Andre Jaun

Chapter 5: Physics of energetic ions

This chapter reviews the progress accomplished since the redaction of the first ITER Physics Basis (1999 Nucl. Fusion 39 2137-664) in the field of energetic ion physics and its possible impact on burning plasma regimes. New schemes to create energetic ions simulating the fusion-produced alphas are introduced, accessing experimental conditions of direct relevance for burning plasmas, in terms of the Alfvenic Mach number and of the normalised pressure gradient of the energetic ions, though orbit characteristics and size cannot always match those of ITER. Based on the experimental and theoretical knowledge of the effects of the toroidal magnetic field ripple on direct fast ion losses, ferritic inserts in ITER are expected to provide a significant reduction of ripple alpha losses in reversed shear configurations. The nonlinear fast ion interaction with kink and tearing modes is qualitatively understood, but quantitative predictions are missing, particularly for the stabilisation of sawteeth by fast particles that can trigger neoclassical tearing modes. A large database on the linear stability properties of the modes interacting with energetic ions, such as the Alfven eigenmode has been constructed. Comparisons between theoretical predictions and experimental measurements of mode structures and drive/damping rates approach a satisfactory degree of consistency, though systematic measurements and theory comparisons of damping and drive of intermediate and high mode numbers, the most relevant for ITER, still need to be performed. The nonlinear behaviour of Alfven eigenmodes close to marginal stability is well characterized theoretically and experimentally, which gives the opportunity to extract some information on the particle phase space distribution from the measured instability spectral features. Much less data exists for strongly unstable scenarios, characterised by nonlinear dynamical processes leading to energetic ion redistribution and losses, and identified in nonlinear numerical simulations of Alfven eigenmodes and energetic particle modes. Comparisons with theoretical and numerical analyses are needed to assess the potential implications of these regimes on burning plasma scenarios, including in the presence of a large number of modes simultaneously driven unstable by the fast ions.

Alfven eigenmode experiments in tokamaks and stellarators

In tokamaks and stellarators, measurements of electromagnetic fluctuations in the presence of resonant particle drive, including fusion-produced alphas, reveal the excitation of Alfven eigenmodes (AE), related under certain conditions to a degradation in the fast-particle confinement. The balance between the drive and the background damping is investigated using active diagnostic systems to excite and measure the AE spectrum in terms of frequencies and damping rates. At JET, saddle-coil antennae drive low toroidal mode number (n 1%) during the creation of the magnetic X-point. In the presence of resonant fast particles, information on the instability drive is obtained: low-n modes are found to be stable in the presence of NBI with upsilon(parallel to)/upsilon(A) P-thresh, with 2.5 MW < P-thresh < 5 MW; under these conditions, intrinsically driven TAE and EAE are clearly observed in the magnetic fluctuation spectra, with no measurable effect on the plasma performance.

The toroidicity-induced Alfvén eigenmode structure in DIII-D: Implications of soft x-ray and beam-ion loss data

The internal structure of the toroidicity-induced Alfven eigenmode (TAE) is studied by comparing soft x-ray profile and beam ion loss data taken during TAE activity in the DIII-D tokamak [W. W. Hei ...

Toroidal mode conversion in the ICRF

Mode conversion is studied in the ion cyclotron range of frequencies (ICRF), taking into account the toroidal geometry relevant for tokamaks. The global wavefields obtained using the gyrokinetic toroidal PENN code illustrate how the fast wave propagates to the neighbourhood of the ion-ion hybrid resonance, where it is converted to a slow wave that deposits the wave energy through resonant Landau and cyclotron interactions with the particles. The power deposition profiles obtained are dramatically different from the toroidal resonance absorption, showing that Buddens fluid model is not a good approximation in the torus. Radially and poloidally localized wavefield structures characteristic of slow wave eigenmodes are predicted, which could be used in experiments to form transport barriers and to interact with fast particles.

Evaluating the Use of ICT in Engineering Education.

This paper is based on an evaluation of a mixed mode course called Learning Numerical Methods for Partial Differential Equations from the Web. The authors discuss the impact of information communication technology (ICT) on the provision of tertiary education and cite the course as an example of how it can be used at the subject level. The course employed ICT in a number of different ways. The introductory part of the course was held in a specifically designed video-conferencing facility that had a range of ICT capabilities. The design of the room is critiqued as is the use that was made of it. Throughout the paper the authors emphasize the point that ICT is a powerful tool for teaching and learning but failure to plan, deliver and assess ICT-based courses on sound pedagogical grounds merely means that poor teaching and learning practices are disseminated more widely and more quickly. On the basis of our evaluation we propose a simple set of questions that can be used to evaluate the best use of ICT in engineering education.

Experimental test of damping models for n=1 toroidal Alfven eigenmodes in JET

The damping rate of the n = 1 toroidal Alfven eigenmodes (TAE) mode in Ohmic-heated JET plasmas has been measured and compared with the prediction of the kinetic NOVA-K code, which includes electron and ion Landau damping of the global shear-Alfven wave field, collisional damping, and radiative damping. It was found that the calculated damping rate is too small to account for the measured value under these experimental conditions. A relatively weak dependence of the damping rate on the normalized Larmor radius is observed experimentally.

Isotope mass scaling of AE damping rates in the JET tokamak plasmas

The damping of radially extended Alfven eigenmodes in tokamak plasmas is investigated in JET discharges with different ion mass. The comparison of damping measurements with predictions of a gyro-kinetic model indicates that mode conversion into kinetic Alfven waves is the dominant damping mechanism for Alfven eigenmodes in the plasma core.

Stability of Alfvén eigenmodes in optimized tokamaks

Alfven eigenmodes (AEs) with intermediate toroidal mode numbers are modelled using the global gyrokinetic PENN code to determine the stability of high performance tokamak discharges in the presence of energetic particles. A large plasma pressure and a weak magnetic shear in the core give rise to radially extended kinetic AEs, which are stabilized by the high shear at the edge of a divertor (X point) configuration. Large values for the safety factor and the ion Larmor radius in reversed shear operation may however trigger drift kinetic Alfven eigenmode instabilities that could affect the alpha particle confinement in a reactor.

Stability of global drift-kinetic Alfven eigenmodes in DIII-D

Global Alfven eigenmodes are studied using two different models for the plasma and the results compared with the instability threshold measured experimentally. Fluid-resistive models predict that continuum damped toroidicity induced Alfven modes (TAE) are formed in the frequency range of the experimental instabilities, but using realistic values of the resistivity makes a stability analysis impossible for computational reasons. The kinetic plasma model solves this problem by taking into account the ion Larmor radius and the resonant Landau interactions between the particles and the wavefield. As a consequence drift-kinetic Alfven eigenmodes (DKAE) are created by toroidal coupling between the global TAE wavefield, the mode converted kinetic Alfven, ion-acoustic and drift waves. The power transfers between the wave and the particles show that the drift character of the wavefield in the core destabilizes DKAE modes through resonant interactions with the fast beam ions. The predicted beam pressure instability threshold is in agreement with the one measured experimentally

Global Alfven eigenmode stability in thermonuclear tokamak plasmas

Relying on the good agreement observed between the gyrokinetic PENN model and the low toroidal mode number n damping measurements from JET, the stability of Alfven eigenmodes (AEs) is predicted for reactor relevant conditions. Full non-local wave-particle power transfers are computed between global wavefields and alpha particles in an ITER reference equilibrium, showing that low-n eigenmodes (n similar or equal to 2) are strongly damped and intermediate-n eigenmodes (n similar or equal to 12) with a global radial extension are stable with a damping rate gamma/omega similar or equal to 0.02. Even though an excitation of alpha particle driven instabilities remains in principle possible in reactors, this study suggests that realistic operation scenarios exist where all the AEs of global character are stable.