Drift wave solitons and zonal flow: implications for staircase formation

Abstract 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 <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:mrow> <mml:mi mathvariant="bold">E</mml:mi> </mml:mrow> <mml:mo>×</mml:mo> <mml:mrow> <mml:mi mathvariant="bold">B</mml:mi> </mml:mrow> </mml:mrow> </mml:math> ‘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 <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:mrow> <mml:mi mathvariant="bold">E</mml:mi> </mml:mrow> <mml:mo>×</mml:mo> <mml:mrow> <mml:mi mathvariant="bold">B</mml:mi> </mml:mrow> </mml:mrow> </mml:math> staircase observed in simulations, which may contribute to the formation of micro transport barriers and enhance plasma confinement.