Gyrokinetic theory represents a significant step towards achieving accurate simulations of microturbulence in magnetized plasmas [Garbet-10]. The periodic motion of a charged particle around the magnetic field line is averaged out rigorously, keeping the effect of the small Larmor radius. In this way the computing resources required are largely reduced. This allows accurate simulations of microturbulence of spatial scales larger than Larmor radius, for which the typical timescales are much larger that the gyrofrequency.

The computer code used at the Laboratorio Nacional de Fusión (LNF) is called EUTERPE [Jost-00, Kornilov-04, Kleiber-12], a global non-linear electromagnetic gyrokinetic code developed and maintained at the Max-Planck-Institut für Plasmaphysik at Greifswald with the distinctive feature that it has been designed to

allow any magnetic configuration whose MHD equilibrium can be computed by VMEC [Hirshman-98]. Thus, it is the appropriate tool for microturbulence simulations in TJ-II, which has a complicated magnetic geometry.

Within the framework of this project we study the following topics by means of gyrokinetic simulations:

**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. 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].

**Microinstabilities in TJ-II.** The density and temperature gradients in fusion plasmas constitute sources of free energy that trigger the development of different instabilities: Ion Temperature Gradient (ITG), Electron Temperature Gradient (ETG), Trapped Electron Modes (TEM), among them. Each instability possesses different signatures and effects [Horton-99]. One of the objectives of this research project is to clarify the applicability of gyrokinetic simulations to each region and type of TJ-II plasmas and characterize the existing instabilities.

**Numerical investigation of basic statistical features of microturbulence.** Recent analytical results on gyrokinetic absolute statistical equilibria [Zhu-10] and analytically derived phenomenological laws à la Kolmogorov [Barnes-11] might give new insights on the statistical features of the gyrokinetic turbulent state. Also the results of [R. Sánchez-08] deserve to be mentioned, where the transport of tracer particles across a sheared zonal flow in certain gyrokinetic simulations was found to be subdiffusive and Lévy. We will try to gain deeper understanding of these new findings in the course of the project.

**References:**

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

[Barnes-11] M. Barnes et al., Phys. Rev. Lett. 107, 115003 (2011).

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

[Garbet-10] X. Garbet, Y. Idomura, L. Villard, and T. H. Watanabe, Nucl. Fusion 50, 043002 (2010).

[Hirshman-98] S. P. Hirshman and J. Breslau, Phys. Plasmas 5, 2664 (1998).

[Horton-99] W. Horton, Rev. Mod. Phys. 71, 735 (1999).

[Jost-00] G. Jost, Simulation particulaires d’ondes de dérive dans des configurations magnétiques 3D, PhD dissertation, École Polytechnique Fédérale de Lausanne, 2000.

[Kornilov-04] V. Kornilov et al., Phys. Plasmas 11, 3196 (2004).

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

[Kleiber-12] R. Kleiber and R. Hatzky. Comput. Phys. Commun., 183, 2, 305–308 (2012).

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

[R. Sánchez-08] R. Sánchez et al., Phys. Rev. Lett. 101, 205002 (2008).

[Zhu-10] J. Z. Zhu and G. W. Hammett. Phys. Plasmas 17, 122307 (2010).