MHD and plasma control
MHD and plasma control
At the high plasma temperatures and densities as required for an economical fusion reactor, tokamak plasmas are prone to various magnetohydrodynamic (MHD) instabilities. In the core of the plasma, a sawtooth like relaxation oscillation in the pressure is observed when the central safety factor [math]q_0[/math] drop below unity. In the crash of a sawtooth the central part of the plasma is completely mixed by the occurrence of an m=1, n=1 resistive kink mode. At low order rational q-surfaces, neoclassical tearing modes (NTMs) occur. These modes become metastable when the plasma beta (which is defined as the ratio of kinetic over magnetic pressure) reaches some threshold value. Nonlinear growth of the mode then occurs as soon as a sufficiently large initial perturbation is generated. Such a perturbation often is caused by a sawtooth crash.
Sawteeth limit the achievable central pressure, and may lead to the loss of energetic fusion alpha particles. Moreover they are seen to trigger NTMs. However, sawteeth also have the benefit of removing the fusion He-ashes from the plasma core, thus preventing suffocation of the fusion reaction. Neoclassical tearing modes limit the achievable plasma beta and may lead to disruptive termination of the discharge. Therefore active control of sawteeth and NTM is of paramount importance to the development of a tokamak fusion reactor.
In fact, many more MHD instabilities exist like edge localized modes (ELMs), fishbones, or the various types of Alfvén Eigenmodes (TEA, BEA, …). Many of these modes are destabilized by or can affect energetic ion populations (generically called Energetic Particle Modes). Once the international ITER experiment will become operational in a decade, fusion research will enter a new realm in which the hitherto unexplored, complex interplay of all these instabilities and their effects will play an important role. An overall plasma control strategy taking into account the various transport processes and instabilities will have to be developed for the control of burning plasmas.
In this wide field of research our group concentrates on the control of NTMs and sawteeth. Within these topics the whole range from theory, through modelling to experiments is covered. Experiments are being carried out or planned on a number of devices including JET (under EFDA), TEXTOR, AUG, and ITER.
MHD modelling
The modelling activities in the field of MHD and MHD control naturally divided into two categories: 1) physics based modelling, and 2) modelling of the complete feedback loop. Where the first aims at physics understanding of the processes involved, and the second aims at the development and test of robust control strategies.
Neoclassical tearing modes
The modified Rutherford equation provides the canonical model for the nonlinear evolution of NTMs. It can symbolically be written as
[math]\frac{\tau_r}{r_s}\frac{dw}{dt}=r\Delta^{\prime}+r_s\Delta^{\prime}_{boot}-r_s\Delta^{\prime}_{ECCD}-r_s\Delta^{\prime}_{ECRH}+...,[/math]
where each term on the right hand side describes the separate effect on the mode growth of a particular physical process: [math]\Delta^{\prime}[/math] is the classical tearing mode stability parameter; [math]\Delta^{\prime}_{boot}[/math] provides the nonlinear destabilization by the neoclassical bootstrap current, and the final two terms describe the stabilizing effects from local non-inductive current drive or heating inside the magnetic island, respectively. The NTM modelling work is focused on these last two effects. Although the current drive and heating terms enter separately into the modified Rutherford equation, in the experiment the non-inductive current drive will always be accompanied by the effect of the heating. Detailed analyses of the relative importance of these two effects indicate that the effect of the heating is unjustly neglected in much of the current literature.
The studies of mode stabilization as described by the modified Rutherford equation will be supplemented by full 3D MHD modelling of NTMs. This will serve to benchmark the relevant terms in the modified Rutherford equation against a more complete physics model. Finally all modelling results are to be compared to experiments.
Feedback control loops
When studying feedback control strategies, simplified models capturing the essential physics of all elements involved is required. In particular, it is necessary to model each element of the entire control loop. Such control inspired models of the complete feedback loop in case of NTM stabilization or sawtooth period control are being developed. The figure sketches the main elements involved in a model of an NTM feedback control loop.
Figure 1: Feedback loop
The feedback loop in Figure 1 includes the plasma dynamics (the growth of the NTM as given by the modified Rutherford equation), the diagnostics and data acquisition (for example, ECE and Mirnov coils), the data analysis to extract mode location and phase, the actuators (ECRH launcher, and gyrotron power) and their control to achieve the required radial localization (through launcher steering) and deposition in the proper phase of the mode (through timing of the gyrotron power). Finally, the entire feedback loop is closed with the response of the plasma dynamics to these actions. A similar diagram can be made in case of sawtooth period control. Models for each of these components are being developed and implemented in a SIMULINK environment. The models will be used to test different data analysis methods and control strategies, in order to develop a robust controller.
MHD control
Experiments
The group is or has been active in the study of sawtooth and NTM control on a number of experimental devices. Within the EFDA JET Taskforce on MHD the control of sawteeth and NTM by localized ion cyclotron current drive (ICCD) has been investigated. In particular, it was shown that by shortening of the sawtooth period the triggering of NTM could be prevented or delayed to higher values of beta.
Over the past years the focus of experimental activities has been on the TEXTOR tokamak of the Forschungszentrum Jülich GmbH, in Germany. A detailed study of the effect of localized ECCD on sawteeth was performed. The results could be interpreted in terms of the critical shear model for the onset of the sawtooth crash. Also the effect of localized ECCD and ECRH on the growth of tearing modes was investigated in detail (see highlights below). The future work is aimed at towards the realization of tearing mode stabilization and sawtooth period control under full feedback. For this purpose, a novel in-transmission-line ECE diagnostic has been developed.
In the future, experimental work on the feedback control of MHD instabilities by ECRH will be focused on the AUG tokamak at the Max-Planck Institute for Plasma Physics in Garching, Germany. The design has been started of an in-line ECE diagnostic suitable for integration into the AUG ECRH system. Moreover, the chosen design should be scalable to the ITER ECRH system. Finally, implementation in the ITER ECRH feedback control system for NTMs is strived for. The latter in particular demands a CW capable solution for the frequency selective coupler that is to separate the low power ECE radiation from the high power gyrotron radiation in the transmission line.
In-transmision-line ECE
The actuator for the control of sawteeth (i.e. the achievement of a given sawtooth period) or NTMs (i.e. the suppression of an NTM) is the gyrotron power injected to generate localized electron cyclotron current drive (ECCD). It must be ensured that the ECCD power is deposited on the right location (i.e. close to the sawtooth inversion radius, or near the O-point of the magnetic island created by the NTM) to obtain the desired effect.
In order to achieve this under feedback appropriate control signals and actuator steering are necessary. Both the desired as well as the achieved ECCD localization are to be measured. A novel, in-transmission-line electron cyclotron emission (ECE) diagnostic looking along the sight-line of the high power gyrotron beam has been proposed. This way the diagnostics and actuator steering are combined in a single system. Through steering of the gyrotron-ECE beam, a magnetic island or sawtooth inversion radius only needs to be localized in the ECE spectrum at the gyrotron frequency (or just above or below) in order to deposit the gyrotron power exactly on top of it (or on its high or low field side). A proof-of-principle experiment on such an in-line ECE diagnostic and its application for feedback control of NTMs and sawteeth is underway on TEXTOR.
In 2007 the in-line ECE diagnostic has been built and commissioned. First experiments in late 2007 and early 2008 have proven the possibility to measure the ECE spectrum coming back into the gyrotron transmission line. Sufficient gyrotron stray power reduction has been achieved to measure the ECE even during extended periods (< 3 s) of high power gyrotron operation.
Figure 2: The figure illustrates the principle of in-transmission-line ECE measurements for feedback control of the ECRH power deposition.
Launcher control
A crucial element in the NTM or sawtooth control loops is the control of the mechanical launcher through which the steering of the ECRH/ECE wave beam is performed. For effective suppression of instabilities it is important that the alignment between the ECCD power deposition and the location of a NTM or sawtooth inversion radius is achieved within a limited period of time with a certain spatial accuracy. These positioning requirements demand for robust feedback control techniques which guarantee stability and system performance. Dedicated controllers have been designed for the TEXTOR ECRH launcher, on the basis of its dynamical properties as obtained from Frequency Response Function measurements. Physical system limitations as induced by friction, nonlinear dynamics, resonances, time delays etc. etc. are thereby identified. Frequency domain tuning procedures are used to derive controllers which account for these limitations and result in optimal performance in terms of operational stability, maximum bandwidth and positioning accuracy. Simulation models, which are representative of the TEXTOR ECRH launcher, are used in the controller design process. A copy of the TEXTOR ECRH launcher is available in a lab-environment for implementation, testing and optimalization of the derived controllers. Based on the expertise and insights gained from these experiments, comparable techniques will also be developed for the AUG ECRH launcher.
The set points for steering of the TEXTOR ECRH launcher will be generated from the inline ECE data. The algorithms for generation of such trajectories are under development.
Figure 3: The TEXTOR ECRH launcher
Highlights
Suppression of m=2, n=1 by localized ECRH in TEXTOR
Though TEXTOR plasmas generally do not reach the beta values required to trigger NTM, reproducible tearing modes can be triggered with the help of resonant magnetic perturbations (RMP) as generated by the dynamic ergodic divertor (DED). The latter is formed by a set of helical coils that can be powered to generate a dominantly m/n = 3/1, 6/2 or 12/4 RMP at the edge of the plasma. In its 3/1 configuration, the 2/1 side band provides the dominant RMP inside the plasma and can routinely trigger a m=2, n=1 tearing mode. These modes have formed the basis for an extensive study on the effects of ECRH and ECCD on their stability (Reference: E. Westerhof, et al. Nucl. Fusion 47 (2007) 85). It was shown that under TEXTOR conditions the mode suppression can almost entirely be attributed to the effect of localized heating inside the island, whereas the effect of the non-inductively drive current is negligible. 2D ECE-Imaging measurements have been used to diagnose the local temperature perturbation inside the island. The measured temperature perturbations and the observed changes in the growth rate of the magnetic island are consistent with modelling of these results on the basis of modified Rutherford equation (Reference: I.G.J. Classen, et al., Phys. Rev. Letters 98 (2007) 035001).
Figure 4: The figure shows the width of the m=2, n=1 magnetic island island as a function of the location of the ECRH power deposition. Efficient suppression of the mode is only obtained when the power deposition coincides almost exactly with the position of the island. This indicates that the suppression of the island is mainly caused by the power deposited inside the island.
First results from the TEXTOR in-transmission-line ECE diagnostic
On TEXTOR an in-transmission-line ECE diagnostic has been developed and commissioned (Reference: J.W. Oosterbeek, et al., submitted to Review of Scientific Instruments (2008)). The separation of the high power gyrotron beam and the low power backward propagation ECE waves is achieved by means of a resonant dielectric plate. The resonant plate has a maximum in transmission of 95% at the gyrotron frequency (140 GHz) and maxima in reflection of about 35% at the chosen ECE frequencies (132.5, 135.5, 138.5, 141.5, 144.5, and 147.5 GHz). At the same time the reflection at the gyrotron frequency has a minimum of a bout -25 dB, which serves to reduce the reflection of gyrotron stray radiation into the ECE beam line. The reflected ECE beam is then coupled into a radiometer horn by means of a series of flat mirrors and a final focusing mirror. The figures show the design of this quasi-optical system and a picture of the final system as installed on TEXTOR.
Figure 5: Inside view of the inline ECE diagnostic showing beam path
Extensive tests have been performed, which have shown that the system performs according to the theoretical expectations. In particular, the gyrotron stray radiation at the radiometer horn is successfully reduced to levels below 1 W, which guarantees the safe operation of the ECE radiometer. A further 80 dB notch-filter ensures that the gyrotron stray radiation entering the radiometer is well below the level of the ECE radiation to be measured. Measurements of the ECE spectrum have been obtained during high power ECRH pulses demonstrating the possibility of in-line ECE measurements.
Figure 6: The figures show the results of in-line ECE measurements for TEXTOR discharge #106913, with a 2 s, 400 kW ECRH pulse. Before ECRH clear sawteeth are observed and sawtooth inversion is seen between the 132.5 and 135.5 GHz channels. As the 140 GHz resonace is on the high field side of the tokamak, this indicates that the 140 GHz ECRH power deposition will occur well outside the sawtooth inversion. After switch-on of ECRH the sawteeth disappear as expected for heating outside the inversion radius.
Collaborations
- Institute for Energy Research 4 – Plasma Physics, Forschungszentrum Jülich GmbH, Jülich, Germany: TEXTOR-team
- Systems and Control Engineering, TU/e, Eindhoven, Netherlands: P. Nuij, M. Steinbuch, E.M.M. Demarteau
- TNO, Delft, Netherlands: N. Doelman, G. Witvoet
- Max-Planck Institute for Plasma Physics, Garching, Germany: AUG-, and ECRH-teams
- Istituto di Fisica del Plasma, CNR Milano, Milano, Italy: S. Cirant, S. Nowak
- DRFC, CEA-Cadarche, St. Paul-lez-Durance, France: G.T.A. Huysmans
- EFDA JET Taskforce on MHD
- EFDA Topical Group on MHD
- EFDA Taskforce on Integrated Tokamak Modelling
