Excitation of toroidally localized harmonics of global Alfven eigenmodes

The spherical tokamak NSTX and the upgraded, higher toroidal field, NSTX-U, routinely create plasmas with large un-thermalized populations of super-Alfvenic fast ions. This population of non-thermal energetic ions excites a broad spectrum of Alfvenic waves, from the lower frequency (approximate to 30 kHz-approximate to 200 kHz) toroidal Alfven eigenmodes (Cheng and Chance 1986 Phys. Fluids 29 3695), to the higher frequency (400 kHz-3 MHz) global Alfven eigenmodes (GAEs) and compressional Alfven eigenmodes (Goedbloed 1975 Phys. Fluids 18 1258). In this paper we present evidence that the GAE non-linearly excite modes, presumably GAE, at frequencies consistent with non-linear or 3-wave coupling. The observation of the excitation of 2(nd) harmonic GAE through the intrinsic non-linearity of Global Alfven modes demonstrates that the non-linear terms can act as an exciter-antenna inside the plasma, broadcasting at harmonics of the mode frequency and with concomitantly shorter wavelengths. As with experiments using external antenna to excite otherwise weakly stable Alfvenic modes, this data can provide information about the stability of modes at harmonics of the GAE. It may also provide information on the nature of the non-linearities in the wave dispersion equation or a direct measure of the mode amplitude (Smith et al 2006 Phys. Plasmas 13 042504). We also report that the short wavelength 2(nd) harmonic GAE can be strongly toroidally localized. The observation that the shorter wavelength (n approximate to 20) 2(nd) harmonic modes can be toroidally localized potentially has implications for the impact of fast-ion driven instabilities on fast-ion confinement in ITER and future fusion reactors (Gorelenkov et al 2014 Nucl. Fusion 54 125001).