Subdominant modes and optimization trends of DIII-D reverse magnetic shear configurations**This manuscript has been authored by UT-Battelle, LLC under Contract No. DE-AC05- 00OR22725 with the U.S. Department of Energy. The United States Government retains and the publisher, by accepting the article for publication, acknowledges that the United States Government retains a non-exclusive, paid-up, irrevocable, world-wide license to publish or reproduce

Abstract

Alfvén Eigenmodes (AE) and magneto-hydrodynamic (MHD) modes are destabilized in DIII-D reverse magnetic shear configurations and may limit the performance of the device. We use the reduced MHD equations in a full 3D system, coupled with equations of density and parallel velocity moments for the energetic particles (with gyro-fluid closures) as well as the geodesic acoustic wave dynamics, to study the properties of instabilities observed in DIII-D reverse magnetic shear discharges. The aim of the study consists in finding ways to avoid or minimize MHD and AE activity for different magnetic field configurations and neutral beam injection (NBI) operational regimes. The simulations show at the beginning of the discharge, before the reverse shear region is formed, a plasma that is AE unstable and marginally MHD stable. As soon as the reverse shear region appears, ideal MHD modes are destabilized with a larger growth rate than the AEs. Both MHD modes and AEs coexist during the discharge, although the MHD modes are more unstable as the reverse shear region deepens. The simulations indicate the destabilization of Beta induced AE (BAE), Toroidal AE (TAE), elliptical AE (EAE) and reverse shear AE (RSAE) at different phases of the discharges, showing a reasonable agreement between the frequency range of the dominant modes in the simulations and the diagnostic measurements. A further analysis of the NBI operational regime indicates that the AE stability can be improved if the NBI injection is off axis, because on-axis injection leads to AEs with larger growth rate and frequency. In addition, decreasing the beam energy or increasing the NBI relative density (the ratio between the energetic particle and thermal plasma density) leads to AEs with larger growth rate and frequency, so an NBI operation in the weakly resonant regime requires higher beam energies than in the experiment (). The MHD linear stability can be also improved if the reverse shear region and the q profile near the magnetic axis are in between the rational surfaces q = 2 and q = 1, particularly if there is a region in the core with negative shear, avoiding a flat q profile near the magnetic axis. The simulations also show a smooth transition between MHD modes and low frequency AE, no critical , pointing out an overlap between MHD and AE activity for modes with frequencies lower than 30 kHz. This is in the range of beta acoustic Alfven eigenmodes (BAAE) and BAE.