One-dimensional modelling of limit-cycle oscillation and H-mode power scaling

Abstract

To understand the connection between the dynamics of microscopic turbulence and the macroscale power scaling in the L-I-H transition in magnetically confined plasmas, a new time-dependent, one-dimensional (in radius) model has been developed. The model investigates the radial force balance equation at the edge region of the plasma and applies the quenching effect of turbulence via the E × B flow shear rate exceeding the shear suppression threshold. By slightly ramping up the heating power, the spatio-temporal evolution of turbulence intensity, density and pressure profiles, poloidal flow and E × B flow selfconsistently displays the L-H transition with an intermediate phase (I-phase) characterized by limit-cycle oscillations. Since the poloidal flow is partially damped to the neoclassical flow in the edge region, the numerical results reveal two different oscillation relationships between the E × B flow and the turbulence intensity depending on which oscillation of the diamagnetic flow or poloidal flow is dominant. Specifically, by including the effects of boundary conditions of density and temperature, the model results in a linear dependence of the H-mode access power on the density and magnetic field. These results imply that the microscopic turbulence dynamics and the macroscale power scaling for the L-H transition are strongly connected.

The role of turbulence–flow interactions in L- to H-mode transition dynamics: recent progress

“…An additional complication is the treatment of the transition between the closed and open field-line region requiring correct implementation of sheath boundary conditions for the SOL. Several modeling results show a poloidal flow increase concomitantly with an ion pressure-gradient increase at the transition [64,65]. Other simulations results do not show a clearly separated trigger signature in advance of the increase in the pressure gradient/diamagnetic flow [70].…”

“…This condition depends on the Reynolds stress, the flow-damping rate, and the pressure-gradient scale length. A rigorous analysis of the predator-prey system described in [26] can be found in the literature [65,78] but is beyond the scope of this paper. However, a simple model for the energy exchange between turbulence and flows is discussed in section 5.…”

“…1D models have recently also been used to investigate L-H power-threshold scaling [60,65]. 2D and 3D fluid models [66][67][68][69][70][71][72][73], mostly in simplified slab or toroidal slab geometry, have been used to model the L-H transition sequence for high collisionality regimes, with equation systems appropriate for interchange or resistive ballooning turbulence.…”

Study on the L–H transition power threshold with RF heating and lithium-wall coating on EAST

“…These results suggest that the transition behaviour might be different even if input power is marginal to the transition threshold. A recent numerical approach of transition dynamics ( [43], and references therein), which demonstrated that LCOs appear when the input power is close to the transition threshold, should take more variations into consideration. This may not be the effect of the wall changes, since the wall material in the divertor was unchanged and heavy lithium wall coating was conducted in both campaigns.…”

Sparse identification of a predator-prey system from simulation data of a convection model

“…Ordinary differential equation (ODE) models for the L-H transition are based on the predator-prey relationship between zonal flow and turbulent flow, and incorporate a potential energy related to the pressure profile as an additional state variable [4][5][6][7][8][9][10][11][12] . Miki et al 13 and Wu et al 14 have both suggested 1D partial differential equation (PDE) models for the L-H transition based on this predator-prey relationship.…”