Abstract : In inhomogeneous magnetized plasma, drift-wave (DW) turbulence can generate banded sheared flows, called zonal flows (ZFs), which significantly affect turbulent transport. Since DW wavelengths are typically less than the corresponding ZF scales L, the traditional wave-kinetic theory calculates the DW Hamiltonian under the approximation of infinite L, leading to a geometrical-optics model of DWs as classical quasiparticles. However, this model happens to be inconsistent and, unless modified ad hoc, cannot reproduce important features of ZF-DW interactions. We propose a different approach. By starting with the modified Hasegawa-Mima equation (or alternatively, the modified Terry-Horton equation), we rigorously derive a model in which finite-L corrections are retained and DWs are generally described as quantum particles with finite wavelength. Then, inhomogeneous DW turbulence is understood as effective quantum plasma where the ZF velocity serves as a collective field through which DWs interact [1-5]. The talk will briefly overview this general theory and then focus on its recent applications to the following topics: (i) propagating solitary structures and their relation to ZFs ; (ii) nonlinear oscillations of collisionless ZFs ; (iii) cross-scale interactions in DW turbulence ; and (iv) the Dimits shift .
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 D. E. Ruiz, M. E. Glinsky, and I. Y. Dodin, Wave kinetic equation for inhomogeneous drift-wave turbulence beyond the quasilinear approximation, J. Plasma Phys. 85, 905850101 (2019).
 H. Zhu, Y. Zhou, and I. Y. Dodin, On the structure of the drifton phase space and its relation to the Rayleigh-Kuo criterion of the zonal-flow stability, Phys. Plasmas 25, 072121 (2018).
 H. Zhu, Y. Zhou, D. E. Ruiz, and I. Y. Dodin, Wave kinetics of drift-wave turbulence and zonal flows beyond the ray approximation, Phys. Rev. E 97, 053210 (2018).
 H. Zhu, Y. Zhou, and I. Y. Dodin, On the Rayleigh-Kuo criterion for the tertiary instability of zonal flows, Phys. Plasmas 25, 082121 (2018).
 Y. Zhou, H. Zhu, and I. Y. Dodin, Formation of solitary zonal structures via the modulational instability of drift waves, Plasma Phys. Control. Fusion 61, 075003 (2019).
 H. Zhu, Y. Zhou, and I. Y. Dodin, Nonlinear saturation and oscillations of collisionless zonal flows, arXiv:1902.04970, to appear in New J. Phys.
 yet to be unpublished.