Damped eigenmode saturation in plasma fluid turbulence

Abstract

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.

Role of subdominant stable modes in plasma microturbulence

“…19 From analysis of a diverse set of instability models, it has been established that damped eigenmode excitation is intrinsic to many physical systems and parameter regimes. 16 The question of whether the damped eigenmode physics of reduced fluid models extends to comprehensive models like gyrokinetics is one of the motivations for the present work. This paper will proceed as follows: In Sec.…”

“…[15][16][17][18][19] Simple fluid models with only two or three eigenmodes permit detailed nonlinear analysis. These studies established that any damped root of the linear dispersion relation is universally excited by nonlinear mode coupling and grows exponentially from an initial state in which amplitudes are infinitesimally small.…”

Validation metrics for turbulent plasma transport

“…Through this and other nonlinear processes, energy is transferred from linearly unstable modes (generally with small k x ) to stable modes at a variety of different wavenumbers, [161][162][163] saturating the turbulence and generally resulting in a wavenumber spectrum broad in both k x and k y . Therefore, if we want to test whether a given model is accurately capturing the nonlinear dynamics of the turbulence at an even deeper level than the frequency-based comparisons above allow, we should first examine the fidelity of the model in capturing this wavenumber spectrum.…”

On secondary and tertiary instability in electromagnetic plasma microturbulence

“…To understand the zonal flow dynamics quantitatively, however, both their drive and their depletion mechanisms have to be considered. The latter, in the form of nonlinear mode interaction [27][28][29] or the action of magnetic perturbations on the residual flow [5,30,31], is counteracted by the former: the energy transfer from the linear mode to the zonal mode via sidebands-a process often referred to as secondary instability, as zonal flows saturate the linear mode at the onset of turbulence. The growth rate of the secondary instability gives valuable insights into the zonal flow picture, and its dependence on β is one of the primary subjects of this paper.…”