Zonal flow hysteresis from wave-flow resonances in forced Hasegawa-Mima turbulence

We show that drift wave-zonal flow resonances induce bistability of zonal flows. Consequently, zonal flow exhibits hysteresis under cyclic forcing. This is demonstrated employing the simplest model of plasma turbulence, i.e., the forced Hasegawa-Mima (HM) system. Notice that the HM system has no natural instabilities, hence an external forcing is required. Similar behavior of zonal flows due to wave-flow resonances is expected to emerge in more physical model systems, hosting spontaneous instabilities like the Hasegawa-Wakatani model for resistive drift wave turbulence driven by density gradient and plasma resistivity or more complex three-field reactive fluid models for ion temperature gradient driven turbulence, etc., under cyclic variation of the free-energy source. This hysteresis is distinct from the L-H transition hysteresis observed during cyclic input power ramp, which results as a consequence of the bistability of the mean radial electric field in tokamaks.