The self-consistent nonlinear interaction of drift waves (DWs) and zonal flow (ZF) is investigated using nonlinear gyrokinetic theory, with both spontaneous excitation and beat-driving of ZF by DWs treated on the same footing. DW solitons are formed in nonlinear DW–ZF interactions and are confined between radially spaced micro-barriers induced by spontaneously excited ZF (SZF). The resulting radial structures in nonlinear DW–ZF interactions exhibit a similar pattern to the 'staircase' observed in numerical simulations. These micro-barriers are generated by the repulsive response due to SZF, which, as a general property demonstrated in this work, also generates an attractive nonlinear potential in the DW equation. Meanwhile, the nonlinear potential due to beat-driven ZF is always attractive and, as such, always serves as a potential well to contribute to soliton formation. For SZF from initial noise, the simultaneous excitation of solitons and micro-barriers is found to be universal due to the zero-frequency nature of ZF and the spatial structure of the Reynolds stress. The present analysis thus provides a potential first-principles-based interpretation of the staircase observed in simulations, which may contribute to the formation of micro transport barriers and enhance plasma confinement.
This paper investigates the nonlinear interaction between drift waves and zonal flow, which can lead to the formation of solitons and micro-barriers, similar to the 'staircase' pattern observed in simulations. The analysis provides a potential first-principles-based interpretation of this phenomenon, which may contribute to the formation of micro transport barriers and enhance plasma confinement.