The importance of zonal flows for the self-regulation of turbulence in fusion plasmas and the concomitant transport reduction is generally recognized. The understanding of the regulating effect of sheared flows gave rise to the shear decorrelation paradigm [Biglari-90]. Zonal flows can be generated by the non-linear interaction of unstable modes and are expected to be eventually damped by collisional (neoclassical) processes. For times short in comparison to the collision time or in hot, low-collisionality plasmas, the non-collisional limit is relevant. The damping of zonal flows in the collisionless limit was first tackled from the analytical point of view by Rosenbluth and Hinton in the axisymmetric case [Rosenbluth-98] and more recently the theory of non-collisional damping of zonal flows has been developed for helical devices [Sugama-05, Sugama-06]. The theory was further extended for any stellarator [Mishchenko-08, Kleiber-10, Helander-11], finding that, depending on the magnetic geometry, several oscillation frequencies appear in the linear relaxation of the system. We aim to understand the collisionless damping of zonal flows in TJ-II and its possible connection with recent experimental measurements of long-range correlations [Pedrosa-08, Alonso-12].
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