Axisymmetric global Alfvén eigenmodes in the TCV tokamak

Global Alfvén eigenmodes (GAEs) with toroidal mode number n=0 (i.e., axisymmetric) have been observed in the toroidicity-induced, ellipticity-induced, and above non-circularity-induced frequency ranges in the TCV tokamak. The observed periodicity of the n=0 GAEs, caused by the periodic structure of the Alfvén continuum, demonstrates the fundamental nature of these modes. A radial splitting of the n=0 GAEs has been observed. This observation is consistent with the recently observed radial splitting of GAEs in the sub-cyclotron frequency range. Linear MHD codes were used to compute the n=0 Alfvén continuum and the corresponding eigenmode structures. The modeling confirms that the n=0 GAEs are located only below the minima of the Alfvén continuum, in contrast to the sub-cyclotron-frequency GAEs, for which modes above the continuum maxima are also observed. The n=0 GAEs have been observed in a variety of discharge types, including low- and high-density plasmas, positive- and negative-triangularity configurations, and discharges with neutral beam injection in both co-current and counter-current directions. A key factor for the appearance of n=0 GAEs is a positive gradient in the particle energy distribution function, ∂f/∂E>0 (bump-on-tail), which has been confirmed by TRANSP calculations for all discharges.