7th Asia-Pacific Conference on Plasma Physics, 12-17 Nov, 2023 at Port Messe Nagoya

Roles of phase space turbulence related to zonal flows
in magnetically confined plasmas
M. Sasaki1, M. Nakata2, K. Itoh3, 4 , T. Kobayashi2, H.Arakawa5
1
College of Industrial Technology, Nihon University, 2 National Institute for Fusion Science,
3
Frontier Research Institute, Chubu University, 4 Research Center for Plasma Turbulence, Kyushu
University, 5 Faculty of Medical Sciences, Kyushu University
e-mail (speaker): sasaki.makoto@nihon-u.ac.jp
Transport of particle and heat in magneticallyconfined plasmas is dominated by the nonlinear
evolution of turbulence. Drift wave type turbulence,
which is driven by the inhomogeneities of density andtemperature, has a quasi-two-dimensional structure; it
has the long/short wavelength along/perpendicular to themagnetic field [1]. Such turbulence nonlinearly drives
larger scale structures, such as zonal flows and streamers[2]. The spatio-temporal dynamics of turbulence isdominated by the zonal flows and the streamers.
Consequently, abrupt transport, ballistic propagation[3-5] or formation of stationary (long-lived) corrugationsof plasma profiles occur [6, 7]. In this study, thefundamental processes which trigger these various
turbulence behaviors is focused on by considering thenonlinear interaction between turbulence and larger scale
structures theoretically.
Wave-kinetic theory is one of the theoreticalframeworks to treat the interaction between the
turbulence and the larger scale structures [2]. In thisframework, the turbulence wave-packet is treated as aquasi-particle, and its distribution function in the phasespace is considered, where the phase space consists of
the wavenumber space and real space. Namely, thewavenumber spectrum of turbulence intensity which
distributes in space is obtained by solving thewave-kinetic equation. The evolution equation for the
turbulence distribution function has a same mathematicalstructure as the Boltzmann equation. Turbulent
quasi-particles propagate at group velocities determinedby the drift wave dispersion relation and are subject toeddy stretching effect due to the spatial inhomogeneous
Doppler shifts caused by the macroscopic structures. A
mechanism of the particle trapping by electrostatic
potentials exists for the Boltzmann equation, and thetypical vortex structure called BGK vortex exits in thephase space. Similarly, the turbulence trapping occurs forthe wave-kinetics. In this study, the turbulence trappingin the phase space is focused on, and the resulting
turbulence dynamics is discussed.
The interaction between the turbulence and the zonal
flows is considered by performing the direct numericalsimulation of the wave-kinetics. The zonal flows havethe shear in the radial direction, so that the turbulence
eddy suffers the stretching effect, and the turbulence
trapping occurs. The turbulence trapping in the phasespace corresponds to the phase locking of turbulenceclump in the zonal flow. For the cases of the drift wave

Fig.1: Spatio-temporal dynamics of turbulence
intensity for cases of ZF (left) and GAM (right).
turbulence, the turbulence clump accumulates in thenegative curvature (2nd radial derivatives) of the zonal
flow, and the exclusion of turbulence occurs in thepositive curvature region. Similar asymmetry ofturbulence with respect to the sign of flow curvature canbe seen in turbulence simulations e.g. [9]. In toroidal
plasmas, there are two zonal flow branches;
non-oscillation branch of stationary zonal flows (ZFs),
and the oscillation branch of geodesic acoustic modes(GAMs). Based on the turbulence trapping, theturbulence behavior is very different in each state. For
the ZFs case, the turbulence clump is spatially localized,
because the ZFs does not propagate in space (left panelof Fig. 1). As a result, the stationary profile corrugation
occurs [6]. On the other hand, for the case of the GAMs,which propagate radially, the ballistic propagation ofturbulence is driven, like avalanches [5], as shown in theright panel of Fig. 1. In this way, the vortex formation in
the phase space drastically affects the spatio-temporal
dynamics of turbulence.
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[3] F. Kin, et. al., Phys. Plasmas, 26, 4 (2019).
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[5] M. Sasaki, et. al., Sci. Rep., 7, 16767 (2017).
[6] M. Sasaki, et. al., Phys. Plasmas, 28, 11 (2021).
[7] X. Garbet, et. al., Phys. Plasmas, 28, 4 (2021).
[8] P. Kaw, et. al., PPCF 44, 51 (2001).
[9] G. Dif-Pradalier, et. al., Phys. Rev. Lett., 114, 085004(2015).