noiseless case. Finally, a different method of averaging, that reduces the uncertainty significantly, is suggested. The methodology is also extended to the case where damping is included, and it is explained how to include the cylindrical geometry.

A model-based, multichannel, real-time capable sawtooth crash detector

Control of the time between sawtooth crashes, necessary for ITER and DEMO, requires real-time detection of the moment of the sawtooth crash. In this paper, estimation of sawtooth crash times is demonstrated using the model-based interacting multiple model (IMM) estimator, based on simplified models for the sawtooth crash. In contrast to previous detectors, this detector uses the spatial extent of the sawtooth crash as detection characteristic. The IMM estimator is tuned and applied to multiple ECE channels at once. A model for the sawtooth crash is introduced, which is used in the IMM algorithm. The IMM algorithm is applied to seven datasets from the ASDEX Upgrade tokamak. Five crash models with different mixing radii are used. All sawtooth crashes that have been identified beforehand by visual inspection of the data, are detected by the algorithm. A few additional detections are made, which upon closer inspection are seen to be sawtooth crashes, which show a partial reconnection. A closer inspection of the detected normal crashes shows that about 42% are not well fitted by any of the full reconnection models and show some characteristics of a partial reconnection. In some case, the measurement time is during the sawtooth crashes, which also results in an incorrect estimate of the mixing radius. For data provided at a sampling rate of 1 kHz, the run time of the IMM estimator is below 1 ms, thereby fulfilling real-time requirements.