From numerical simulation and analytical modeling it is shown that fast ions can resonate with plasma waves at fractional values of the particle drift-orbit transit frequency when the plasma wave amplitude is sufficiently large. The fractional resonances, which are caused by a nonlinear interaction between the particle orbit and the wave, give rise to an increased density of resonances in phase space which reduces the threshold for stochastic transport. The effects of the fractional resonances on spatial and energy transport are illustrated for an energetic particle geodesic acoustic mode but they apply equally well to other types of MHD activity.

Alfvén instabilities can reduce the central magnetic shear via redistribution of energetic ions. They can sustain a steady state internal transport barrier as demonstrated in this DIII-D tokamak experiment. Improvement in burning plasma performance based on this mechanism is discussed.

Alfvén instabilities excited by energetic ions are used as a means to reduce the central magnetic shear in a tokamak via redistribution of energetic ions. When the central magnetic shear is low enough, ballooning modes become stable for any plasma pressure gradient and an internal transport barrier (ITB) with a steep pressure gradient can exist. This mechanism can sustain a steady-state ITB as demonstrated by experimental data from the DIII-D tokamak. It can also produce a shear in toroidal and poloidal plasma rotation. Possible application of this technique to use the energetic α particles for improvement of burning plasma performance is discussed.

We report the first experimental observations of fast-ion loss in a tokamak due to energetic particle driven geodesic acoustic modes (EGAMs). A fast-ion loss detector installed on the DIII-D tokamak observes bursts of beam ion losses coherent with the EGAM frequency. The EGAM activity results in a significant loss of beam ions, comparable to the first orbit losses. The pitch angles and energies of the measured fast-ion losses agree with predictions from a full orbit simulation code SPIRAL, which includes scattering and slowing-down. © 2012 IAEA, Vienna.

Effects of the energetic-ion-driven Geodesic Acoustic modes (GAM and E-GAM) on the toroidally passing energetic ions and the concomitant change of the neutron yield of beam-plasma fusion reactions in tokamaks are considered. It is shown that due to large perturbations of the plasma density, the resonant energetic ions driving the instability can be considerably slowed down for a few tens of the particle transit periods, which is much less than the collisional slowing down time. The time of the collisionless slowing down is actually determined by the period of the particle motion within the resonance island arising because of the GAM / E-GAM. Being trapped in the island, the resonant particles can not only lose their energy but also gain it. One more effect of GAMs is the flattening on the distribution function of the resonant particles. Due to conservation of the canonical angular momentum during a GAM / E-GAM instability, the change of the particle energy is accompanied by a radial displacement of the resonant particle for a distance up to the poloidal Larmor radius of energetic ions. The particles are displaced inwards or outwards, depending on the direction of their motion along the magnetic field. Expressions describing the change of the neutron yield due to GAM modes are derived. It is found that the distortion of the velocity distribution of the resonant particles can lead to a considerable drop of the neutron emission even when effects of the particle radial displacement are small. The developed theory is applied to an E-GAM experiment on the DIII-D tokamak. Relations for the period of the motion within the resonance island of passing (both well passing and marginally passing) particles and the width of the resonance of the energetic particles with GAM modes and low-frequency Alfvé modes are derived.

Prompt neutral beam-ion loss due to non-resonant scattering caused by toroidicity-induced and reversed shear Alfvén eigenmodes (TAE/RSAEs) have been observed in DIII-D. The coherent losses are of full-energy beam ions born on unperturbed trapped orbits that would carry them close to a fast-ion loss detector (FILD) within one poloidal transit. However, in the presence of AEs, the particles are expelled from the plasma before completing their first poloidal orbits. The loss signals on FILD emerge within 100 μs after the beam switch-on (which is the time scale of a single poloidal transit) and oscillate at mode frequencies. Time-resolved loss measurements show a linear dependence on the AE fluctuation amplitude and a radial 'kick' of ∼10 cm by an n = 2 RSAE at δB/B 1 × 10-3 can be directly inferred from the measurements. Full-orbit modelling of the fast-ion displacement caused by the AEs is in good quantitative agreement with the measurements. Direct interactions of the mode and the beam-ion orbit can account for a large fraction of fast-ion losses observed in such DIII-D discharges. The first orbit non-resonant loss mechanism may also contribute to enhanced localized losses in ITER and future reactors. A new diagnostic method of the radial displacement is inspired by these findings and can be used to study the interaction between fast ions and various MHD modes as well as three-dimensional fields. © 2013 IAEA, Vienna.

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.

A numerical model describing the expected measurements of neutral beam prompt-losses by a newly commissioned fast ion loss detector (FILD) in DIII-D is presented. This model incorporates the well understood neutral beam deposition profiles from all eight DIII-D beamlines to construct a prompt-loss source distribution. The full range of detectable ion orbit phase space available to the FILD is used to calculate ion trajectories that overlap with neutral beam injection footprints. Weight functions are applied to account for the level of overlap between these detectable orbits and the spatial and velocity (pitch) properties of ionized beam neutrals. An experimental comparison is performed by firing each neutral beam individually in the presence of a ramping plasma current. Fast ion losses determined from the model are in agreement with measured losses.

The stability of α-particle driven shear Alfvén eigenmodes (AE) for nominal burning plasma (BP) parameters in the proposed international tokamak experimental reactor (ITER), fusion ignition research experiment (FIRE) and IGNITOR tokamaks is studied. JET plasma, where fusion as were generated in tritium experiments, is also studied to compare the numerical predictions with the existing experiments. An analytic assessment of toroidal AE (TAB) stability is first presented, where the α-particle β due to the fusion reaction rate and electron drag is simply and accurately estimated in plasmas with central temperature in the range of 7-20 keV. In this assessment the hot particle drive is balanced against ion-Landau damping of the background douterons, and electron collision effects and stability boundaries are determined. Then two numerical studies of AE instability are presented. In one, the HIgh-n STability (HINST) code is used to predict the instabilities of low and moderately high frequency Alfvén modes. HINST computes the non-perturbative solutions of the AE including effects of ion finite Larmor radius, orbit width, trapped electrons etc. The stability calculations are repeated using the global code NOVAK. We show that for these plasmas the spectrum of the least stable AE modes is at medium-/high-n numbers. In HINST, TAEs are locally unstable due to the α pressure gradient in all the devices under consideration except IGNITOR. However, NOVAK calculations show that the global mode structure enhances the damping mechanisms and produces stability for the nominal FIRE proposal and near-marginal stability for the nominal ITER proposal. NBI ions produce a strong stabilizing effect for JET. However, in ITER, the beam energies needed to penetrate to the core must be high (∼1 MeV) so that a diamagnetic drift frequency comparable to that of α-particles is produced by the beam ions which induces a destabilizing effect. A serious question remains whether the perturbation theory used in NOVAK overestimates the stability predictions, so that it is premature to conclude that the nominal operation of all three BP proposals without neutral beam injection are stable (or marginally stable) to AEs.