Nonlinear interaction and turbulence transition in the limiting regimes of plasma edge turbulence
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RESEARCH
Nonlinear interaction and turbulence transition in the limiting regimes of plasma edge turbulence Di Qi
and Andrew J. Majda
* Correspondence:
[email protected] Department of Mathematics and Center for Atmosphere and Ocean Science, Courant Institute of Mathematical Sciences, New York University, New York, NY 10012, USA
Abstract We study the nonlinear coupling mechanism and turbulent transition in magnetically confined plasma flows based on two representative limiting regime dynamics. The two-field flux-balanced Hasegawa–Wakatani (BHW) model is taken as a simplified approximation to the key physical processes in the energy-conserving nonlinear plasma flows. The limiting regimes separate the effects of finite non-adiabatic resistivity and extreme non-normal dynamics to enable a more detailed investigation on each individual aspect with the help of various mathematical tools. We adopt the strategy from the selective decay theory used for the simpler one-field system to develop new crucial a priori estimations in the two-field model framework. The competing effects from model dissipation, finite particle resistivity, as well as the nonlinear interaction with a zonal mean state to induce dual direction energy transports are characterized from the systematic analysis. Non-normal dynamics with aligned eigendirections is also shown to go through a sharp transition from turbulence to regularized zonal flows. The diverse phenomena implied from the limiting regime analysis are further confirmed from direct numerical simulations of the BHW model.
1 Introduction Nonlinear interactions between the turbulent non-zonal waves and the self-organized zonal flow play a critical role in many observed phenomena from natural and experimental systems [9,10,13,17,19]. One example of particular interest comes from the generation and development of turbulent transport in the edge regime of toroidal magnetically confined plasmas [2,3,5,8,14]. The nonlinear exchange of energy among wide scales can be developed from secondary instability and lead to the emergence of persistent large-scale zonal structures from the turbulent transition [21,22]. This phenomenon is also related with the Dimits shift [4,25,28] which refers to a nonlinear upshift in the amplitude of the turbulent flow transport. To understand the fundamental physics in such complex nonlinear systems is crucial with significant practical importance such as the achievement of controlled fusion; thus, it still attracts extensive researches in theoretical and numerical exploration of the mechanisms in representative fusion plasma phenomena [1,11,12,26].
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D. Qi, A. J. Majda Res Math Sci (2020)7:22
The use of simplified model framework plays an important role in identifying the key physical constituents for the analysis of plasma confinement and anomalous transport. Among them, the one-field Hasegawa–Mima (HM) [2,6] and the two-field Hasegawa– Wakatani (HW) [7,18,27] models provide simplified formulations for t
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