M.R. de Baar

Experimental studies of instabilities and confinement of energetic particles on JET and MAST

In preparation for next step burning plasma devices such as ITER, experimental studies of instabilities and confinement of energetic ions were performed on Joint European Torus (JET) and on Mega-Amper Spherical Tokamak (MAST) with innovative diagnostic techniques, in conventional and shear-reversed plasmas, exploring a wide range of effects for energetic ions. A compendium of recent results testing capabilities of the present-day facilities for burning plasma relevant study is presented in this paper. Alpha tail production using 3rd harmonic ion-cyclotron resonance heating (ICRH) of He-4 beam ions has been employed on JET for studying He-4 of the megaelectronvolt energy range in a neutron-free environment. The evolution of ICRH-accelerated ions of He-4 with E >= 1.7 MeV and D with E >= 500 keV was assessed from nuclear gamma-ray emission born by the fast ions colliding with Be and C impurities. A simultaneous measurement of spatial profiles of fast He-4 and fast D ions relevant to ITER was performed for the first time in positive and strongly reversed magnetic shear discharges. Time-resolved gamma-ray diagnostics for ICRH-accelerated He-3 and H minority ions allowed changes in the fast ion distribution function to be assessed in the presence of unstable toroidal Alfven eigenmodes (TAEs) and sawteeth. A significant decrease of gamma-ray intensity from protons with E >= 5 MeV was detected during the tornado modes. This was interpreted as tomado-induced loss of fast ions with the drift orbit width, Delta(f), comparable to the minor radius of tokamak a. Experiments performed in the opposite case, Delta f/a = 500 keV, have shown excitation of numerous Alfven eigenmodes without a significant degradation of the fast ion confinement. The stabilizing effect of fast particles on monster sawteeth was experimentally found to fail in low-density plasmas with high power ion cyclotron resonance frequency (ICRF)-heating. The transition from the monster to short-period grassy sawteeth was investigated with different ICRF phasing, which controls the pinch-effect and radial distribution of ICRF-accelerated ions. Instabilities excited by super-Alfvenic beam ions were investigated on the spherical tokamak MAST. Due to higher values of beta and a higher proportion of fast ions on MAST than on JET, a wider variety of modes and nonlinear regimes for the Alfven instabilities were observed, including the explosive TAE-regimes leading to the formation of hole-clump pairs on the fast ion distribution function. The MAST and START data showed that TAE and chirping modes decrease both in their mode amplitudes and in the number of unstable modes with increasing beta.

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.

Control of the tokamak safety factor profile with time-varying constraints using MPC

A controller is designed for the tokamak safety factor profile that takes real-time-varying operational and physics limits into account. This so-called model predictive controller (MPC) employs a prediction model in order to compute optimal control inputs that satisfy the given limits. The use of linearized models around a reference trajectory results in a quadratic programming problem that can easily be solved online. The performance of the controller is analysed in a set of ITER L-mode scenarios simulated with the non-linear plasma transport code RAPTOR. It is shown that the controller can reduce the tracking error due to an overestimation or underestimation of the modelled transport, while making a trade-off between residual error and amount of controller action. It is also shown that the controller can account for a sudden decrease in the available actuator power, while providing warnings ahead of time about expected violations of operational and physics limits. This controller can be extended and implemented in existing tokamaks in the near future.

Intermediate frequency band digitized high dynamic range radiometer system for plasma diagnostics and real-time Tokamak control.

An intermediate frequency (IF) band digitizing radiometer system in the 100-200 GHz frequency range has been developed for Tokamak diagnostics and control, and other fields of research which require a high flexibility in frequency resolution combined with a large bandwidth and the retrieval of the full wave information of the mm-wave signals under investigation. The system is based on directly digitizing the IF band after down conversion. The enabling technology consists of a fast multi-giga sample analog to digital converter that has recently become available. Field programmable gate arrays (FPGA) are implemented to accomplish versatile real-time data analysis. A prototype system has been developed and tested and its performance has been compared with conventional electron cyclotron emission (ECE) spectrometer systems. On the TEXTOR Tokamak a proof of principle shows that ECE, together with high power injected and scattered radiation, becomes amenable to measurement by this device. In particular, its capability to measure the phase of coherent signals in the spectrum offers important advantages in diagnostics and control. One case developed in detail employs the FPGA in real-time fast Fourier transform (FFT) and additional signal processing. The major benefit of such a FFT-based system is the real-time trade-off that can be made between frequency and time resolution. For ECE diagnostics this corresponds to a flexible spatial resolution in the plasma, with potential application in smart sensing of plasma instabilities such as the neoclassical tearing mode (NTM) and sawtooth instabilities. The flexible resolution would allow for the measurement of the full mode content of plasma instabilities contained within the system bandwidth.

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.

Alfven mode stability and wave-particle interaction in the JET tokamak: prospects for scenario development and control schemes in burning plasma experiments

We have investigated the effect of different ion cyclotron resonance frequency (ICRF) heating schemes, of error field modes, of the plasma shape and edge magnetic shear, and of the ion delB drift direction on the stability of Alfven eigenmodes (AEs). The use of multi-frequency or 2nd harmonic minority ICRF heating at high plasma density gives rise to a lower fast ion pressure gradient in the plasma core and to a reduced mode activity in the Alfven frequency range. Externally excited low-amplitude error fields lead to a much larger AE instability threshold, which we attribute to a moderate radial redistribution of the fast ions. The edge plasma shape has a clear stabilizing effect on high-n, radially localized AEs. The damping rate of n = 1 toroidal AEs is a factor 3 higher when the ion VB drift is directed towards the divertor. These results represent a useful step towards the extrapolation of current scenarios to the inclusion of fusion-born alpha particles in ITER, with possible application for feedback control schemes for the various ITER operating regimes.

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.

Robust sawtooth period control based on adaptive online optimization

The systematic design of a robust adaptive control strategy for the sawtooth period using electron cyclotron current drive (ECCD) is presented. Recent developments in extremum seeking control (ESC) are employed to derive an optimized controller structure and offer practical tuning guidelines for its parameters. In this technique a cost function in terms of the desired sawtooth period is optimized online by changing the ECCD deposition location based on online estimations of the gradient of the cost function. The controller design does not require a detailed model of the sawtooth instability. Therefore, the proposed ESC is widely applicable to any sawtoothing plasma or plasma simulation and is inherently robust against uncertainties or plasma variations. Moreover, it can handle a broad class of disturbances. This is demonstrated by time-domain simulations, which show successful tracking of time-varying sawtooth period references throughout the whole operating space, even in the presence of variations in plasma parameters, disturbances and slow launcher mirror dynamics. Due to its simplicity and robustness the proposed ESC is a valuable sawtooth control candidate for any experimental tokamak plasma, and may even be applicable to other fusion-related control problems.

Effect of hysteresis in JET ITB plasma with LHCD

A strong ITB was sustained in a reversed shear discharge in JET during a long time interval after a significant reduction in plasma heating power. The observed ITB evolution is reminiscent of the effect of hysteresis, associated in theory with turbulence suppression due to shear of the plasma rotation. The mechanism of ITB sustainment was analysed. Modelling of the plasma heating and current profile was done using the TRANSP and JETTO transport codes. The resulting q-profile evolution was verified by comparison with the pitch angle ? = Bp/Bt deduced from motional Stark effect measurements (where Bp and Bt are the poloidal and toroidal magnetic field, respectively). Turbulence stability was analysed using the gyro-kinetic code Kinezero. It was shown that the strong negative magnetic shear produced by LHCD and sustained mainly by the bootstrap current in the plasma core is responsible for the turbulence stabilization. Stabilization due to shear of the plasma rotation and finite ? -stabilization play a complimentary role. The effect of bootstrap and LH driven currents on magnetic shear in JET discharges was analysed.

Temporally resolved plasma composition measurements by collective Thomson scattering in TEXTOR (invited).

Fusion plasma composition measurements by collective Thomson scattering (CTS) were demonstrated in recent proof-of-principle measurements in TEXTOR [S. B. Korsholm et al., Phys. Rev. Lett. 106, 165004 (2011)]. Such measurements rely on the ability to resolve and interpret ion cyclotron structure in CTS spectra. Here, we extend these techniques to enable temporally resolved plasma composition measurements by CTS in TEXTOR, and we discuss the prospect for such measurements with newly installed hardware upgrades for the CTS system on ASDEX Upgrade.