The internal structure of the toroidicity-induced Alfvén 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. Heidbrink et al., Nucl. Fusion 37, 1411 (1997)] with predictions from theories based on ideal magnetohydrodynamic (MHD), gyrofluid, and gyrokinetic models. The soft x-ray measurements indicate a centrally peaked eigenfunction, a feature which is closest to the gyrokinetic model's prediction. The beam ion losses are simulated using a guiding center code. In the simulations, the TAE eigenfunction calculated using the ideal MHD model acts as a perturbation to the equilibrium field. The predicted beam ion losses are an order of magnitude less than the observed ∼6%-8% losses at the peak experimental amplitude of δBr/B0≃2-5×10-4. © 2001 American Institute of Physics.

The numerical methods used in the full particle-orbit following SPIRAL code are described and a number of physics studies performed with the code are presented to illustrate its capabilities. The SPIRAL code is a test-particle code and is a powerful numerical tool to interpret and plan fast-ion experiments in tokamaks. Gyro-orbit effects are important for fast ions in low-field machines such as NSTX and to a lesser extent in DIII-D. A number of physics studies are interlaced between the description of the code to illustrate its capabilities. Results on heat loads generated by a localized error-field on the DIII-D wall are compared with measurements. The enhanced Triton losses caused by the same localized error-field are calculated and compared with measured neutron signals. Magnetohydrodynamic (MHD) activity such as tearing modes and toroidicity-induced Alfvén eigenmodes (TAEs) have a profound effect on the fast-ion content of tokamak plasmas and SPIRAL can calculate the effects of MHD activity on the confined and lost fast-ion population as illustrated for a burst of TAE activity in NSTX. The interaction between ion cyclotron range of frequency (ICRF) heating and fast ions depends solely on the gyro-motion of the fast ions and is captured exactly in the SPIRAL code. A calculation of ICRF absorption on beam ions in ITER is presented. The effects of high harmonic fast wave heating on the beam-ion slowing-down distribution in NSTX is also studied. © 2013 IOP Publishing Ltd.

Core localized Alfv́n eigenmodes in DIII-D [J. L. Luxon, Nucl. Fusion 42, 614 (2002)] and Joint European Torus (JET) [P. H. Rebut and B. E. Keen, Fusion Technol. 11, 13 (1987)] plasmas are driven by deuterium neutral beam ions traveling well below the Alfv́n speed. Modes are observed in reverse magnetic shear discharges with deuterium ion velocities as low as 0.23 and 0.16 of the Alfv́n speed parallel to the magnetic field in DIII-D and JET plasmas, respectively. Ellipticity-induced Alfv́n eigenmodes in DIII-D and toroidicity-induced Alfv́n eigenmodes in JET are excited by deuterium ions traveling well below the fundamental passing ion resonance condition, indicating the role of high-order resonances in driving these modes. NOVA-K analysis reveals many high-order resonances as contributing to the mode drive at high central safety factor due to the correspondingly large poloidal orbit width and the decrease in the perpendicular scale length of the modes. © 2008 American Institute of Physics.

Intense axisymmetric oscillations driven by suprathermal ions injected in the direction counter to the toroidal plasma current are observed in the DIII-D tokamak. The modes appear at nearly half the ideal geodesic acoustic mode frequency, in plasmas with comparable electron and ion temperatures and elevated magnetic safety factor (q_{min}>or=2). Strong bursting and frequency chirping are observed, concomitant with large (10%-15%) drops in the neutron emission. Large electron density fluctuations (n[over ]_{e}/n_{e} approximately 1.5%) are observed with no detectable electron temperature fluctuations, confirming a dominant compressional contribution to the pressure perturbation as predicted by kinetic theory. The observed mode frequency is consistent with a recent theoretical prediction for the energetic-particle-driven geodesic acoustic mode.

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 Alfván velocity, Vfast VAlfvén, and high fast ion beta. The ratio Vfast VAlfvén 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 120 kHz, the toroidal Alfván eigenmodes (TAE) with a frequency range of 50 kHz to 200 kHz, and the compressional and global Alfván eigenmodes (CAE and GAE, respectively) between 300 kHz 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 losses are also seen with bursts of multiple, large amplitude TAE. The latter is of particular significance for ITER; the transport of fast ions from the expected resonance overlap in phase space of a "sea" of large amplitude TAE is the kind of physics expected in ITER. The internal structure and amplitude of the TAE and EPMs has been measured with quadrature reflectometry and soft x-ray cameras. The TAE bursts have internal amplitudes of ñ n=1% and toroidal mode numbers 21 and can have a toroidal mode number n>1. The range of the frequency chirp can be quite large and the resonance can be through a fishbone-like precessional drift resonance, or through a bounce resonance. © 2006 American Institute of Physics.

Because alpha particle losses can have a significant influence on tokamak reactor viability, the loss of deuterium–tritium alpha particles from the Tokamak Fusion Test Reactor (TFTR) [K. M. McGuire et al., Phys. Plasmas 2, 2176 (1995)] has been measured under a wide range of conditions. In TFTR, first orbit loss and stochastic toroidal field ripple diffusion are always present. Other losses can arise due to magnetohydrodynamic instabilities or due to waves in the ion cyclotron range of frequencies. No alpha particle losses have yet been seen due to collective instabilities driven by alphas. Ion Bernstein waves can drive large losses of fast ions from TFTR, and details of those losses support one element of the alpha energy channeling scenario. © 1996, American Institute of Physics. All rights reserved.

A summary is presented of recent alpha-particle experiments on the tokamak fusion test reactor. Alpha particles are generally well confined in MHD-quiescent discharges, and alpha heating of electrons has been observed. The theoretically predicted toroidicity-induced Alfvén eigenmode has been seen in discharges of ≤ 1 MW of alpha power, but only in plasmas with weak magnetic shear. © 1997 IOP Publishing Ltd.

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 Alfvén 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. © 2013 IAEA, Vienna.