Experimental and numerical investigation of the Doppler-shifted resonance condition for high frequency Alfvén eigenmodes on ASDEX Upgrade

The Doppler-shifted resonance condition for high frequency Alfvénic eigenmodes has been extensively studied on ASDEX Upgrade in the presence of one or a combination of two neutral beam injected (NBI) fast ion populations. In general, only centrally deposited NBI sources drive these modes, while off-axis sources globally stabilize the mode activity. For the case of a single central NBI source, the observed trend is: the highest frequency modes are driven by the lowest energy and lowest pitch angle NBI sources, in line with the expectation from the Doppler-shifted resonance condition. The expected mode frequencies are determined analytically from the two-fluid cold plasma dispersion relation and the most unstable frequency relation, while the mode growth rates are estimated using the fast ion slowing down distribution functions from the ASCOT code. The overall mode frequency trend in a source-to-source variation is tracked, although a systematic overestimate of ∼1 MHz is observed. Possible causes of this overestimate include the finite size of the resonant fast ion drift orbit and non-linear effects such as mode sideband formation. Alternatively, the expected mode frequencies are determined by tracking the growth rate maxima trajectories, this method improves the agreement with the experimentally measured values. A combination of two central mode-driving NBI sources results in the suppression of the mode driven by the lowest energy and the lowest pitch angle NBI source. Computing the analytically expected mode frequency following the method outlined above, again, generally tracks the experimentally observed trend. The mode's Alfvénic nature allows for a practical application to track the core hydrogen fraction by following the mode frequency changes in response to a varying ion mass density. Such application is demonstrated in a discharge where the average ion mass is varied from ∼2mp to ∼1.5mp (where mp is the proton mass) via a hydrogen puff in a deuterium plasma, in the presence of a strong mode activity. The expected mode frequency changes are computed from the existence of the resonance condition, and the values track the measured results with an offset of ∼0.5 MHz. Overall, the results suggest an intriguing possibility to monitor and control the D-T ion fraction in the core of a fusion reactor in real time using a non-invasive diagnostic.