Search

Magnetic reconnection in W7-X is studied by means of global numerical simulations in a series of models of increasing complexity. The magnetic geometry ranges from that of a cylinder to the full three-dimensional field of W7-X, and the equations solved range from ideal magnetohydrodynamics (MHD) to gyrokinetics. We simulate plasmas from the first operation phase with electron cyclotron current drive (ECCD). These are characterized by an equilibrium magnetic field featuring an ECCD-distorted ‘humped’ profile of the rotational transformι, withι= 1 in two radial locations. Such plasmas generally show sawtooth activity, hence motivating the present study. We pay particular attention to the role of equilibrium current density gradients in the destabilization of reconnecting modes. When the equilibrium temperature and density gradients are artificially suppressed (to eliminate the pressure gradient drive), the perturbed electrostatic potential is radially localized between the locations at whichι= 1. This is shown with a purely collisionless gyrokinetic model, in cylindrical geometry. In the real toroidal geometry of W7-X, for a non-ideal MHD model including a uniform resistivity, electron inertia and (numerical) viscosity, the same qualitative behaviour is observed. In particular, even if a resonant (m,n) = (1, −1) perturbation is initialized, the most unstable mode is the (m,n) = (−4, 4), wheremandnare the poloidal and toroidal mode numbers, respectively. Other modes are destabilized due to geometric coupling. The growth rate of this instability scales asη1/3, whereηis the plasma resistivity, thus suggesting that ECCD drives ideal MHD stable W7-X plasmas towards non-ideal marginality. An ideal magnetohydrodynamic analysis confirms the result. A fluid-kinetic hybrid version of theEUTERPEcode shows that gyrokinetic ions have a stabilizing effect on these modes. For W7-X relevant collisionalities, the growth rate scales linearly with the electron skin depth,de. Implications of our results for sawtoothing W7-X operation are discussed.

Neutral beam injection (NBI) system has been proved to affect sawtooth activities through both producing energetic particles and supplying torque applied to the plasma. The impact of NBI on sawtooth crashes has been studied in the EAST tokamak, which is equipped with co- and counter NBIs. Statistical analysis shows that both strong co- and counter-NBI yield stronger sawtooth activities than cases when heating power is weak. A minimum sawtooth period is observed at a counter-NBI power of 0.2 MW. This is linked to zero-plasma rotation and a non-rotating precursor mode of the sawtooth instability. This indicates that the sawtooth instability is stabilized by plasma rotation as previously suggested. The fast-ion content differs between co- and counter-NBI, so energetic particles might additionally contribute to the sawtooth activities.

The effect of sawteeth on impurity dynamics is studied with the XTOR-2F code. Non-linear full 3D MHD simulations including appropriate fluid equations for heavy impurities show that the presence of regular sawtooth crashes affects the impurity behaviour. A spatial non-uniformity of 5% in post-crash impurity density profiles persists due to 2D structures of impurity density which appear during sawtooth crashes. They are shown to be mainly driven by the E × B velocity, and are responsible for the sudden impurity transport in the core plasmas.

The 110 GHz and the new 140 GHz gyrotron systems for electron cyclotron resonance heating (ECRH) and ECCD on TEXTOR are described and results of ECRH experiments with the 110 GHz system are reported. Central ECRH on Ohmic plasmas shows the presence of an internal electron transport barrier near q = 1. This is confirmed by modulated ECRH experiments. A central barrier is also indicated by ECRH in radiatively improved (RI) mode discharges and up to two barriers are seen with ECRH during the current ramp phase. ECRH control of sawteeth is reported for both Ohmic and RI mode target plasmas.

A dynamical analysis applied to a reduced resistive magnetohydrodynamics model is shown to explain the chronology of the nonlinear destabilization of modes observed in tokamak sawteeth. A special emphasis is put on the nonlinear self-consistent perturbation of the axisymmetric m = n = 0 mode that manifests through the q-profile evolution. For the very low fusion-relevant resistivity values, the q-profile is shown to remain almost unchanged on the early nonlinear timescale within the central tokamak region, which supports a partial reconnection scenario. Within the resistive region, indications for a local flattening or even a local reversed-shear of the q-profile are given. The impact of this ingredient in the occurrence of the sawtooth crash is discussed. Fil: Firpo, Marie C.. Ecole Polytechnique; Francia. Centre National de la Recherche Scientifique; Francia Fil: Ettoumi, W.. Ecole Polytechnique; Francia. Centre National de la Recherche Scientifique; Francia Fil: Farengo, R.. Comision Nacional de Energia Atomica. Gerencia del Area de Investigaciones y Aplicaciones no Nucleares. Gerencia de Fisica (CAB); Argentina. Comisión Nacional de Energía Atómica. Gerencia del Area de Energía Nuclear. Instituto Balseiro; Argentina Fil: Ferrari, Hugo Emilio. Comision Nacional de Energia Atomica. Gerencia del Area de Investigaciones y Aplicaciones no Nucleares. Gerencia de Fisica (CAB); Argentina. Comisión Nacional de Energía Atómica. Gerencia del Area de Energía Nuclear. Instituto Balseiro; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina Fil: Garcia Martinez, Pablo Luis. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina Fil: Lifschitz, A. F.. Ecole Polytechnique; Francia. Centre National de la Recherche Scientifique; Francia

The former Berlin electron-beam ion-trap was moved to Greifswald. One of the first aims after the reinstallation was the continuation of experiments using mixed ensembles of low- and high-Z ions for further studies of the previously reported sawtooth-like oscillations of the trap plasma. First results of these studies for xenon/argon mixtures are presented.

Resistive magneto-hydrodynamic instabilities are expected to limit the performance of nuclear fusion reactors. Prime examples are the sawtooth instability and the neoclassical tearing modes. The sawtooth instability will affect the refueling of the plasma core and the fast particle concentration. In reactor relevant conditions, the sawtooth can also trigger secondary instabilities. These are the neo-classical tearing modes, which can deteriorate the plasma performance or even disrupt the discharge. These modes (sawteeth and tearing modes) appear at specific locations in the tokamak plasma, associated with the distribution of the current density and the toroidal magnetic field. Localized current drive from electron cyclotron waves is foreseen as a possible actuator for the width of the tearing modes and the period of the sawteeth. Magnetic pick-up coils, electron cyclotron emission (ECE) and soft X-ray emission are the most likely sensors. A system approach for real-time detection, localisation and control of resistive magneto-hydrodynamic modes in tokamaks is presented. The system combines an ECE diagnostic for sensing of the instabilities in the same sight-line with a steerable Electron Cyclotron Resonant Heating and Current Drive (ECRH/CD) antenna. A model for the sawtooth is used to derive the linearized input-output relations (transfer functions) from the varying deposition location of high power Electron Cyclotron waves to the sawtooth period. The transfer functions are derived around a large collection of operating points. Proportional-integral-integral (PII) action can be applied to achieve fast and perfect tracking, while satisfying robustness constraints. The launcher dynamics seriously affects the closed loop performance in present-day experiments. Special emphasis is put on the issue of real-time sawtooth period detection. An algorithm based on time-scale wavelet theory and edge detection for accurate real-time sawtooth period estimation has been developed. The period is estimated by detecting subsequent crashes. The realized accuracy of the detection algorithm is well below the uncertainty of the crash period for most crashes. Multi-resolution analysis enables distinction between different sizes of sawtooth crashes due to the different sizes of wavelets (scales), resulting in an algorithm, which is robust and accurate. A methodology for fast detection of q m/n 2/1 tearing modes and retrieval of their location, rotation frequency and phase is presented. Set-points to establish alignment of the ECRH/CD deposition location with the centre of the tearing mode are generated in real-time and forwarded in closed-loop to the steerable launcher and as a modulation pulse train to the gyrotron. © 2011 IEEE.

In nuclear fusion the sawtooth instability is an important plasma phenomenon, having both positive and negative effects on the tokamak plasma. Control of its period is essential in future nuclear fusion reactors. This paper presents a control oriented model of the sawtooth instability, with current drive as input and sawtooth period as output, and validates it with a more extended model and experimental data. This model is numerically implemented and combined with PI-controllers in a feedback loop. Simulations show that closed loop control of the system to a desired sawtooth period is indeed possible, even when time delay is added to the feedback loop. © 2010 AACC.

Tokamak plasmas in nuclear fusion are subject to various instabilities. A clear example is the sawtooth instability, which has both positive and negative effects on the plasma. To optimize between these effects control of the sawtooth period is necessary. This paper presents a simple control oriented model, from current drive (input) to sawtooth period (output), which can mimic the most relevant aspects of the sawtooth instability. It also shows some simulation results, including a static input-output map and a comparison with experimental data.

We use a semi analytical model to investigate the mechanisms underlying the saw tooth instability dynamics in storage rings. We discuss its interplay with other effects, such as the multiple Touschek scattering and derive an upper limit for the power emission associated with such an instability.

Stability of the steady-state bunch distribution described by the Haissinski solution [J. Haissinski, Nuovo Cimento {bold 18B}, 72 (1973)] is studied above the threshold of microwave instability. It is shown that instability may lead to a new self-consistent state corresponding to particles trapped in a separatrix of an unstable mode. The free energies of the two solutions are compared. The relaxation oscillations between the new and Haissinski solutions are possible and may be related to the sawtooth instability observed recently in the experiments [P. Krejcik {ital et} {ital al}., (unpublished)]. {copyright} {ital 1996 The American Physical Society.}

The cycling dynamics of the internal kink mode, which drives sawtooth oscillations in tokamak plasmas, is studied using the three dimensional, non-linear magnetohydrodynamic (MHD) code XTOR-2F [H. Lütjens and J.-F. Luciani, J. Comput. Phys. 229, 8130 (2010)]. It is found that sawtooth cycling, which is characterized by quiescent ramps and fast crashes in the experiment, can be recovered in two-fluid MHD provided that a criterion of diamagnetic stabilization is fulfilled. The simulation results indicate that diamagnetic effects alone may be sufficient to drive sawteeth with complete magnetic reconnection in high temperature Ohmic plasmas.

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. (C) 2011 American Institute of Physics.

In the standard scenario of tokamak plasma operation, sawtooth crashes are the main perturbations that can trigger performance-degrading, and potentially disruption-generating, neoclassical tearing modes. This Letter demonstrates sawtooth pacing by real-time control of the auxiliary power. It is shown that the sawtooth crash takes place in a reproducible manner shortly after the removal of that power, and this can be used to precisely prescribe, i.e., pace, the individual sawteeth. In combination with preemptive stabilization of the neoclassical tearing modes, sawtooth pacing provides a new sawtooth control paradigm for improved performance in burning plasmas.

The design of the ITER electron cyclotron launchers recently reached the preliminary design level -the last major step before design finalization. The ITER ECH system contains 24 installed gyrotrons providing a maximum ECH injected power of 20 MW through transmission lines towards the tokamak. There are two EC launcher types both using a front steering mirror; one Equatorial Launcher for plasma heating and four Upper Launchers (UL) for plasma mode stabilization (neoclassical tearing modes and the sawtooth instability). A wide steering angle of the ULs allows to focus on magnetic islands which are expected on the rational magnetic flux surfaces q = 1 (sawtooth instability), q = 3/2 and q = 2 (NTMs).

In this article an algorithm for optimized realtime sensing of crashes for control purposes is presented. The algorithm is based on time-scale wavelet theory and edge-detection. It is designed for the control of the sawtooth instability, a relaxation oscillator, in fusion plasmas. However, in principle, it can be applied to any periodic crash, measured with any temporally resolved data. It is argued that the detection of crashes has considerably less delay and detects crashes with higher temporal accuracy than other linear methods; this holds especially for very noisy measurements.

External n = 1 magnetic fields are applied in RFX-mod and DIII-D low safety factor Tokamak plasmas to investigate their interaction with the internal MHD dynamics and in particular with the sawtooth instability. In these experiments the applied magnetic fields cause a reduction of both the sawtooth amplitude and period, leading to an overall stabilizing effect on the oscillations. In RFX-mod sawteeth eventually disappear and are replaced by a stationary m = 1, n = 1 helical equilibrium without an increase in disruptivity. However toroidal rotation is significantly reduced in these plasmas, thus it is likely that the sawtooth mitigation in these experiments is due to the combination of the helically deformed core and the reduced rotation. The former effect is qualitatively well reproduced by nonlinear MHD simulations performed with the PIXIE3D code. The results obtained in these RFX-mod experiments motivated similar ones in DIII-D L-mode diverted Tokamak plasmas at low q 95. These experiments succeeded in reproducing the sawtooth mitigation with the approach developed in RFX-mod. In DIII-D this effect is correlated with a clear increase of the n = 1 plasma response, that indicates an enhancement of the coupling to the marginally stable n = 1 external kink, as simulations with the linear MHD code IPEC suggest. A significant rotation braking in the plasma core is also observed in DIII-D. Numerical calculations of the neoclassical toroidal viscosity (NTV) carried out with PENT identify this torque as a possible contributor for this effect.