Description
Transport bifurcation and hysteresis remain fundamental challenges for reduced modeling of plasma turbulence. Turbulent transport is not determined solely by external control parameters such as background gradients or flow shear, but depends strongly on the macroscopic turbulent state. Numerical studies of local turbulence systems, including the Hasegawa–Wakatani model and gyrokinetic simulations, have demonstrated the existence of two distinct quasi-stationary turbulent regimes under identical control conditions. This bistability indicates that an additional state variable is required to characterize the effective plasma state and motivates the development of a reduced transport model based on a free-energy framework.
In this work, we construct a reduced transport model based on an effective plasma state variable representing the macroscopic turbulence structure. The turbulent state is described by an effective variable x, whose dynamics are formulated using a Langevin-type stochastic equation. The model is derived from a pseudo free-energy landscape exhibiting a double-well structure near a critical parameter regime. Stochastic forcing represents intrinsic turbulent variability, while nonlinear feedback between turbulence and transport self-consistently determines the effective potential.
The model reproduces key features observed in numerical studies, including hysteresis, stochastic transitions between turbulent states, and long-lived metastable behavior. The framework suggests an analogy with phase-separation dynamics, where evolution is governed by an effective free-energy landscape under stochastic forcing.
The present approach is motivated by the broader challenge of constructing macroscopic transport descriptions from microscopic turbulent dynamics. By introducing an effective free-energy framework for turbulent transport, the model provides a coarse-grained description in which bistability and stochastic transitions emerge naturally from underlying nonlinear interactions. This perspective suggests a possible route toward bridging microscopic turbulence dynamics and global transport modeling. For example, numerical simulations of the proposed model demonstrate that identical particle sources can lead to distinct steady-state density profiles with different evolutionary pathways, reflecting transport bistability and history dependence. The framework thus offers a conceptual basis for describing hysteresis and probabilistic behavior in plasma confinement within a reduced transport formulation.