N.N. Gorelenkov

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.

Energetic particle physics in fusion research in preparation for burning plasma experiments

The area of energetic particle (EP) physics in fusion research has been actively and extensively researched in recent decades. The progress achieved in advancing and understanding EP physics has been substantial since the last comprehensive review on this topic by Heidbrink and Sadler (1994 Nucl. Fusion 34 535). That review coincided with the start of deuterium?tritium (DT) experiments on the Tokamak Fusion Test Reactor (TFTR) and full scale fusion alphas physics studies.Fusion research in recent years has been influenced by EP physics in many ways including the limitations imposed by the ?sea? of Alfv?n eigenmodes (AEs), in particular by the toroidicity-induced AE (TAE) modes and reversed shear AEs (RSAEs). In the present paper we attempt a broad review of the progress that has been made in EP physics in tokamaks and spherical tori since the first DT experiments on TFTR and JET (Joint European Torus), including stellarator/helical devices. Introductory discussions on the basic ingredients of EP physics, i.e., particle orbits in STs, fundamental diagnostic techniques of EPs and instabilities, wave particle resonances and others, are given to help understanding of the advanced topics of EP physics. At the end we cover important and interesting physics issues related to the burning plasma experiments such as ITER (International Thermonuclear Experimental Reactor).

Measurements and modeling of Alfvén eigenmode induced fast ion transport and loss in DIII-D and ASDEX Upgrade

Neutral beam injection into reversed magnetic shear DIII-D and ASDEX Upgrade plasmas produces a variety of Alfvenic activity including toroidicity-induced Alfven eigenmodes and reversed shear Alfven eigenmodes (RSAEs). These modes are studied during the discharge current ramp phase when incomplete current penetration results in a high central safety factor and increased drive due to multiple higher order resonances. Scans of injected 80 keV neutral beam power on DIII-D showed a transition from classical to AE dominated fast ion transport and, as previously found, discharges with strong AE activity exhibit a deficit in neutron emission relative to classical predictions. By keeping beam power constant and delaying injection during the current ramp, AE activity was reduced or eliminated and a significant improvement in fast ion confinement observed. Similarly, experiments in ASDEX Upgrade using early 60 keV neutral beam injection drove multiple unstable RSAEs. Periods of strong RSAE activity are accompanied ...

Collective fast ion instability-induced losses in National Spherical Tokamak Experiment

A wide variety of fast ion driven instabilities are excited during neutral beam injection (NBI) in the National Spherical Torus Experiment (NSTX) [Nucl. Fusion 40, 557 (2000)] due to the large ratio of fast ion velocity to Alfven velocity, Vfast∕VAlfven, and high fast ion beta. The ratio Vfast∕VAlfven in ITER [Nucl. Fusion 39, 2137 (1999)] and NSTX is comparable. The modes can be divided into three categories: chirping energetic particle modes (EPM) in the frequency range 0 to 120kHz, the toroidal Alfven eigenmodes (TAE) with a frequency range of 50kHz to 200kHz, and the compressional and global Alfven eigenmodes (CAE and GAE, respectively) between 300kHz and the ion cyclotron frequency. Fast ion driven modes are of particular interest because of their potential to cause substantial fast ion losses. In all regimes of NBI heated operation we see transient neutron rate drops, correlated with bursts of TAE or fishbone-like EPMs. The fast ion loss events are predominantly correlated with the EPMs, although ...

On velocity space interrogation regions of fast-ion collective Thomson scattering at ITER

The collective Thomson scattering (CTS) diagnostic proposed for ITER is designed to measure projected 1D fast-ion velocity distribution functions at several spatial locations simultaneously. The frequency shift of scattered radiation and the scattering geometry place fast ions that caused the collective scattering in well-defined regions in velocity space, here dubbed interrogation regions. Since the CTS instrument measures entire spectra of scattered radiation, many different interrogation regions are probed simultaneously. We here give analytic expressions for weight functions describing the interrogation regions, and we show typical interrogation regions of the proposed ITER CTS system. The backscattering system with receivers on the low-field side is sensitive to fast ions with pitch |p| = |v∥/v| 0.6–0.8. Additionally, we use weight functions to reconstruct 2D fast-ion distribution functions, given two projected 1D velocity distribution functions from simulated simultaneous measurements with the back- and forward scattering systems.

Active and Fast Particle Driven Alfven Eigenmodes in Alcator C-Mod

Alfven eigenmodes sAEsd are studied to assess their stability in high density reactor relevant regimes where Ti < Te and as a diagnostic tool. Stable AEs are excited with active magnetohydrodynamics antennas in the range of the expected AE frequency. Toroidal Alfven eigenmode sTAEd damping rates between 0.5%, g / v , 4.5% have been observed in diverted and limited Ohmic plasmas. Unstable AEs are excited with a fast ion tail driven by H minority ion cyclotron radio frequency sICRFd heating with electron densities in the range of ne = 0.5‐2 3 10 20 m ˛3 . Energetic particle modes or TAEs have been observed to decrease in frequency and mode number with time up to a large sawtooth collapse, indicating the role fast particles play in stabilizing sawteeth. In the current rise phase, unstable modes with frequencies that increase rapidly with time are observed with magnetic pick-up coils at the wall and phase contrast imaging density fluctuation measurements in the core. Modeling of these modes constrains the calculated safety factor profile to be very flat or with slightly reversed shear. AEs are found to be more stable for an inboard than for central or outboard ICRF resonances in qualitative agreement with modeling.

Alfvén eigenmodes driven by Alfvénic beam ions in JT-60U

Instabilities with frequency chirping in the frequency range of Alfven eigenmodes have been found in the domain 0.1% < βh < 1% and vb||/vA ~1 with high energy neutral beam injection in JT-60U. One instability with a frequency inside the Alfven continuum spectrum appears and its frequency increases slowly to the toroidicity induced Alfven eigenmode (TAE) gap on the timescale of an equilibrium change ( ≈ 200 ms). Other instabilities appear with a frequency inside the TAE gap and their frequencies change very quickly by 10-20 kHz in 1-5 ms. During the period when these fast frequency sweeping (fast FS) modes occur, abrupt large amplitude events (ALEs) often appear with a drop of neutron emission rate and an increase in fast neutral particle fluxes. The loss of energetic ions increases with a peak fluctuation amplitude of θ/Bθ. An energy dependence of the loss ions is observed and suggests a resonant interaction between energetic ions and the mode.

A threshold for excitation of neoclassical tearing modes

Stability criterion for neoclassical tearing modes is obtained from the drift kinetic equation. A finite amplitude of a magnetic island is required for mode excitation. The threshold is determined by the ratio of the transversal and the parallel transport near the island when the flattening of the pressure profile eliminates the bootstrap current. A number of supershots from the database of the Tokamak Fusion Test Reactor (TFTR) [D. J. Grove and D. M. Meade, Nucl. Fusion 25, 1167 (1985)] are compared with the theory. In cases where the modes were observed in experiment the stability criterion was violated.

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.

Wave driven fast ion loss in the National Spherical Torus Experiment

Spherical tokamaks have relatively low toroidal field which means that the fast-ion Larmor radius is relatively large (ρfi>0.04 ap) and the fast ion velocity is much greater than the Alfven speed (Vfi>2 VAlfven). This regime of large Larmor radius and low Alfven speed is a regime in which fast ion driven instabilities are potentially virulent. It is therefore an important goal of the present proof-of-principle spherical tokamaks to evaluate the role of fast ion driven instabilities in fast ion confinement. This paper presents the first observations of fast ion losses in a spherical tokamak resulting from energetic particle driven modes. Two classes of instabilities are responsible for the losses. Multiple, simultaneously bursting modes in the toroidal Alfven eigenmode frequency gap cause neutron drops of up to 15%. A bursting, chirping mode identified as precession and/or bounce resonance fishbone also causes significant neutron drops. Both modes are usually present when the losses are observed.