Different combinations of on-axis and off-axis neutral beams are injected into DIII-D plasmas that are unstable to reversed shear Alfvén eigenmodes (RSAE) and toroidal Alfvén eigenmodes (TAE). The variations alter the classically expected fast-ion gradient ∇β f in the plasma interior. Off-axis injection reduces the amplitude of RSAE activity an order of magnitude. Core TAEs are also strongly stabilized. In contrast, at larger minor radius, the fast-ion gradient is similar for on-and off-axis injection and switching the angle of injection has a weaker effect on the stability of TAEs. The average mode amplitude correlates strongly with the classically expected profile but the measured profile relaxes to similar values independent of the fraction of off-axis beams. The observations agree qualitatively with a 'critical-gradient' model of fast-ion transport.

Energetic particle (EP) transport from local high-n toroidal Alfvén eigenmodes (TAEs) and energetic particle modes (EPMs) is simulated with a gyrokinetic code. Linear and nonlinear simulations have identified a parameter range where the longwave TAE and EPM are unstable alongside the well-known ion-temperature-gradient (ITG) and trapped-electron-mode (TEM) instabilities. A new eigenvalue solver in GYRO facilitates this mode identification. States of nonlinearly saturated local TAE/EPM turbulent intensity are identified, showing a “soft” transport threshold for enhanced energetic particle transport against the TAE/EPM drive from the EP pressure gradient. The very long-wavelength (mesoscale) TAE/EPM transport is saturated partially by nonlinear interaction with microturbulent ITG/TEM-driven zonal flows. Fixed-gradient-length, nonlinearly saturated states are accessible over a relatively narrow range of EP pressure gradient. Within this range, and in the local limit employed, TAE/EPM-driven transport more closely resembles drift-wave microturbulent transport than “stiff” ideal MHD transport with a clamped critical total pressure gradient. At a higher, critical EP pressure gradient, fixed-gradient nonlinear saturation fails: EP transport increases without limit and background transport decreases. Presumably saturation is then obtained by relaxation of the EP pressure gradient to near this critical EP pressure gradient. If the background plasma gradients driving the ITG/TEM turbulence and zonal flows are weakened, the critical gradient collapses to the TAE/EPM linear stability threshold. Even at the critical EP pressure gradient there is no evidence that TAE/EPM instability significantly increases transport in the background plasma channels.

A verification and validation study is carried out for a sequence of reversed shear Alfv en instability time slices. The mode frequency increases in time as the minimum (q min ) in the safety factor profile decreases. Profiles and equilibria are based upon reconstructions of DIII-D discharge (#142111) in which many such frequency up-sweeping modes were observed. Calculations of the frequency and mode structure evolution from two gyrokinetic codes, GTC and GYRO, and a gyro-Landau fluid code TAEFL are compared. The experimental mode structure of the instability was measured using time-resolved two-dimensional electron cyclotron emission imaging. The three models reproduce the frequency upsweep event within 610% of each other, and the average of the code predictions is within 68% of the measurements; growth rates are predicted that are consistent with the observed spectral line widths. The mode structures qualitatively agree with respect to radial location and width, dominant poloidal mode number, ballooning structure, and the up-down asymmetry, with some remaining differences in the details. Such similarities and differences between the predictions of the different models and the experimental results are a valuable part of the verification/validation process and help to guide future development of the modeling efforts.

A simple radial transport code for predicting the fusion alpha density profiles in an ITER burning plasma unstable to Alfvén eigenmodes (AEs) is illustrated. This extends earlier work by Angioni et al (2009 Nucl. Fusion 49 055013) treating the fusion alpha transport from high-n micro-turbulence to include marginal stability (or 'stiff') transport from alpha-driven low-n AEs. The local alpha density gradient AE thresholds are provided by physically realistic linear gyrokinetic code simulations. The transported alpha density profiles are compared to the alpha classical slowing-down profiles dependent on the birth rate source profiles. The base case thermal plasma (and hence source) profiles are taken from a theory-based core transport and H-mode pedestal prediction of ITER performance by Kinsey et al (2011 Nucl. Fusion 51 083001). The distinction between the alpha particle and the much smaller alpha energy transport loss is emphasized. The AE transport is localized to the mid-core radii with the high-n micro-turbulence controlling the transport loss of low energy alphas at the edge. Edge energy loss is about 100-fold smaller than particle loss. Even with the worst case boundary condition, only about 0.1% of net heating is lost and escaping alphas can be characterized as very hot helium.

This paper reports verification and validation of linear simulations of Alfvén eigenmodes in the current ramp phase of DIII-D L-mode discharge #159243 using gyrokinetic, gyrokinetic-MHD hybrid, and eigenvalue codes. Using a classical fast ion profile, all simulation codes find that reversed shear Alfvén eigenmodes (RSAE) are the dominant instability. The real frequencies from all codes have a coefficient of variation of less than 5% for the most unstable modes with toroidal mode number n = 4 and 5. The simulated RSAE frequencies agree with experimental measurements if the minimum safety factor q min is adjusted, within experimental errors. The simulated growth rates exhibit greater variation, and simulations find that pressure gradients of thermal plasmas make a significant contribution to the growth rates. Mode structures of the dominant modes agree well among all codes. Moreover, using a calculated fast ion profile that takes into account the diffusion by multiple unstable modes, a toroidal Alfvén eigenmode (TAE) with n = 6 is found to be unstable in the outer edge, consistent with the experimental observations. Variations of the real frequencies and growth rates of the TAE are slightly larger than those of the RSAE. Finally, electron temperature fluctuations and radial phase shifts from simulations show no significant differences with the experimental data for the strong n = 4 RSAE, but significant differences for the weak n = 6 TAE. The verification and validation for the linear Alfvén eigenmodes is the first step to develop an integrated simulation of energetic particles confinement in burning plasmas incorporating multiple physical processes. Nuclear Fusion

Recent experiments with the DIII-D tilted neutral beam injection (NBI) varying the beam energetic particle (EP) source profiles have provided strong evidence that unstable Alfven eigenmodes (AE) drive stiff EP transport at a critical EP density gradient [Heidbrink et al 2013 Nucl. Fusion 53 093006]. Here the critical gradient is identified by the local AE growth rate being equal to the local ITG/TEM growth rate at the same low toroidal mode number. The growth rates are taken from the gyrokinetic code GYRO. Simulation show that the slowing down beam-like EP distribution has a slightly lower critical gradient than the Maxwellian. The ALPHA EP density transport code [Waltz and Bass 2014 Nucl. Fusion 54 104006], used to validate the model, combines the low-n stiff EP critical density gradient AE mid-core transport with the Angioni et al (2009 Nucl. Fusion 49 055013) energy independent high-n ITG/TEM density transport model controling the central core EP density profile. For the on-axis NBI heated DIII-D shot 146102, while the net loss to the edge is small, about half the birth fast ions are transported from the central core r/a < 0.5 and the central density is about half the slowing down density. These results are in good agreement with experimental fast ion pressure profiles inferred from MSE constrained EFIT equilibria.

Results from experiments on DIII-D [J. L. Luxon, Fusion Sci. Technol. 48, 828 (2005)] aimed at developing high b steady-state operating scenarios with high-q min confirm that fast-ion transport is a critical issue for advanced tokamak development using neutral beam injection current drive. In DIII-D, greater than 11 MW of neutral beam heating power is applied with the intent of maximizing b N and the noninductive current drive. However, in scenarios with q min > 2 that target the typical range of q 95 ¼ 5-7 used in next-step steady-state reactor models, Alfv en eigenmodes cause greater fast-ion transport than classical models predict. This enhanced transport reduces the absorbed neutral beam heating power and current drive and limits the achievable b N . In contrast, similar plasmas except with q min just above 1 have approximately classical fast-ion transport. Experiments that take q min > 3 plasmas to higher b P with q 95 ¼ 11-12 for testing long pulse operation exhibit regimes of better than expected thermal confinement. Compared to the standard high-q min scenario, the high b P cases have shorter slowing-down time and lower rb fast , and this reduces the drive for Alfv enic modes, yielding nearly classical fast-ion transport, high values of normalized confinement, b N , and noninductive current fraction. These results suggest DIII-D might obtain better performance in lower-q 95 , high-q min plasmas using broader neutral beam heating profiles and increased direct electron heating power to lower the drive for Alfv en eigenmodes. V C 2015 AIP Publishing LLC. [http://dx.

The unstable spectrum of Alfvén eigenmodes (AEs) driven by neutral beam-sourced energetic particles (EPs) in a benchmark DIII-D discharge (142111) is calculated in a fully gyrokinetic model using the GYRO code's massively parallel linear eigenvalue solver. One cycle of the slow (equilibrium scale) frequency sweep of the reverse shear Alfvén eigenmode (RSAE) at toroidal mode number