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Funding Information: This work is supported by US DOE Contracts DE-SC0020337, DE-AC05-00OR22725, DE-FC02-04ER54698, DE-AC02-09CH11466 and DE-SC0015878. This research used resources of the National Energy Research Scientific Computing Center (NERSC), a US Department of Energy Office of Science User Facility located at Lawrence Berkeley National Laboratory, operated under Contract No. DE-AC02-05CH11231 using NERSC Award FES-ERCAP20598. The ASCOT5 project was partially funded by the Academy of Finland Project Nos. 324759 and 298126. The ASCOT5 project has received funding from the European Research Council under Grant Agreement No. 647121. This ASCOT5 project has been carried out within the framework of the EUROfusion consortium and has received funding from the Euratom Research and Training Programme under Grant Agreement No. 633053. X. Wang’s work has been carried out within the framework of the EUROfusion Consortium, funded by the European Union via the Euratom Research and Training Programme (Grant Agreement No. 101052200—EUROfusion). The views and opinions expressed herein do not necessarily reflect those of the European Commission. | openaire: EC/H2020/647121/EU//PLASMA | openaire: EC/H2020/633053/EU//EUROfusion An imaging neutral particle analyzer (INPA) provides energy and radially resolved measurements of the confined fast-ion population ranging from the high-field side to the edge on the midplane of the DIII-D tokamak. In recent experiments, it was used to diagnose fast-ion flow in the INPA-interrogated phase-space driven by multiple, marginally unstable Alfvén eigenmodes (AEs). The key features of this measured fast-ion flow are: (I) a fast-ion flow from q min and the injection energy (81 keV) towards lower energies and plasma periphery.(II) A flow from the same location towards higher energies and the plasma core, (III) a phase-space 'hole' at the injected energy and plasma core and (IV) a pile-up at the plasma core at lower energies ( 1/460 keV). Ad hoc energetic particle diffusivity modelling of TRANSP significantly deviates from the observation. Comparably, a reduced modelling, i.e. a combination of NOVA-K and ASCOT5 code with the measured mode structure and amplitude, generally reproduce some key features of the observed phase-space flow, but largely failed to interpret fast ion depletion near the plasma axis. At last, self-consistent, first-principle multi-phase hybrid simulations that include realistic neutral beam injection and collisions are able to reproduce most features of the time-resolved phase-space flow. During consecutive hybrid phases, an RSAE consistent with the experiment grows and saturates, redistributing the injected fast ions. The resulting synthetic INPA images are in good agreement with the measurement near the injection energy. The simulations track the fast-ion redistribution within the INPA range, confirming that the measured fast-ion flow follows streamlines defined by the intersection of phase-space surfaces of constant magnetic moment μ and constant E′ = nE + ωP φ, where n and ω are the instability toroidal mode number and frequency, and E and P φ the ion energy and toroidal canonical momentum. Nonperturbative effects are required to reproduce the depletion of fast ions near the magnetic axis at the injection energy.

Transport of fast ions along certain local phase space paths, referred to as fast ion phase-space flow, has been systematically measured by an imaging neutral particle analyzer (INPA) in three plasma regimes, which are well-below, near, and well-above the Alfvén eigenmode stability threshold (Du et al 2021 Phys. Rev. Lett. 127 235002). (1) In plasmas well-below the Alfvén eignenmodes (AE) stability threshold, fast ions are well-confined on passing particle orbits without noticeable transport over the phase space. The observed INPA images agree well with the synthetic INPA images, using the fast ion distribution predicted by neoclassical theory. (2) In plasmas near the AE stability threshold, INPA images in the presence of AE activity moderately deviate from those without AE activity. The image difference can be well interpreted by AE-driven, phase-space fast ion flow. Paths of this flow over the velocity space (or streamlines) are reconstructed by the intersection lines of curved Eʹ and µ surfaces, referred to as Eʹ and µ line (where E ′ ≡ E − ( ω / n ) P ζ ; E, P ζ and µ are the energy, canonical toroidal momentum and magnetic moment of ions; ω and n are the angular frequency and toroidal mode number of AEs, respectively). Resonant fast ions move radially inward by gaining energy and move radially outward by losing energy and the trajectory well aligns with the Eʹ and µ lines that pass through the mode resonances near the injection energy of neutral beams. (3) In plasmas well-above the AE stability threshold, fast ion phase-space dynamics shows additional features. Fast ions are transported out of the birth positions so promptly along the streamlines that the slowing-down process from the injection energy is not observable, exhibiting strong critical gradient behavior at local phase space. As a result, the increase of electron temperature is very small, in spite of an increase of beam power by ∼ 45 % . It should be emphasized that the directions of phase-space transport, induced by AEs with different frequencies, structures and mode numbers, do not largely differ.

Coupling a high-performance core to a low heat flux divertor is a crucial step for ITER and a Fusion Pilot Plant or DEMO. Experiments in DIII-D recently expanded the steady-state hybrid scenario to high density and divertor impurity injection to study the feasibility of a radiating mantle solution. This work presents the physics basis for trade-offs between density, current drive and stability to tearing modes (TMs) at high β. EC power is crucial to tailor the plasma profiles into a passively stable state, and to eject impurities from the core. Off-axis EC depositions decrease the heating efficiency, but calculated electron heat transport coefficients show that this effect is partially mitigated by improved confinement inside the EC deposition. Additionally, the reduction in pressure is recovered by increasing the density. This favourable scaling of confinement with density was observed in high power plasmas for years, and this work provides a comprehensive explanation. ELITE predictions indicate that a path in peeling-ballooning stability opens up for certain conditions of density, power, q 95 and shaping, allowing the edge pressure to continue increasing without encountering a limit. In the core, calculated anomalous fast-ion diffusion coefficients are consistent with density fluctuation measurements in the toroidicity-induced Alfvén eigenmode range, showing that smaller fast-ion losses contribute to the enhanced confinement at high density. The edge integration study shows that divertor heat loads can be reduced with Ne and Ar injection, but this eventually triggers a cascade of n = 1, 2, 3 core TMs. We can now show that impurity radiation in the core is small and it is not the cause for the drop in confinement at high Ar and Ne injection rates. The overlap between the core TMs is consistent with the loss of pressure as estimated by the Belt model for the coupled rational surfaces. Optimization of these trade-offs has achieved plasmas with sustained H 98y2 = 1.7, f GW = 0.7 and ∼85% mantle radiation. The scenario and its variations at higher density and on- vs off-axis EC heating has been studied as a candidate for an integrated solution for several reactor designs, such as ITER, ARC, and the ARIES-ACT1 case, showing promising results in terms of fusion power and gain.

Various properties of the energetic particle-induced geodesic acoustic mode (EGAM) are explored in this large database analysis of DIII-D experimental data. EGAMs are n = 0 modes with m = 0 electrostatic potential fluctuations (where n/m = toroidal/poloidal mode number), m = 1 density fluctuations, and m = 2 magnetic fluctuations. The fundamental frequency (∼20–40 kHz) of the mode is typically below that of the traditional geodesic acoustic mode frequency. EGAMs are most easily destabilized by beams in the counter plasma current (counter-I p) direction as compared to co-I p and off-axis beams. During counter beam injection, the mode frequency is found to have the strongest linear dependence (correlation coefficient r = −0.71) with the safety factor (q). The stability of the mode in the space of q and poloidal beta (β p) shows a clear boundary for the mode stability. The stability of the mode depends more strongly on damping rate than on fast-ion drive for a given injection geometry.

Recent DIII-D experiments show that sawtooth stability is strongly affected by anisotropic fast ions from neutral beam injection (NBI) in both negative and positive triangularity plasmas. Fast ions from co-current NBI are stabilizing for the sawtooth stability, resulting in longer sawtooth periods. On the other hand, fast ions from counter-current NBI are destabilizing, leading to small and frequent sawteeth. The relative change of sawtooth period and amplitude is more than a factor of two. These observations appear to hold in both plasma shapes. Non-perturbative toroidal modeling, utilizing the magnetohydrodynamic-kinetic hybrid stability code MARS-K (Liu et al 2008 Phys. Plasmas 15 112503), reveals an asymmetric dependence of the stability of the n = 1 (n is the toroidal mode number) internal kink mode on the injection direction of NBI, being qualitatively consistent with the experimentally observed sawtooth behavior. The MARS-K modeling results suggest that anisotropic fast ions affect the mode growth rate and frequency through both adiabatic and non-adiabatic contributions. The asymmetry of the internal kink mode instability relative to the NBI direction is mainly due to the non-adiabatic contribution of passing fast ions, which stabilize (destabilize) the internal kink with the co-(counter-) current NBI as compared to the fluid counterpart. However, finite orbit width (FOW) correction to passing particles partially cancels the asymmetry. Trapped particles are always stabilizing due to precessional drift resonance. Modeling also shows that fast ions affect the internal kink in a similar manner in both negative and positive triangularity plasmas, although being slightly more unstable in the negative triangularity configuration already in the fluid limit. The similarity is mainly attributed to the fact that the mode is localized in the plasma core region, with very similar eigenmode structures in both negative and positive configurations. Furthermore, MARS-K modeling indicates that other factors, such as the plasma rotation and the drift kinetic effects of thermal plasmas, weakly modify the mode stability as compared to the drift kinetic resonance effects and FOW correction of fast ions.

We report mode structure measurements of coherent ion cyclotron emission (ICE) and sub-cyclotron modes on DIII-D. Through a dedicated experiment, we aimed to characterize a variety of modes via the upgraded ICE diagnostic in both L- and H-mode plasmas. In the L-mode plasmas, autopower spectrum peaks at harmonics of the ion cyclotron frequency f ci were observed and are localized in the core of the plasma. Sub-cyclotron modes (f ∼ 0.5f ci) were also observed in L-mode plasmas when the toroidal magnetic field strength was lowered from B T = 2.17 T. In H-mode plasmas, many ICE harmonics localized to the plasma edge were observed, with some exceeding the nominal ICE diagnostic bandwidth of f ∈ [0, 100] MHz. Polarization estimates made using an orthogonal pair of vertical and horizontal magnetic pickup loops on the outer wall of the machine indicate that ICE and sub-cyclotron modes have compressional polarization at the plasma edge, the latter being consistent with simulation efforts for comparable DIII-D plasmas. For all modes, the same harmonics are observed on both the centerpost and outer wall loops, indicating that ICE is poloidally extended. Finally, toroidal mode numbers were calculated using three outer wall loops for both core ICE and sub-cyclotron modes in L-mode plasmas. The sub-cyclotron case served as a benchmark for our calculation method, with measured numbers of n ∈ [−24, −18] roughly agreeing with heuristic estimates of n ∈ [−20, −13]. Core ICE mode numbers were measured to be n ∈ [−10, 5], which is comparable to measurements made on other machines.

The eigenfunction of an instability contains information about energy flow in the wave. In this study, the amplitude and phase of electron cyclotron emission radiometer data from hundreds of DIII-D reversed shear Alfvén eigenmodes (RSAE) and toroidicity-induced Alfvén eigenmodes (TAE) are analyzed along the outboard horizontal midplane. The radial phase profile can be flat, linearly rising or falling, convex or concave; in other words, a wide variety of shapes is observed. For a particular mode, often the radial phase profile remains approximately constant as the mode evolves in time but sometimes it changes rapidly. Many TAEs and some RSAEs have phase profiles that are rather flat where the mode amplitude is largest but rise steadily by ∼ 2 π at large major radius. Rapid phase changes are observed when the frequencies of an RSAE and TAE overlap and the modes couple. The phase profile depends weakly on the fast-ion gradient that would appear in the absence of wave-induced transport. Linear and quadratic fits to the phase profiles, together with many plasma parameters, are assembled into RSAE and TAE databases. In both cases, large variability is observed. For RSAEs, the strongest phase dependencies are on electron temperature T e, RSAE mode frequency, and the density of carbon impurities. For TAEs, the strongest dependencies are on beam power and major radius of the mode. In general, the average RSAE radial phase profile is essentially flat but the TAE profile has non-zero slope and curvature.

A fast wave interferometer (FWI), which can measure ion mass density, has been developed on DIII-D for its use on future fusion reactors, as well as for the study of ion behavior in current plasma devices. The frequency of the fast waves used for the FWI is around 60 MHz, and require antennas and coaxial cables or waveguides, which, unlike traditional mirror-based optical interferometers, are less susceptible to neutron/gamma-ray radiation and are relatively immune to impurity deposition and erosion as well as alignment issues. The bulk ion density evaluated using FWI show good agreement with that derived from CO2 interferometry within about 15%. When the ion mass density measurement by FWI is combined with an electron density measurement from CO2 interferometry, Z eff measurements are also enabled and are in agreement with those from visible Bremsstrahlung measurements. Additionally, large-bandwidth FWI measurements clearly resolve 10–100 kHz coherent modes and demonstrate its potential as a core fluctuation diagnostic, sensitive to both magnetic and ion density perturbations.

A comprehensive suite of diagnostics has allowed detailed measurements of the Alfvén eigenmode (AE) spatial structure and subsequent fast-ion transport in the ASDEX Upgrade (AUG) tokamak [1]. Reversed shear Alfvén eigenmodes (RSAEs) and toroidal induced Alfvén eigenmodes (TAEs) have been driven unstable by fast ions from ICRH as well as NBI origin. In ICRF heated plasmas, diffusive and convective fast-ion losses induced by AEs have been characterized in fast-ion phase space. While single RSAEs and TAEs eject resonant fast ions in a convective process directly proportional to the fluctuation amplitude, δB/B, the overlapping of multiple RSAE and TAE spatial structures and wave–particle resonances leads to a large diffusive loss, scaling as (δB/B)2. In beam heated discharges, coherent fast-ion losses have been observed primarily due to TAEs. Core localized, low amplitude NBI driven RSAEs have not been observed to cause significant coherent fast-ion losses. The temporal evolution of the confined fast-ion profile in the presence of RSAEs and TAEs has been monitored with high spatial and temporal resolution. A large drop in the central fast-ion density due to many RSAEs has been observed as q min passes through an integer. The AE radial and poloidal structures have been obtained with unprecedented details using a fast SXR as well as 1D and 2D ECE radiometers. GOURDON and HAGIS simulations have been performed to identify the orbit topology of the escaping ions and study the transport mechanisms. Both passing and trapped ions are strongly redistributed by AEs.