Matthew Lilley

Energetic Particle Instabilities in Fusion Plasmas

Remarkable progress has been made in diagnosing energetic particle instabilities on present-day machines and in establishing a theoretical framework for describing them. This overview describes the much improved diagnostics of Alfven instabilities and modelling tools developed world-wide, and discusses progress in interpreting the observed phenomena. A multi-machine comparison is presented giving information on the performance of both diagnostics and modelling tools for different plasma conditions outlining expectations for ITER based on our present knowledge.

Effect of dynamical friction on nonlinear energetic particle modes

A fully nonlinear model is developed for the bump-on-tail instability including the effects of dynamical friction (drag) and velocity space diffusion on the energetic particles driving the wave. The results show that drag provides a destabilizing effect on the nonlinear evolution of waves. Specifically, in the early nonlinear phase of the instability, the drag facilitates the explosive scenario of the wave evolution, leading to the creation of phase space holes and clumps that move away from the original eigenfrequency. Later in time, the electric field associated with a hole is found to be enhanced by the drag, whereas for a clump it is reduced. This leads to an asymmetry of the frequency evolution between holes and clumps. The combined effect of drag and diffusion produces a diverse range of nonlinear behaviors including hooked frequency chirping, undulating, and steady state regimes. An analytical model is presented, which explains the aforementioned diversity. A continuous production of hole-clump pairs in the absence of collisions is also observed.

Recent experiments on Alfvén eigenmodes in MAST

The developments of advanced tokamak scenarios as well as the employment of a new neutral beam injection (NBI) source with higher power and beam energy up to ≈65keV have significantly broadened the frequency range and the variety of Alfv´ en eigenmodes (AEs) excited by the super-Alfv´ enic NBI on the spherical tokamak MAST. During recent experiments on MAST, several distinct classes of beam-driven AEs have been identified, with different modes being most unstable in different MAST scenarios. In MAST discharges with elevated monotonic q(r)-profiles and NBI power 3MW, chirping modes starting in the frequency range 150kHz decreased in frequency down to ≈20kHz as q(0) decreased and then smoothly transformed to long-living modes with a weakly-varying frequency and a n = 1 kink-mode structure. The bolometer data suggest that the long-living modes can be responsible for fast ion losses on MAST, while the charge-exchange data show that a coupling between these modes and other low-frequency modes can cause a collapse of toroidal plasma rotation with a subsequent disruption. In MAST

Adiabatic description of long range frequency sweeping

A theoretical framework is developed to describe long range frequency sweeping events in the 1D electrostatic bump-on-tail model with fast particle sources and collisions. The model includes three collision operators (Krook, drag (dynamical friction) and velocity space diffusion), and allows for a general shape of the fast particle distribution function. The behaviour of phase space holes and clumps is analysed in the absence of diffusion, and the effect of particle trapping due to separatrix expansion is discussed. With a fast particle distribution function whose slope decays above the resonant phase velocity, hooked frequency sweeping is found for holes in the presence of drag collisions alone.

Doppler-shifted cyclotron resonance of fast ions with circularly polarized shear Alfvén waves

The Doppler-shifted cyclotron resonance between fast ions and shear Alfven waves (SAWs) has been experimentally investigated with a test-particle fast-ion (Li+) beam launched in the helium plasma of the Large Plasma Device [Gekelman et al., Rev. Sci. Instrum. 62, 2875 (1991)]. Left- or right-hand circularly polarized SAWs are launched by an antenna with four current channels. A collimated fast-ion energy analyzer characterizes the resonance by measuring the nonclassical spreading of the averaged beam signal. Left-hand circularly polarized SAWs resonate with the fast ions but right-hand circularly polarized SAWs do not. The measured fast-ion profiles are compared with simulations by a Monte Carlo Lorentz code that uses the measured wave field data.

Compressional Alfvén and ion-ion hybrid modes in the deuterium-tritium plasma of a spherical tokamak power plant

A discrete spectrum of compressional Alfven eigenmodes and ion-ion hybrid eigenmodes is found to exist above the tritium ion cyclotron frequency in the deuterium-tritium (D-T) plasma of a spherical tokamak power plant (STPP) [H. R. Wilson et al., 19th IAEA Fusion Energy Conference (IAEA, Lyon, France, 2002), No. FT/1-4]. An equilibrium magnetic well formed in a STPP, as a result of plasma diamagnetism, causes all externally launched electromagnetic waves to propagate from the side of high total magnetic field, and it is this well that forms discrete spectra in the ion cyclotron resonance heating frequency range near the plasma core. The eigenmodes, as well as the position of the mode conversion layers, are obtained in a one-dimensional magnetic field geometry [S. C. Cowley et al., Phys. Fluids B 3, 2066 (1991)], relevant for the STPP, which will necessarily operate at high β. The possibility of using the discrete spectrum probed with an external antenna, or driven by energetic ions, for measuring the D-T ...

Kinetic theory of phase space plateaux in a non-thermal energetic particle distribution

The transformation of kinetically unstable plasma eigenmodes into hole-clump pairs with temporally evolving carrier frequencies was recently attributed to the emergence of an intermediate stage in the mode evolution cycle, that of an unmodulated plateau in the phase space distribution of fast particles. The role of the plateau as the hole-clump breeding ground is further substantiated in this article via consideration of its linear and nonlinear stability in the presence of fast particle collisions and sources, which are known to affect the production rates and subsequent frequency sweeping of holes and clumps. In particular, collisional relaxation, as mediated by e.g. velocity space diffusion or even simple Krook-type collisions, is found to inhibit hole-clump generation and detachment from the plateau, as it should. On the other hand, slowing down of the fast particles turns out to have an asymmetrically destabilizing/stabilizing effect, which explains the well-known result that collisional drag enhances holes and their sweeping rates but suppresses clumps. It is further demonstrated that relaxation of the plateau edge gradients has only a minor quantitative effect and does not change the plateau stability qualitatively, unless the edge region extends far into the plateau shelf and the corresponding Landau pole needs to be taken into account.