L. Delgado-Aparicio

On the formation and stability of long-lived impurity-ion snakes in Alcator C-Mod

Long-lived (1, 1) ?snake? modes were discovered nearly three decades ago, but basic questions regarding their formation, stability, and superb particle confinement?shown by surviving tens to hundreds of sawtooth cycles?have remained unanswered. High-resolution spectroscopic imaging diagnostics permit studies of heavy-impurity-ion snakes with unprecedented temporal and spatial resolution, making it possible to positively identify the SXR signals with specific ion charge states and to infer, for the first time, the perturbed impurity density, Zeff, and resistivity at the centre of these long-lived helical modes. The results show a new scenario for the formation of heavy-impurity-ion snakes, which can begin as a broad 1/1 kink asymmetry of the central impurity-ion density, that grows and undergoes a seamless transition to a large crescent-shaped helical island-like structure inside q?<?1, with a regularly sawtoothing core. This type of formation departs strongly from the nonlinear island model based on a modified Rutherford equation proposed originally to describe the pellet-induced snakes and expanded further to account for the impurity effects (e.g. and ). These new high-resolution observations show details of their evolution and the accompanying sawtooth oscillations that suggest important differences between the density and temperature dynamics, ruling out a purely pressure-driven process. Instead, many features arise naturally from nonlinear interactions in a 3D MHD model that separately evolves the plasma density and temperature.

Physics of radiation-driven islands near the tokamak density limit

In previous work (Gates and Delgado-Aparicio 2012 Phys. Rev. Lett. 108 165004), the onset criterion for radiation-driven islands (Rebut et al 1985 Proc. 10th Int. Conf. on Plasma Physics and Controlled Nuclear Fusion Research 1984 (London, UK, 1984) vol 2 (Vienna: IAEA) p 197) in combination with a simple cylindrical model of tokamak current channel behaviour was shown to be consistent with the empirical scaling of the tokamak density limit (Greenwald et al 1988 Nucl. Fusion 28 2199). A number of the unexplained phenomena at the density limit are consistent with this novel physics mechanism. In this work, a more formal theoretical underpinning, consistent with cylindrical tearing mode theory, is developed for the onset criteria of these modes. The appropriate derivation of the radiation-driven addition to the modified Rutherford equation (MRE) is discussed. Additionally, the ordering of the terms in the MRE is examined in a regime near the density limit. It is hoped that, given the apparent success of this simple model in explaining the observed global scalings, it will lead to a more comprehensive analysis of the possibility that radiation-driven islands are the physics mechanism responsible for the density limit. In particular, with modern diagnostic capabilities detailed measurements of current densities, electron densities and impurity concentrations at rational surfaces should be possible, enabling verification of the concepts described above.

A predictive model for the tokamak density limit

We reproduce the Greenwald density limit, in all tokamak experiments by using a phenomenologically correct model with parameters in the range of experiments. A simple model of equilibrium evolution and local power balance inside the island has been implemented to calculate the radiation-driven thermo-resistive tearing mode growth and explain the density limit. Strong destabilization of the tearing mode due to an imbalance of local Ohmic heating and radiative cooling in the island predicts the density limit within a few percent. Furthermore, we found the density limit and it is a local edge limit and weakly dependent on impurity densities. Our results are robust to a substantial variation in model parameters within the range of experiments.

A new objective for EUV lithography, EUV microscopy, and 2D x-ray imaging

This paper describes a new objective for EUV lithography, EUV-microscopy, and 2D x-ray imaging, which similar to the well-known Schwarzschild objective and which consists of two concentric, convex and concave, spherical reflectors. Its essentially new feature is that it satisfies the Bragg condition for the wavelength of interest at every point on the surfaces of both reflectors. The reflectors would be spherical multi-layer structures with a uniform 2d-spacing, in the case of EUV radiation, and spherically bent crystals, in the case of x-rays. Thanks to this new feature, it is possible to obtain two-dimensional EUV or x-ray images from a large area, at once. The advantage for EUV lithography would be that an entire mask could be imaged onto a wafer, at once, and that a scanning of the mask by a narrow beam of EUV radiation – which is being used with present systems because the Bragg condition can only locally be satisfied - would no longer be necessary.