de Marco Baar

Demonstration of sawtooth period locking with power modulation in TCV plasmas

Corroborating evidence is presented that the sawtooth period can follow the modulation frequency of an externally applied high power electron cyclotron wave source. Precise, fast and robust open loop control of the sawtooth period with a continuously changing reference period has been achieved. This period locking is not associated with the crash, but with the phase evolution of the inter-crash dynamics. This opens new possibilities of open loop control for physics studies and maybe for reactor performance control.

Optical boundary reconstruction of tokamak plasmas for feedback control of plasma position and shape

A new diagnostic is developed to reconstruct the plasma boundary using visible wavelength images. Exploiting the plasmas edge localized and toroidally symmetric emission profile, a new coordinate transform is presented to reconstruct the plasma boundary from a poloidal view image. The plasma boundary reconstruction is implemented in MATLAB and applied to camera images of Mega-Ampere Spherical Tokamak discharges. The optically reconstructed plasma boundaries are compared to magnetic reconstructions from the offline reconstruction code EFIT, showing very good qualitative and quantitative agreement. Average errors are within 2 cm and correlation is high. In the current software implementation, plasma boundary reconstruction from a single image takes 3 ms. The applicability and system requirements of the new optical boundary reconstruction, called OFIT, for use in both feedback control of plasma position and shape and in offline reconstruction tools are discussed.

Feedback control of the sawtooth period through real time control of the ion cyclotron resonance frequency

Modification of the sawtooth period through ion cyclotron resonance frequency (ICRF) heating and current drive has been demonstrated in a number of experiments. The effect has been seen to depend critically on the location of the ICRF absorption region with respect to the q = 1 flux surface. Consequently, for ICRF to be a viable tool for sawtooth control, one must be able to control the ICRF absorption location in real time so as to follow variations in the location of the q = 1 surface. To achieve this, the JET ICRF system has been modified to allow the JET real time central controller to control the frequency of the ICRF generators. An algorithm for real time determination of the sawtooth period has been developed and a closed loop controller, which modifies the frequency of the ICRF generators to bring the measured sawtooth period to the desired reference value, has been implemented. This paper shows the first experimental demonstration of closed loop sawtooth period control by real time variation of the ICRF wave frequency.

Systematic design of a sawtooth period feedback controller using a Kadomtsev-Porcelli sawtooth model

A systematic methodology for structured design of feedback controllers for the sawtooth period is presented, based on dedicated identification of the sawtooth dynamics. Therefore, a combined Kadomtsev-Porcelli model of a sawtoothing plasma actuated by an electron cyclotron current drive system has been set-up. This is used to derive the linearized input-output relations (transfer functions) from the varying deposition location of the electron cyclotron waves (ECW) to the sawtooth period. These transfer functions are derived around a large collection of operating points. Assessment of these control-relevant transfer functions shows that a sawtooth period controller requires an integral (I) action to guarantee closed-loop stability with zero steady-state error. Additional proportional-integral (PI) action can be applied to further increase the closed-loop performance. The parameters of both the I and PII controllers have been optimized in terms of stability, performance and robustness. Moreover, the effect of the mechanical ECW launcher on the closed-loop performance is studied for realistic cases. It is shown that the launcher dynamics seriously affects the achievable closed-loop performance in present-day experiments.

Numerical demonstration of injection locking of the sawtooth period by means of modulated EC current drive

In this paper the sawtooth period behaviour under periodic forcing by electron cyclotron waves is investigated. The deposition location is kept constant while the gyrotron power is modulated with a certain period and duty cycle. Extensive simulations on a representative dynamic sawtooth model show that when this modulation is properly chosen, the sawtooth period quickly synchronizes to the same period and remains locked at this value. It is shown that the range of modulation periods and duty cycles over which sawtooth period locking occurs, depends on the deposition location, but is particularly large for depositions near the q = 1 surface. The simulation results reveal a novel approach to control the sawtooth period in open loop, based on injection locking, which is a well-known technique to control limit cycles of non-linear dynamic oscillators. The locking and convergence results are therefore used in a simple open-loop locking controller design, with which accurate sawtooth period tracking to any desired value is indeed demonstrated. Injection locking appears to let the sawtooth period converge to the modulation period quickly, partly because it does not suffer from slow EC mirror launcher dynamics. Moreover, simulations show that the method has a relatively large robustness against general uncertainties and disturbances. Hence, injection locking is expected to outperform conventional sawtooth control methods using a variable deposition location and constant gyrotron power. Finally, the recent result with sawtooth pacing is shown to be a special case of the general locking effect.

Density Perturbation Studies by Means of Pulsed Radar Reflectometry

A four‐channel pulsed radar reflectometry system has been developed for the Rijnhuizen Tokamak Project. The system combines a high spatial and temporal resolution with limited access demands to the tokamak plasma. Steady‐state density profiles as measured with the pulsed radar system match very well to the profiles as measured by Thomson scattering and by interferometry. As will be illustrated in this paper, the diagnostic is able to follow fast phenomena as pellet injection and plasma disruptions as well as MHD oscillations.

Real-time optical plasma boundary reconstruction for plasma position control at the TCV Tokamak

A dual, high speed, real-time visible light camera setup was installed on the TCV tokamak to reconstruct optically and in real-time the plasma boundary shape. Localized light emission from the plasma boundary in tangential view, broadband visible images results in clearly resolved boundary edge-features. These projected features are detected in real-time and transformed to the poloidal plane to obtain a measurement of the plasma boundary. Plasma boundary reconstructions of diverted plasma discharges are presented, showing agreement of within 1 cm compared with magnetic equilibrium reconstruction. The resulting real-time plasma shape measurement is applied in a feedback control loop for the plasma position, demonstrating effective stabilization and tracking of the plasma vertical position.

Sawtooth period control strategies and designs for improved performance

The sawtooth instability is associated with the triggering of neo-classical tearing modes, core fuelling, α-confinement and the exhaust of thermal helium. Sawtooth control is therefore important for optimal reactor performance in ELMy H-modes. Control schemes for the sawtooth period have been published in the literature, but the systematic design of high-performance controllers (yielding accurate and fast convergent responses) has not been addressed. In this work, three control strategies for high-performance sawtooth control are presented using electron cyclotron current drive (ECCD). Both degrees of freedom of the ECCD actuator will be explored and combined with advanced controller designs. First, the ECCD deposition location is used as a control variable, for which a gain-scheduled feedback controller and static feedforward control is derived. Second, the use of the driven current as a control variable is explored, and a simple controller is designed based on the identified dynamics. In the third approach both control variables are joined in an overall controller design, which enables the combination of high-performance control of the sawtooth period and control of the gyrotron power. Time-domain simulations with a combined Kadomtsev-Porcelli sawtooth model show that each strategy obtains a better closed-loop performance than standard linear feedback techniques on merely the deposition location.

Explicit approximations to estimate the perturbative diffusivity in the presence of convectivity and damping. III. Cylindrical approximations for heat waves traveling inwards

In this paper, a number of new explicit approximations are introduced to estimate the perturbative diffusivity (χ), convectivity (V), and damping (τ) in cylindrical geometry. For this purpose, the harmonic components of heat waves induced by localized deposition of modulated power are used. The approximations are based on the heat equation in cylindrical geometry using the symmetry (Neumann) boundary condition at the plasma center. This means that the approximations derived here should be used only to estimate transport coefficients between the plasma center and the off-axis perturbative source. If the effect of cylindrical geometry is small, it is also possible to use semi-infinite domain approximations presented in Part I and Part II of this series. A number of new approximations are derived in this part, Part III, based upon continued fractions of the modified Bessel function of the first kind and the confluent hypergeometric function of the first kind. These approximations together with the approximations based on semi-infinite domains are compared for heat waves traveling towards the center. The relative error for the different derived approximations is presented for different values of the frequency, transport coefficients, and dimensionless radius. Moreover, it is shown how combinations of different explicit formulas can be used to estimate the transport coefficients over a large parameter range for cases without convection and damping, cases with damping only, and cases with convection and damping. The relative error between the approximation and its underlying model is below 2% for the case, where only diffusivity and damping are considered. If also convectivity is considered, the diffusivity can be estimated well in a large region, but there is also a large region in which no suitable approximation is found. This paper is the third part (Part III) of a series of three papers. In Part I, the semi-infinite slab approximations have been treated. In Part II, cylindrical approximations are treated for heat waves traveling towards the plasma edge assuming a semi-infinite domain.

Nonlinear control for stabilization of small neoclassical tearing modes in ITER

In this paper, the feasibility of feedback stabilization of neoclassical tearing modes at small island sizes, corresponding to otherwise unstable island sizes in ITER scenario 2, is demonstrated. The islands are stabilized by application of electron cyclotron resonance heating and current drive in a regime where the application of current drive in open loop normally results in a complete suppression of the island. By applying current drive in closed loop with feedback of real-time measurements of the island width, complete suppression is avoided and the island is stabilized at a specific reduced size. In contrast to complete suppression, control of islands at a specific size will allow the manipulation of a plasmas current density profile in hybrid scenarios. Three conceptual (non-)linear feedback controllers with varying complexity, performance, robustness and required model knowledge are introduced. Simulations show the theoretical feasibility of small island stabilization at a specific reduced width. The controllers are applied to the generalized Rutherford equation, which governs the island evolution subject to electron cyclotron current drive. A strategy for the gradual implementation of the controllers is suggested. Stabilization of small islands by feedback control will allow the use of system identification to extend the model knowledge on the evolution of small islands, and in addition will extend the operational regime.