Kim and Diamond predicted that the transition from L-mode to H-mode can be explained by an intermediate, quasi-periodic transient stage, where turbulence, zonal flow, mean shear flow and the pressure gradient are coupled. In particular the interaction between turbulence and shear flows is important for the L-H transition. Increasing the heating power does not lead to an enhancement of the pressure gradient in L-mode. Instead only the fluctuation level of the turbulence increases. With increasing fluctuation level also the drive of the zonal flow increases. At some point the drive overcomes the zonal flow damping rate. A finite zonal flow then begins to grow and extract kinetic energy from the turbulence and thereby acts to suppress the turbulence amplitude. This leads to saturation of the turbulence. However, as turbulence is suppressed the zonal flow drive also reduces. For input powers just below the transition threshold, self-regulation between turbulence and
zonal flows occurs as an oscillatory behavior, characteristic for predator-prey systems. These predator-prey oscillations have been observed in various devices at the L-H transition.

A turbulence suppression criterion was established which states that turbulence is suppressed when the energy transfer rate from the turbulence into the shear flow exceeds the effective growth rate of turbulence. In this case, the turbulence collapses. This criterion was confirmed in experiments in EAST, DIII-D and Alcator C-mod.

In ASDEX Upgrade the limit.cycle oscillations (LCOs) close to the L-H transition were studied in detail. In ASDEX Upgrade, the regime at the L-H transition is called the I-phase. The magnetic signature of the I-phase was studied and scaling laws for the frequency were established. It was also shown that the predator-prey oscillations are not governed by the interaction between turbulence and zonal flows, but by that between turbulence and the flow associated with the background ion pressure gradient. This is also consistent with the magnetic signature, which can be explained via the stringer-spin up. However, the difference between zonal flow and ExB background shear does not really make a difference for the turbulence suppression due to energy transfer. Therefore, the turbulence suppression criterion holds here as well.     

relevant publications

T.Eich, P.Manz 'The separatrix operational space of ASDEX Upgrade due to interchange-drift-Alfvén turbulence', Nuclear Fusion 61, 086017 (2021)

P. Manz et al. 'Zonal flow triggers the L-H transition in the Experimental Advanced Superconducting Tokamak' Physics of Plasmas 19, 072311 (2012)

G.R. Tynan et al. 'Turbulent-driven low-frequency sheared E × B flows as the trigger for the H-mode transition' Nucl. Fusion 53 073053 (2013)

M. Cavedon et al 'Interplay between turbulence, neoclassical and zonal flows during the transition from low to high confinement mode at ASDEX Upgrade' Nucl. Fusion 57 014002 (2017)

G. Birkenmeier et al 'Magnetic structure and frequency scaling of limit-cycle oscillations close to L- to H-mode transitions' Nucl. Fusion 56 086009 (2016)

P. Manz et al. 'Poloidal asymmetric flow and current relaxation of ballooned transport during I-phase in ASDEX Upgrade' Physics of Plasmas 23, 052302 (2016)

O. Grover, T. Eich, P. Manz et al. 'Reduced model for H-mode sustainment in unfavorable ∇B drift configuration in ASDEX Upgrade', Nuclear Fusion 64, 056020 (2024)

O. Grover, P. Manz et al. 'Experimentally corroborated model of pressure relaxation limit cycle oscillations in the vicinity of the transition to high confinement in tokamaks', Nuclear Fusion 64, 026001 (2024)

M.Xu et al. 'Frequency-Resolved Nonlinear Turbulent Energy Transfer into Zonal Flows in Strongly Heated L-Mode Plasmas in the HL-2A Tokamak' Phys. Rev. Lett. 108, 245001 (2012)

G.S. Xu et al. 'Dynamics of L–H transition and I-phase in EAST'  Nucl. Fusion 54 103002 (2014)

G.S. Xu et al. 'Study of the L–I–H transition with a new dual gas puff imaging system in the EAST superconducting tokamak' Nucl. Fusion 54 013007 (2014)