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We propose an efficient approximation to the nonlinear phase diversity (PD) method for wavefront reconstruction and correction from intensity measurements with potential of being used in real-time applications. The new iterative linear phase diversity (ILPD) method assumes that the residual phase aberration is small and makes use of a first-order Taylor expansion of the point spread function (PSF), which allows for arbitrary (large) diversities in order to optimize the phase retrieval. For static disturbances, at each step, the residual phase aberration is estimated based on one defocused image by solving a linear least squares problem, and compensated for with a deformable mirror. Due to the fact that the linear approximation does not have to be updated with each correction step, the computational complexity of the method is reduced to that of a matrix-vector multiplication. The convergence of the ILPD correction steps has been investigated and numerically verified. The comparative study that we make demonstrates the improved performance in computational time with no decrease in accuracy with respect to existing methods that also linearize the PSF.

AbstractElectron cyclotron resonance heating (ECRH) systems for next-step large fusion devices operate in continuous wave power in the multimegawatt range. The unique feature of narrow and well-localized power deposition assigns a key role to ECRH for different tasks, such as plasma start-up, electron heating, current drive, magnetohydrodynamic (MHD) control and profile shaping. The integration of high-power microwave diplexers in the transmission lines will improve the flexibility and efficiency while simultaneously reducing the complexity of large ECRH systems. They can serve as power or beam combiners, as slow and fast directional switches to toggle the power from continuously operating gyrotrons between two launchers, and as discriminators of low-power electron cyclotron emission (ECE) signals from high-power ECRH using a common transmission line and antenna. Among various design options a resonant diplexer with a narrow resonance was selected for application at ASDEX Upgrade. The design is driven by the specific physics requirements for MHD control experiments and possible use for line-of-sight ECE. The compact, waveguide-compatible design features a feedback-controlled mirror drive for tracking of the resonator to the gyrotron frequency. High-power, long-pulse tests were performed with the 140-GHz ECRH system for the stellarator W7-X. Results on the transmission characteristics, power combination, and stationary and controlled distribution of the input power to two outputs are presented. The qualification for in-line ECE was investigated.

AbstractNeoclassical tearing modes (NTMs) deteriorate high-pressure tokamak plasma confinement and can be suppressed by electron cyclotron current drive (ECCD). In order to obtain efficient suppression, the ECCD power needs to be deposited at the center of an NTM magnetic island. To enhance efficiency, this power also needs to be synchronized in phase with the rotation of the island. The problem is that of real-time detection and precise localization of the island(s) in order to provide the feedback signal required to control the ECCD power deposition area with an accuracy of 1 to 2 cm. Existing schemes based on mode location, equilibrium reconstruction, and plasma profile measurements are limited in positional and temporal accuracy and moreover will become very complex when applied to ITER. To overcome these limitations, it is proposed to provide the feedback signal from electron cyclotron emission (ECE) measurements taken along the identical line of sight as traced by the incident ECCD millimeter-wave beam but in reverse direction. Experiments on TEXTOR have demonstrated a proof of principle. These measurements motivate the further development and the implementation of such an ECCD-aligned ECE system for NTM control in larger fusion machines. Possible implementation of such a system on ASDEX-Upgrade, based on waveguides equipped with a fast directional switch, is presented in this paper. Possible further development for ITER is also discussed.

In this article wave field extrapolation in bounded and unbounded homogeneous media is studied. A generally applicable description for any type of homogeneous medium with arbitrary boundary conditions is developed. The extrapolation theory is based on the Kirchhoff integral in the frequency domain. In several steps this Kirchhoff integral is transformed into a straightforward extrapolation expression. First, Green’s function is expanded in an infinite series of eigenfunctions belonging to the lateral directions. Second, the wave field extrapolation operation is diagonalized by choosing a base of eigenfunctions for the Hilbert function space. Further facilitation of the extrapolation problem for both bounded and unbounded homogeneous media is achieved by employing one‐way wave equations. These one‐way wave equations decompose a wave field into a downstream and an upstream traveling wave field. The final result is a comprehensive description of both forward and inverse wave field extrapolation, which can easily be applied to quite complicated extrapolation problems in any type of homogeneous medium.