Localized 2^nd Harmonic Global Alfvén Eigenmodes on NSTX(-U)

When GAE are present in NSTX, modes are also commonly observed at the second frequency harmonic. The modes are weak, as would be expected if they were the result of non-linear terms in the wave equation. In the low field, low n shots, the second harmonic GAE wavelengths and frequencies are consistent with expectations from non-linear modeling. However, at higher fields, high toroidal mode number (shorter wavelengths), the qualitative behavior of the 2^nd harmonic GAE becomes more complex. Previous studies have found that the unstable GAE frequencies and toroidal mode numbers scale nearly linearly with toroidal field. The GAE toroidal mode number is < 6 for toroidal field below about 3 kG, and over 10 at the highest toroidal fields reached on NSTX-U of about 6 kG. While the observed frequencies at high field are still consistent with non-linear modeling, the toroidal mode numbers (wavelengths) are not well defined. Rather, the 2^nd harmonic modes, with expected toroidal mode numbers of order 20, become toroidally localized. The toroidal array of magnetic sensors has limited coverage, but the toroidal asymmetry in mode amplitude is quite clear. Conversely, the fundamental ICE instability, with somewhat higher frequencies than the 2^nd harmonic GAE, but lower toroidal mode numbers, is toroidally symmetric within measurement uncertainties. No strong toroidal asymmetries of CAE at similar frequencies with toroidal mode numbers 10 to 14 have been seen. These observations could have an impact on modeling for even Toroidal Alfvén eigenmodes in ITER, as the toroidal mode numbers are expected to be large on ITER.