The full-wave effects behind the predator-prey oscillations and its relation to the finite Dimits shift

As known commonly, some drift-wave (DW) turbulence can be suppressed above the linear threshold of homogeneous-plasma "primary" instabilities. This threshold modification, called the Dimits shift, is attributed to the secondary instability, which drains out the turbulence energy by spontaneously forming zonal flows (ZFs). The finite value of the Dimits shift is often explained in terms of the tertiary instability (TI), which makes intense ZFs unstable. However, the TI theory does not explain the so-called predator-prey oscillations in the DW--ZF system. We present an analytical model and quasilinear simulations of the predator-prey oscillations using a quantumlike Wigner--Moyal formalism [Zhu et al., PRE 97, 053210 (2018)]. We show that these oscillations can be governed by full-wave effects and thus may not be adequately captured by the wave kinetic equations, contrary to some literature. In particular, the predator-prey oscillations occur only when the ZF scale is less than the ion sound radius. The influence of these oscillations on the ZF saturation and the Dimits shift is discussed.