Edge Turbulence and its Interaction with the Equilibrium

Abstract

Tokamak edge turbulence is studied using three dimensional computations in a transcollisional, electromagnetic gyrofluid model. All scales between the ion gyroradius and the profile scale length are carried for up to the transport time scale. Profiles and the MHD equilibrium are time dependently self consistent. Basic properties of the turbulence are shown. Zonal flows are compressible and not in equilibrium, though the electric field profile on larger scales is indeed in equilibrium. Edge turbulence in the closed field line region maintains its character whether a scrape-off layer is present, though in the SOL region it becomes interchange like. Divertor separatrix topology is briefly considered, with little effect on the general turbulence/equilibrium situation. Basic situation of the tokamak edgeThe physical situation of the tokamak edge is defined by its parameters. The profile scale length L ⊥ is very short compared to the minor and major radii a and R and therefore the scale ratios L ⊥ /qR and 2L ⊥ /R which determine the general roles of the parallel dynamics and the toroidal interchange forcing are very small. Drift wave turbulence occupies mostly the perpendicular wavenumber range 0.1 > k ⊥ ρ s > 1 and involves frequencies in the range of the diamagnetic frequency at each scale, or about 0.1 to 1 times c s /L ⊥ [1,2]. Here, c s is the acoustic sound speed and ρ s is the ion sound gyroradius. The parallel wavenumber range is limited by the flux surface geometry to k qR ∼ 1 as larger values involve stronger dissipation/damping [2] and smaller values are disallowed by the geometry, specifically field line connection [3]. Due to the small size of L ⊥ /qR the electron thermal transit is not arbitrarily fast; indeed the statementμ ≡ (m e /M i )(qR/L ⊥ ) 2 > 1 essentially defines the edge region in which strongly nonadiabatic electron dynamics is expected [4,5]. The drift wave collisionality given by C = (0.51ν e L ⊥ /c s )μ is also larger than unity, so that the physics of collisional drift wave turbulence [2] and its associated self sustained turbulence nonlinear instability [6,7] enters. In modern tokamaks the edge pressure is large enough to make the drift Alfvén parameterβ = (4πp e /B2 )(qR/L ⊥ ) 2 also larger than unity, so that the drift wave physics becomes electromagnetic [8]. These features together all lead one to expect a robust physical situation in which none of the familiar restrictive limits (linearity, electrostatic adiabatic electrons, or even MHD) are applicable.This also applies to scale separation. While it is still reasonable to study edge turbulence within a local model in order to diagnose its basic character, the drift parameter δ = ρ s /L ⊥ is typically larger than 10 −2 , so that the longer wavelength component of the drift wave spectrum runs up against the limits placed by the scale length. Here, electromagnetic drift wave turbulence runs into the MHD equilibrium itself, as defined by the balances describing the Pfirsch-Schlüter currents. Indeed, as the turbulence drives zonal ExB fl...

High sensitive vectorial $\dot{B}$Ḃ-probe for low frequency plasma waves

“…These findings are in agreement with the local slab model of drift waves, where parallel currents are driven by parallel pressure gradients [19]. A quantitative analysis of the parallel force balance equation [20] in the given collisional low-temperature plasma of Vineta reveals the observation as so-called electrostatic drift waves.…”

On the phase velocity in between weak and strong plasma edge turbulence

“…Simulations for a circular plasma cross-section with toroidal axisymmetry have been carried out with the three-dimensional gyrofluid electromagnetic turbulence model GEMR [36,37]. GEMR simulates the densities, parallel velocities, parallel and perpendicular temperatures, and parallel and perpendicular parallel heat fluxes for ions and electrons, respectively.…”

Turbulent transport across shear layers in magnetically confined plasmas

“…However, the ejection mechanism of plasma blobs can only be observed in simulations with self-consistently generated instead of seeded blobs. Such a simulation is provided by the three-dimensional gyrofluid turbulence model GEMR [26]. The GEMR model assumes a circular cross-section with toroidal axisymmetry.…”

“…Drift waves preferentially propagate in the poloidal direction and not in the radial one across the shear layer as interchange modes do. In this presentation, experimental data which in the present detail can only be obtained in a low temperature plasma device as the one in the TJ-K stellerator [25], and gyrofluid simulations carried out with the GEMR code [26] are studied to develop a drift-wave based model for blob ejection consistent with the recent observations in the high temperature plasmas in ASDEX Upgrade, Alcator C-Mod and TJ-II [20][21][22].…”