"Realistic characterization of chirping instabilities in tokamaks"

 

 

 

In tokamak plasmas, the dynamics of phase-space structures with their associated frequency chirping is a topic of major interest in connection with mechanisms for fast ion losses. The onset of phase-space holes and clumps which produce chirping phenomena, has been theoretically shown to be related to the emergence of an explosive solution of an integro-differential, nonlocal cubic equation [1,2] that governs the early mode amplitude evolution in the nonlinear regime near marginal stability. We have extended the analysis of the model to quantitatively account for multiple resonance surfaces of a given mode in the presence of drag and diffusion (due to collisions and microturbulence) operators. Then a more realistic criterion is found, that takes into account the details of the mode structure and the variation of transport coefficients in phase space, to determine whether steady state solutions can or cannot exist. Stable steady state solutions indicate that chirping oscillations do not arise, while the lack of steady solutions due to the predominance of drag, is indicative that a frequency chirping response is likely in a plasma. Waves measured in experiments have been analyzed using NOVA and NOVA-K codes, with which we can realistically account for the mode structure and varying resonance responses spread over phase space. In the experiments presently analyzed, compatibility has been found between the theoretical predictions for whether chirping should or should not arise and the experimental observation or lack of observation of Alfvénic eigenmodes in NSTX, DIII-D and TFTR. We have found that stochastic diffusion due to microturbulence is the dominant energetic particle transport mechanism in many plasma experiments, and its strength is the key as to whether chirping solutions are likely to arise.

[1] H L Berk, B N Breizman and M Pekker, PRL 76, 1256 (1996).
[2] M K Lilley, B N Breizman and S E Sharapov, PRL 102, 195003 (2009).