Damped eigenmode saturation in plasma fluid turbulence

A broad sample of fluid models for instability-driven plasma turbulence is surveyed to determine whether saturation involving damped eigenmodes requires special physics or is a common property of plasma turbulence driven by instability. Previous investigations have focused exclusively on turbulence in the core of tokamak discharges. The models surveyed here apply to a wide range of physical mechanisms for instability, turbulent mode coupling, and parameter regimes, with the common modeling feature that the physics has been reduced to a two-field fluid description. All the models have regimes in which damped eigenmodes saturate the instability by damping the fluctuation energy at a rate comparable to the injection rate by the unstable eigenmode. A test function derived from model parameters is found to predict when damped eigenmodes provide saturation. This confirms that a critical condition for saturation by damped eigenmodes is that the damping rate of the damped eigenmode does not greatly exceed the growth rate. For the quadratic dispersion relation of two-field models, this tends to hold in regimes of stronger instability and for regimes with strong gradients and strong diamagnetic frequency. Nonlinear coupling also matters. Strong coupling can overcome the effects of heavy damping, while weak coupling can prevent a damped eigenmode from saturating turbulence even though it is not heavily damped. This study indicates that damped eigenmodes represent a pervasive mechanism for the saturation of plasma instability in fluid descriptions, complementing recent works showing these effects in comprehensive gyrokinetic models.