Collisionless damping of zonal flows

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].

1177eul_100_44_64STD-3small

Simulation of collisionless relaxation of a zonal initial perturbation in the TJ-II geometry (click to watch a video of the simulation in avi format)

References:
[Alonso-12]J. A. Alonso, et. al., Nucl. Fusion, 52, 6, 63010 (2012).

[Biglari-90] H. Biglari, P. H. Diamond, and P. W. Terry, Phys. Fluids B 2, 1 (1990).

[Helander-11] P. Helander et al., Plasma Phys. Control. Fusion 53, 054006 (2011).

[Kleiber-10] R. Kleiber, R. Hatzky, and A. Mishchenko, Contrib. Plasma Phys. 50, 766 (2010).

[Pedrosa-08] M. A. Pedrosa et al., Phys. Rev. Lett. 100, 215003 (2008).

[Rosenbluth-98] M. N. Rosenbluth and F. L. Hinton, Phys. Rev. Lett. 80, 724 (1998).

[Sugama-05] H. Sugama and T. H. Watanabe, Phys. Rev. Lett. 94, 115001 (2005).

[Sugama-06] H. Sugama and T. H. Watanabe, Phys. Plasmas 13, 012501 (2006).