Y. Todo

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.

Linear and nonlinear particle-magnetohydrodynamic simulations of the toroidal Alfvén eigenmode

Linear and nonlinear particle-magnetohydrodynamic (MHD) simulation codes are developed to study interactions between energetic ions and MHD modes. Energetic alpha particles with the slowing-down distribution are considered and the behavior of n=2 toroidal Alfven eigenmodes (TAE modes) is investigated with the parameters pertinent to the present large tokamaks. The linear simulation reveals the resonance condition between alpha particles and TAE mode. In the nonlinear simulation, two n=2 TAE modes are destabilized and alpha particle losses induced thereby are observed. Counterpassing particles are lost when they cross the passing-trapped boundary. They are the major part of lost particles, but trapped particles are also lost appreciably.

Magnetohydrodynamic Vlasov simulation of the toroidal Alfvén eigenmode

A new simulation method has been developed to investigate the excitation and saturation processes of toroidal Alfven eigenmodes (TAE modes). The background plasma is described by a magnetohydrodynamic (MHD) fluid model, while the kinetic evolution of energetic alpha particles is followed by the drift kinetic equation. The magnetic fluctuation of n=2 mode develops and saturates at the level of 1.8×10−3 of the equilibrium field when the initial beta of alpha particles is 2% at the magnetic axis. After saturation, the TAE mode amplitude shows an oscillatory behavior with a frequency corresponding to the bounce frequency of the alpha particles trapped by the TAE mode. The decrease of the power transfer rate from the alpha particles to the TAE mode, which is due to the trapped particle effect of a finite‐amplitude wave, causes the saturation. From the linear growth rate the saturation level can be estimated.

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.

Nonlocal energetic particle mode in a JT-60U plasma

Energetic-ion driven instability in a Japan Atomic Energy Research Institute Tokamak-60 Upgrade (JT-60U) [S. Ishida et al., Phys. Plasmas 11, 2532 (2004)] plasma was investigated using a simulation code for magnetohydrodynamics and energetic particles. The spatial profile of the unstable mode peaks near the plasma center where the safety factor profile is flat. The unstable mode is not a toroidal Alfven eigenmode (TAE) because the spatial profile deviates from the expected location of TAE and the spatial profile consists of a single primary harmonic m∕n=2∕1 where m and n are poloidal and toroidal mode numbers. The real frequency of the unstable mode is close to the experimental starting frequency of the fast frequency sweeping mode. Simulation results demonstrate that energetic-ion orbit width and energetic-ion pressure significantly broaden radial profile of the unstable mode. For the smallest value among the investigated energetic-ion orbit width, the unstable mode is localized within 20% of the minor r...

Properties of energetic-particle continuum modes destabilized by energetic ions with beam-like velocity distributions

Properties of energetic-particle continuum modes (EPMs) destabilized by energetic ions in tokamak plasmas were investigated using a hybrid simulation code for magnetohydrodynamics and energetic particles. The energetic ions are assumed to have beam-like velocity distributions for the purpose of clarifying the dependence on energetic ion velocity. It was found that for beam velocities lower than the Alfven velocity, the unstable modes are EPMs while the toroidal Alfven eigenmodes are unstable for the beam velocities well above the Alfven velocity. The EPMs destabilized by the copassing energetic ions and those destabilized by the counterpassing energetic ions differ in primary poloidal harmonics and spatial locations. The frequencies of the EPMs are located close to the shear Alfven continuous spectrum when they are compared at the spatial peak locations of the primary poloidal harmonic or compared at the spatial tails if the primary poloidal harmonic is m=1. The frequencies of the EPMs were carefully comp...

Nonlinear magnetohydrodynamic effects on Alfvén eigenmode evolution and zonal flow generation

Nonlinear magnetohydrodynamic (MHD) effects on Alfv?n eigenmode evolution were investigated via hybrid simulations of an MHD fluid interacting with energetic particles. The investigation focused on the evolution of an n = 4 toroidal Alfv?n eigenmode (TAE) which is destabilized by energetic particles in a tokamak. In addition to fully nonlinear code, a linear-MHD code was used for comparison. The only nonlinearity in that linear code is from the energetic-particle dynamics. No significant difference was found in the results of the two codes for low saturation levels, ?B/B ~ 10?3. In contrast, when the TAE saturation level predicted by the linear code is ?B/B ~ 10?2, the saturation amplitude in the fully nonlinear simulation was reduced by a factor of 2 due to the generation of zonal (n = 0) and higher-n (n ? 8) modes. This reduction is attributed to the increased dissipation arising from the nonlinearly generated modes. The fully nonlinear simulations also show that geodesic acoustic mode is excited by the MHD nonlinearity after the TAE mode saturation.

Energetic particle physics in JT-60U and JFT-2M

Recent energetic particle physics research in JT-60U and JFT-2M is reported. Alfven eigenmodes (AEs) are investigated in reversed-shear (RS) plasmas in JT-60U where frequency sweeping (FS) modes are observed to follow the q-profile evolution. The RS-induced AE model can explain the FS of the modes within the context of an evolving q-profile. Enhanced energetic ion transport is also investigated with the appearance of modes in the toroidicity-induced AE range of frequency in JT-60U using a multi-channel neutron profile monitor and in JFT-2M using a lost ion probe. Additionally, the ripple loss in the complex toroidal field ripple due to ferritic steel inserts in JFT-2M is shown and compared with model analysis. The simulation code developed to predict ripple loss in JFT-2M will be of use in estimating the heat flux in the complex ripple field of a future device such as ITER.

Simulation of intermittent beam ion loss in a Tokamak Fusion Test Reactor experiment

Recurrent bursts of toroidicity-induced Alfven eigenmodes (TAE) are studied using a self-consistent simulation model. Bursts of beam ion losses observed in the neutral beam injection experiment at the Tokamak Fusion Test Reactor [K. L. Wong et al., Phys. Rev. Lett. 66, 1874 (1991)] are reproduced using experimental parameters. It is found that synchronized TAE bursts take place at regular time intervals of 2.9 ms, which is close to the experimental value of 2.2 ms. The stored beam energy saturates at about 40% of that of the classical slowing down distribution. The stored beam energy drop associated with each burst has a modulation depth of 10%, which is also close to the inferred experimental value of 7%. Surface of section plots demonstrate that both the resonance overlap of different eigenmodes and the disappearance of KAM surfaces in phase space due to overlap of higher-order islands created by a single eigenmode lead to particle loss. Only co-injected beam ions build up to a significant stored energy...

Energetic ion transport by abrupt large-amplitude event induced by negative-ion-based neutral beam injection in the JT-60U

To investigate energetic ion transport induced by bursting modes in the frequency range of Alfven eigenmodes, which is called abrupt large-amplitude events (ALEs) driven by negative-ion-based neutral beam (N-NB) injection, neutron emission profile measurement and charge exchange (CX) neutral particle (flux) measurement using a natural diamond detector have been performed simultaneously in JT-60U. It is found from the CX neutral particle (flux) measurement that energetic neutral particles in a limited energy range (100–370 keV) are enhanced due to ALEs, and the neutron radial profile is flattened. The change in the energetic ion density profile inferred from these measurements indicates that ALEs expel energetic ions from the core region of the plasma and induce both redistribution and loss of energetic ions. It has been shown that the energy range of transported energetic ions is consistent with a resonance condition between energetic ions and ALEs, and the energetic ion transport results from the resonant interaction between energetic ions and ALEs. Further, a fraction of the energetic ion loss has been quantitatively estimated to be ~4%.