Application of simulations and theory of sub-cyclotron frequency modes to DIII-D

Abstract

Theoretical and numerical study of Alfvén eigenmodes (AEs) in the sub-cyclotron frequency range explains the observed frequency scaling with beam parameters in experiments across different devices. Global Alfvén (GAEs) and compressional Alfvén eigenmodes (CAEs) are frequently excited during neutral beam injection (NBI) in the National Spherical Torus Experiment (NSTX/NSTX-U), as well as other beam-heated devices such as MAST and DIII-D. These modes are driven unstable through the Doppler shifted cyclotron resonance with the NBI ions and can be excited in ITER due to super-Alfvénic velocities and anisotropy of the fast ion distribution. Numerical models and theory for sub-cyclotron frequency modes, previously developed and used to study the excitation of GAEs/CAEs in the NSTX(-U), have been successfully applied to explain the DIII-D observations. Simulations for DIII-D demonstrate that the modes with ω/ωci ≈ 0.6, previously mis-identified as compressional Alfvén eigenmodes, have shear polarization and should be identified as the GAEs. Simulation results match the observed frequencies and estimated toroidal mode numbers in DIII-D experiments. Good agreement is found between scaling of the experimentally observed GAE frequencies with NBI parameters for NSTX, NSTX-U and DIII-D and scaling predicted by the theory and simulations. The DIII-D simulation results also demonstrate that GAEs can be excited for larger aspect-ratio devices and smaller (sub- Alfvénic) beam injection velocities, therefore they can be unstable in ITER.

Hybrid simulations of sub-cyclotron compressional and global Alfvén eigenmode stability in spherical tokamaks

“…For instance, cntr-GAEs were routinely excited in the early operation of NSTX-U [9] with v 0 /v A ≈ 1-2, while co-CAEs were rarely observed. In addition, cntr-propagating sub-cyclotron modes have also been observed in dedicated low-field DIII-D discharges [13,14] with v 0 /v A ≈ 1, in agreement with the corresponding HYM simulations [48].…”

Mode structure measurements of ion cyclotron emission and sub-cyclotron modes on DIII-D

“…Here, the negative sign indicates that these modes are propagating counter to the plasma current and the direction of beam injection. These heuristic estimates assume that the modes are centered about the magnetic axis, though it should be noted that simulations of similar modes on DIII-D indicate that the modes may be extended both radially and poloidally [50][51][52]. As shown in figure 13, the observed toroidal mode numbers n ∈ [−24, −18] are roughly in agreement with the heuristic estimates.…”

“…Consequently, sub-cyclotron modes cannot be distinguished between shear and compressional modes on the basis of edge polarization measurements alone. More definitive identification can be achieved by appealing to the resonance condition, dispersion relation, and/or more sophisticated modeling, which concluded that sub-cyclotron modes in DIII-D were most likely GAEs [45,52].…”

“…Sub-cyclotron mode structure has been more widely explored in literature than ICE and can serve as a benchmark to ensure that our toroidal mode number calculation technique is sound. Considering the same case as depicted in figure 10(a) and assuming these are GAEs as per previous DIII-D studies in comparable conditions [45,49,50,52], heuristic estimates can be made for the expected toroidal mode numbers. As derived in the appendix, the two-fluid dispersion relation for shear waves gives:…”

“…While these sub-cyclotron modes are more commonly observed on spherical tokamaks such as NSTX(-U) [41,42] and MAST [43] due to their large super-Alfvénic fast ion populations, they have also been detected in conventional tokamaks such as DIII-D [44,45], AUG [46], and JT-60U [47], especially at lower magnetic field strengths. Detailed measurements and realistic simulations have previously been performed for sub-cyclotron modes on other devices, most notably NSTX [48][49][50][51][52], providing reference points for the new DIII-D measurements discussed here. Hence, while the main focus of this paper is to investigate the spatial mode structure of ICE, measurements of sub-cyclotron modes in DIII-D will also be presented in order to clarify the similarities and differences between these two closely related classes of instabilities.…”