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The physics and transport consequences of the nonlinear trapping of the wave–particle interactions on the transit and bounce time scale are investigated by solving drift kinetic equation including collisions. The nonlinear particle dynamics is governed by a new set of coupled evolution equations for the phase of the wave, the toroidal component of the canonical momentum (radial motion), and the particle energy. The resonant particles are trapped nonlinearly in the phase space in a pendulum-like motion to resolve the linear resonance. The trapping mechanism is similar to that of the superbananas in the neoclassical theory. The nonlinear particle dynamics is employed to facilitate the solution of the drift kinetic equation. It is shown analytically that the particle distribution in the nonlinearly trapped region is flattened when a term of the order of is neglected. Here, δA is the typical magnitude of the normalized perturbed wave field. The trapped and barely circulating particles diffuse collisionally in the phase space. Transport fluxes, wave–particle energy transfer rate and nonlinear damping rate are calculated. The transport coefficients have a new analytic scaling U in the context of the wave–particle interaction, and can be significant even for a small amplitude wave in tokamaks. Here, ν is the collision frequency, r is the minor radius, and U is a function of the wave frequency, aspect ratio, magnetic shear, and mode numbers. It is estimated that when δA ∼ 10−4 for the magnetic perturbation, alpha particle energy loss rate is comparable to that of the neoclassical theory. The energy transfer rate is proportional to part of the particle flux, a new relation, and scales as ν ; the nonlinear damping or growth rate ν. [ABSTRACT FROM AUTHOR]

The confinement of neutral beam injection (NBI) particles in the presence of n = 3 resonant magnetic perturbations (RMPs) in 15 MA ITER DT plasmas has been studied using full orbit ASCOT simulations. Realistic NBI distribution functions, and 3D wall and equilibria, including the plasma response to the externally applied 3D fields calculated with MARS-F, have been employed. The observed total fast-ion losses depend on the poloidal spectra of the applied n = 3 RMP as well as on the absolute toroidal phase of the applied perturbation with respect to the NBI birth distribution. The absolute toroidal phase of the RMP perturbation does not affect the ELM control capabilities, which makes it a key parameter in the confinement optimization. The physics mechanisms underlying the observed fast-ion losses induced by the applied 3D fields have been studied in terms of the variation of the particle canonical angular momentum (δPϕ) induced by the applied 3D fields. The presented simulations indicate that the transport is located in an edge resonant transport layer as observed previously in ASDEX upgrade studies. Similarly, our results indicate that an overlapping of several linear and nonlinear resonances at the edge of the plasma might be responsible for the observed fast-ion losses. The results presented here may help to optimize the RMP configuration with respect to the NBI confinement in future ITER discharges. [ABSTRACT FROM AUTHOR]

In Tokamak á Configuration Variable (TCV), unstable modes excited by resonant interaction between the shear Alfvèn waves in continuum gaps and energetic particles have been observed in scenarios with neutral beam injection (NBI). TCV is a middle-size device ( R 0 / a = 0.88 / 0.25) equipped with a 1 MW , 25 keV tangential neutral beam injector. In this paper the phenomenology of modes excited with on-axis NBI is presented. The Alfvènic nature of the modes has been confirmed investigating their sensitivity against plasma parameters such as NBI energy, toroidal magnetic field, and cross-checking with the predictions from linear kinetic stability code. The mode radial profile is estimated using electron cyclotron emission measurement and agrees well with modelling results. In addition, the fast particle distribution function has been modelled using TRANSP/NUBEAM code. Even with counter-current NBI (leading to higher losses), the drive from the resonant particles is sufficient for the mode excitation. An ad-hoc additional diffusion model allows to estimate the fast particle transport, modifying the fast particle gradient at the mode location and matching the neutron rates. [ABSTRACT FROM AUTHOR]

The transport of beam-generated fast ions has been investigated experimentally at the ASDEX Upgrade tokamak in the presence of sawtooth crashes. After sawtooth crashes, phase space resolved fast-ion D-alpha measurements show a significant reduction of the central fast-ion density—more than 50%—together with an increase at larger radii. The corresponding loss of fast particles, detected by a fast-ion loss detector outside the plasma, is marginal during the crash phase, which proves that the sawteeth internally redistribute fast ions. This is also well reproduced by modelling results in which the fast-ion redistribution is assumed to be in line with the sawtooth-induced change of the magnetic field topology. The simulation, however, underestimates the total amount of redistributed fast ions which can be explained by additional drift effects. In the time intervals between the crashes, a neoclassical fast-ion behaviour is observed. Radial profiles and measured decay rates of the redistributed fast ions show that any anomalous fast-ion diffusion in between sawtooth crashes is well below 0.5 m2 s−1. [ABSTRACT FROM AUTHOR]

The impact of edge localized modes (ELMs) and externally applied resonant and non-resonant magnetic perturbations (MPs) on fast-ion confinement/transport have been investigated in the ASDEX Upgrade (AUG), DIII-D and KSTAR tokamaks. Two phases with respect to the ELM cycle can be clearly distinguished in ELM-induced fast-ion losses. Inter-ELM losses are characterized by a coherent modulation of the plasma density around the separatrix while intra-ELM losses appear as well-defined bursts. In high collisionality plasmas with mitigated ELMs, externally applied MPs have little effect on kinetic profiles, including fast-ions, while a strong impact on kinetic profiles is observed in low-collisionality, low q95 plasmas with resonant and non-resonant MPs. In low-collisionality H-mode plasmas, the large fast-ion filaments observed during ELMs are replaced by a loss of fast-ions with a broad-band frequency and an amplitude of up to an order of magnitude higher than the neutral beam injection prompt loss signal without MPs. A clear synergy in the overall fast-ion transport is observed between MPs and neoclassical tearing modes. Measured fast-ion losses are typically on banana orbits that explore the entire pedestal/scrape-off layer. The fast-ion response to externally applied MPs presented here may be of general interest for the community to better understand the MP field penetration and overall plasma response. [ABSTRACT FROM AUTHOR]

Phase-space time-resolved measurements of fast-ion losses induced by edge localized modes (ELMs) and ELM mitigation coils have been obtained in the ASDEX Upgrade tokamak by means of multiple fast-ion loss detectors (FILDs). Filament-like bursts of fast-ion losses are measured during ELMs by several FILDs at different toroidal and poloidal positions. Externally applied magnetic perturbations (MPs) have little effect on plasma profiles, including fast-ions, in high collisionality plasmas with mitigated ELMs. A strong impact on plasma density, rotation and fast-ions is observed, however, in low density/collisionality and q95 plasmas with externally applied MPs. During the mitigation/suppression of type-I ELMs by externally applied MPs, the large fast-ion bursts observed during ELMs are replaced by a steady loss of fast-ions with a broad-band frequency and an amplitude of up to an order of magnitude higher than the neutral beam injection (NBI) prompt loss signal without MPs. Multiple FILD measurements at different positions, indicate that the fast-ion losses due to static 3D fields are localized on certain parts of the first wall rather than being toroidally/poloidally homogeneously distributed. Measured fast-ion losses show a broad energy and pitch-angle range and are typically on banana orbits that explore the entire pedestal/scrape-off-layer (SOL). Infra-red measurements are used to estimate the heat load associated with the MP-induced fast-ion losses. The heat load on the FILD detector head and surrounding wall can be up to six times higher with MPs than without 3D fields. When 3D fields are applied and density pump-out is observed, an enhancement of the fast-ion content in the plasma is typically measured by fast-ion D-alpha (FIDA) spectroscopy. The lower density during the MP phase also leads to a deeper beam deposition with an inward radial displacement of ≈2 cm in the maximum of the beam emission. Orbit simulations are used to test different models for 3D field equilibrium reconstruction including vacuum representation, the free boundary NEMEC code and the two-fluid M3D-C1 code which account for the plasma response. Guiding center simulations predict the maximum level of losses, ≈2.6%, with NEMEC 3D equilibrium. Full orbit simulations overestimate the level of losses in 3D vacuum fields with ≈15% of lost NBI ions. [ABSTRACT FROM AUTHOR]

The effect of n = 1 magnetic perturbations (MPs) on prompt fast ion losses in DIII-D has been investigated using the light ion beam probe technique. The effect of normalized beta, β n , and the plasma response to the MPs is studied for several MP spectra. Magnetics data show a strong dependence of plasma response to β n that depends on the phase difference in perturbation coils, Δ ϕ U L . For most phases, the response increases with β n , however, the response is suppressed for phases between 180∘ and 240∘. Experimental data from scintillator based fast ion loss detectors shows that relative fluctuation of lost ions (20%–30% of the steady signal) does not diminish across the L- to H-mode transition for Δ ϕ U L = 240 ∘ , despite the 34% decrease in radial response field and 50% decrease in poloidal response field. Simulations of the DIII-D discharges using M3D-C1 and ASCOT5 find that prompt losses from neutral beam injection in each investigated case hit the first wall at several concentrated locations: the vessel floor, midplane diagnostic ports, vessel ceiling, and inner wall. Simulated losses from co-injection neutral beams are born outside the last closed flux surface, corresponding to radial orbit displacements of 3–6 cm due to the MPs. [ABSTRACT FROM AUTHOR]

Evidence of γ-ray emission from fast ions in ASDEX Upgrade (AUG) is presented. The plasma scenarios developed for the experiments involve deuteron or proton acceleration. The observed γ-ray emission level induced by energetic protons is used to determine the effective tail temperature of the proton distribution function that can be compared with neutral particle analyser measurements. More generally the measured emission rate is used to assess the confinement of protons with energies <400 keV in discharges affected by toroidal Alfvén eigenmode instabilities. The derived information on confined ions is combined with observations made with the AUG fast ion loss detector. [ABSTRACT FROM AUTHOR]

Beam modulation effects on Alfvén eigenmode stability have been investigated in a recent DIII-D experiment and show that variations in neutral beam modulation period can have an impact on the beam driven Alfvén eigenmode spectrum and resultant fast ion transport despite similar time-averaged input power. The experiment was carried out during the current ramp phase of L-mode discharges heated with sub-Alfvénic 50–80 kV deuterium neutral beams that drive a variety of Alfvén eigenmodes unstable. The modulation period of two interleaved beams with different tangency radii was varied from shot to shot in order to modify the relative time dependent mix of the beam pitch angle distribution as well as the persistence of a bump-on-tail feature near the injection energy (a feature confirmed by imaging neutral particle analyzer measurements). As the beam modulation period is varied from 7 ms to 30 ms on/off (typical full energy slowing down time of τslow ≈ 50 ms at mid-radius), toroidicity-induced Alfvén eigenmodes (TAEs) located in the outer periphery of the plasma become intermittent and coincident with the more tangential beam. Core mode activity changes from reversed shear Alfvén eigenmodes (RSAEs) to a mix of RSAE and beta-induced Alfvén eigenmodes. Discharges with 30 ms on/off period do not have a persistent bump-on-tail feature, have the lowest average mode amplitude and least fast ion transport. Detailed analysis of an individual TAE using TRANSP kick modeling (Monte Carlo evolution of the distribution function with probabilistic 'kicks' by the AEs) and the resistive MHD code with kinetic fast ions, MEGA, find no strong role of energy gradient drive due to bump-on-tail features. Instead, the observed TAE modulation with interleaved beams is likely a pitch angle dependent result combined with slowing down of the tangential beam between pulses. For the conditions investigated, bump-on-tail contributions to TAE drive were found to be 5% or less of the total drive at any given time. [ABSTRACT FROM AUTHOR]

Fast-particle driven Alfvén Eigenmodes have been observed in low-collisionality discharges with off-axis neutral beam injection (NBI), electron cyclotron resonance heating (ECRH) and a reduced toroidal magnetic field. During NBI and ECRH, toroidicity induced Alfvén Eigenmodes (TAEs) appear in frequency bands close to 200 kHz and energetic-particle-induced geodesic acoustic modes (EGAMs) are observed at about 40 and 80 kHz. When turning off ECRH in the experiment, those beam-driven modes disappear which can be explained by a modification of the fast-ion slowing down distribution. In contrast, coherent fluctuations close to the frequency of the beam-driven TAEs are present throughout the experiment. The modes are even observed during ohmic plasma conditions, which clearly demonstrates that they are not caused by fast particles and suggests an alternative drive, such as turbulence. The mode-induced fast-ion transport has been found to be weak and marginal in terms of the fast-ion diagnostic sensitivities. Measurements of the plasma stored energy, neutron rates, neutral particle fluxes and fast-ion D-alpha spectroscopy show good agreement with neoclassical modelling results from TRANSP. This is further supported by a similarly good agreement between measurement and modelling in cases with and without ECRH and therefore with and without the modes. Instead, a significant level of charge exchange losses are predicted and observed which generate a bump-on-tail fast-ion distribution function that can provide the necessary free energy to EGAMs. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

Tokamak H-mode plasmas frequently exhibit edge-localized modes (ELMs). ELMs allow maintaining sufficient plasma purity and thus enable stationary H-mode. On the other hand in a future device ELMs may cause divertor power flux densities far in excess of tolerable material limits. The size of the energy loss per ELM is determined by saturation effects in the non-linear phase of the ELM, which at present is hardly understood. ASDEX Upgrade is now equipped with a set of fast sampling diagnostics, which is well suited to investigate the chain of events around the ELM crash with appropriate temporal resolution (≤10 µs). Solitary magnetic perturbations (SMPs) are identified as dominant features in the radial magnetic fluctuations below 100 kHz. They are typically observed close (±100 µs) to the onset of pedestal erosion. SMPs are field aligned structures rotating in the electron diamagnetic drift direction with perpendicular velocities of about 10 kms-1. A comparison of perpendicular velocities suggests that the perturbation evoking SMPs is located at or inside the separatrix. Analysis of very pronounced examples showed that the number of peaks per toroidal turn is 1 or 2, which is clearly lower than the corresponding numbers in linear stability calculations. In combination with strong peaking of the magnetic signals this results in a solitary appearance resembling modes like palm tree modes, edge snakes or outer modes. This behaviour has been quantified as solitariness and correlated with main plasma parameters. SMPs may be considered as a signature of the non-linearELMphase originating at the separatrix or further inside. Thus they provide a handle to investigate the transition from linear to non-linear ELM phase. By comparison with data from gas puff imaging processes in the non-linear phase at or inside the separatrix and in the scrape-off layer (SOL) can be correlated. A connection between the passing of an SMP and the onset of radial filament propagation has been found. Eventually the findings related to SMPs may contribute to a future quantitative understanding of the non-linear ELM evolution. [ABSTRACT FROM AUTHOR]

In ITER, magnetic fusion will explore the burning plasma regime. Because such burning plasma is sustained by its own fusion reactions, alpha particles need to be confined (Hazeltine 2010 Fusion Eng. Des. 7-9 85). New experiments using d(3He,p)α and d(d,p)t fusion reaction products were performed in JET. Fusion product loss was measured from MHD-quiescent plasmas with a charged particle activation probe installed at a position opposite to the magnetic field ion gradient drift (see figure 1)--1.77m above mid-plane--in the ceiling of JET tokamak. This new kind of escaping ion detector (Bonheure et al 2008 Fusion Sci. Technol. 53 806) provides for absolutely calibrated measurements. Both the mechanism and the magnitude of the loss are dealt with by this research. Careful analysis shows measured loss is in quantitative agreement with predictions from the classical orbit loss model. However, the comparison with simulated loss radial profile, although improved compared with previous studies in TFTR, Princeton, US (Zweben et al 2000 Nucl. Fusion 40 91), is not fully satisfactory and potential explanations for this discrepancy are examined. [ABSTRACT FROM AUTHOR]