Experimental scaling of compressional Alfvén eigenmode stability

Abstract Both co-propagating and counter-propagating compressional Alfvén eigenmodes (CAE) are relatively ubiquitous in NSTX plasmas with toroidal field strengths of ⩽4.65 kG, but are largely absent in the NSTX-U plasmas with toroidal fields of 5.7–5.9 kG. In this paper we will study the co-propagating CAE. We show that the co-propagating CAE are seen with frequencies 0.4 ω ci ⩽ ω CAE ⩽ ω ci (with the exception of a few unique shots), that toroidal mode numbers are relatively high, ranging from 6 ⩽ n ⩽ 17, and that for plasmas with toroidal field greater than about 3.8 kG, are present for ≈2 &lt; V beam / V A &lt; ≈ 4 where V beam is the maximum injected beam velocity and V A is the core Alfvén velocity and V beam / V A is a crude measure of the fraction of beam-ions capable of resonantly exciting Alfvénic modes. Empirically, the prevalence of CAE activity increases for V beam / V A &gt; 2 which is consistent with the relative lack of CAE in the NSTX-U plasmas from the B tor ≈ 5.9 kG shots which typically have V beam / V A &lt; 2. These results suggest that CAE may be largely absent in ITER where V fast / V A &lt; 2 is expected, but may still be present in proposed ST-based fusion devices similar to ARIES-ST or CTF (Tillack et al 2003 Fusion Eng. Des. 65 215, Voss et al 2008 Fusion Eng. Des. 83 1648). There is a weak empirical scaling of toroidal mode number with toroidal field. We explore the nature of the fast-ion resonances with the simple linear eigenmode code CAEk. Calculations with the CAEk code reasonably match the experimental frequencies. From the calculated eigenmodes we find that 0.5 &lt; <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:mrow> <mml:msub> <mml:mi>k</mml:mi> <mml:mrow> <mml:mo stretchy="false">|</mml:mo> <mml:mo stretchy="false">|</mml:mo> </mml:mrow> </mml:msub> </mml:mrow> <mml:mrow> <mml:mo>/</mml:mo> </mml:mrow> <mml:mrow> <mml:mi>k</mml:mi> </mml:mrow> </mml:mrow> </mml:math> &lt; 1. While calculations of fast-ion drive are beyond the capabilities of this code, by coupling the CAEk code to a simple full-orbit code for the fast-ions we can estimate that the co-propagating CAE are primarily resonant with beam fast-ions with energies below ≈30 keV and that there are typically several strong resonances for each mode. We show that the fast-ion distribution as calculated with TRANSP has gradients at the resonant fast-ion parameters potentially capable of providing drive for the modes.