Scrape-off Layer Width Research Articles

Theoretical understanding of turbulent transport in the SOL

Turbulence in the scrape-off layer (SOL) is investigated using a 2D fluid model for the interchange instability as a paradigm. A constant driving flux governs the dynamics of both the equilibrium and fluctuating parts of the density and electric potential. The turbulent flux exhibits intermittent bursts, called avalanches. These events account for a significant part of the total transport, and are manifested as poloidally localized density fingers, extending towards the far SOL. The time averaged density profile looks exponential, and the SOL width increases weakly with the driving source (scaling exponent 2/9). Viscosity is found to govern the characteristic radial size of convective cells, which in turn control the transport magnitude. The larger ν, the larger the turbulent transport. Finally, the impact on turbulence of local biasing is investigated, possibly modeling Langmuir probe measurements. For a too large extent of the theoretical probe, the density drops by factors at the probe, due to the local build up of a screening vortex. The ambient density is recovered for a sufficiently small probe. In this case, fluctuations exhibit a similar Fourier spectrum at and next to the probe, though the probe still misses a significant number of large bursts. Finally, the experimental probe characteristics are recovered qualitatively when varying the biasing potential.

SOL width scaling from consideration of edge transport in tokamaks

A simple two-point representation of the tokamak scrape-off layer (SOL), based on the parallel and perpendicular energy balance equations, has been used to develop heat flux width scalings for a wide variety of χ ⊥ models in terms of B φ , n sep, q 95, P SOL, R and a. These scalings have been tested against databases of SOL parameters established on COMPASS-D (which exhibits a collisionless SOL), JET Mk IIa divertor and Alcator C-MOD (both of which exhibit strongly collisional SOLs). The better fit scalings to the collisionless dataset all show a positive dependence of SOL width on q 95 and an inverse dependence on n sep. Four of the better fit scalings also show a positive dependence on P SOL and a strong inverse dependance on B φ . In the collisional case a group of 5 models, each with a χ ⊥∝ T 1/2/ n dependence, provide the better fit scalings to both collisional datasets. The derived scalings exhibit a strong inverse dependence on P SOL but are independent of B φ , unlike scalings derived from the commonly used Bohm diffusion model, and four of the five are also independent of n sep.

Behaviour of upstream separatrix density in JET H-mode plasmas

The variation of n Sep e / n e in JET H-modes is described. The upstream separatrix density, n Sep e, was determined using total pressure balance, in conjunction with `onion-skin' modelling and reciprocating Langmuir probe measurements. It was found that the ratio n Sep e / n e was strongly influenced by ELM frequency increasing, proportional to the rate of particle loss to the scrape-off layer (SOL) from ELMs, towards the pedestal density and then saturating. The initial n Sep e / n e ratio and rate of increase were different for horizontal and vertical target configurations with the latter having an initial n Sep e / n e ratio of 0.12. Related information on the behaviour of the density SOL width and the variation of n Sep e / n e with confinement are also presented.

Comparison of theoretical models for scrape-off layer widths with data from COMPASS-D, JET and Alcator C-Mod

The features of a number of theoretical models proposed to explain the cross-field transport in the SOL are summarized. Simple balances of transport parallel and perpendicular to the magnetic field in the SOL allow the derivation of predictions from these models for the power law scalings of the SOL width Δ with the plasma parameters in the two cases of a collisionless and a collisional SOL. Data on the SOL widths for a collisionless SOL from COMPASS-D and for a collisional SOL from JET and Alcator C-Mod are then used to test these models. Remarkably, the data from COMPASS-D, JET and Alcator C-Mod all favour the same small subset of these models. Furthermore, direct comparisons of the theoretical models for the cross-field thermal diffusivities with SOL data from JET and Alcator C-Mod provide some support for this finding. These `best models' can be used to make predictions for MAST, the spherical tokamak at Culham Science Centre, and for ITER.

On defining scrape-off layer widths

A physically motivated, theoretical basis for defining scrape-off layer (SOL) widths is proposed. Applying it to theoretical models proposed for transport in the SOL shows how the width is affected by the form of the cross-field transport and the parallel transport to target plates. For a cross-field diffusivity and a parallel loss time , the estimate , with C typically in the range 0.6-1.0 and and evaluated at the SOL-core interface, is found to provide a physically meaningful and accurate expression for the power SOL width .

Intermittent particle transport in two-dimensional edge turbulence

Interchange turbulence in two dimensions is investigated in the scrape-off layer (SOL) of fusion devices, when driven by a constant core particle influx. Contrary to the standard gradient-driven approach, density is allowed to fluctuate around its average profile. Transverse transport exhibits some of the features of self-organized critical systems, namely inward and outward avalanches, together with a frequency spectrum decrease in 1/f and f−2 at intermediate and high frequencies, respectively. An avalanche occurs when the local radial density gradient exceeds the critical one. A self-sustained particle flux then follows the large radial structures of the electric potential. As observed experimentally, the radial profile of density relative fluctuations decreases from the wall into the core plasma, while that of electric potential relative fluctuations peaks inside the SOL. Equilibrium density exhibits the experimental exponential decrease. An analytical expression of the SOL width ΔSOL is obtained, which maximizes the linear growth rate, when the poloidal modulation of electric potential equilibrium is taken into account. The parametric dependencies of ΔSOL are compared to experimental data.

Toroidicity in the tokamak SOL: effects on poloidal asymmetries, radial current and the L - H transition

A simple isothermal model for the scrape-off layer (SOL) which includes toroidal geometry and radial electric field effects, but ignores viscosity and plasma - neutral interactions, is presented. For finite toroidicity and for the case of zero radial electric field , the model predicts pressure asymmetry in favour of the outer target and a non-zero radial current due to pressure-gradient terms. For the case of non-zero , is changed somewhat. The dependence of the current on the radial electric field, however, is too weak and non-monotonic against to explain experimental results on ion mobility obtained in biasing experiments on the tokamak de Varennes (TdeV). This may indicate that anomalous processes, not considered here, are dominant in TdeV. The direction of the pressure-gradient-driven current is inwards for the `normal' toroidal field (ion drift towards the single null divertor), and outwards for the `reversed' field. The current can cause significant changes in radial flux in the SOL between the two field directions in the case when the SOL width approaches the ion poloidal Larmor radius. Its effect on the SOL is proposed as a mechanism responsible for the dependence on the direction of the toroidal field of the threshold power needed to cause the L - H transition. The dependence of the current on the toroidicity , found in the calculations, suggests that the beneficial effects of the `normal' field direction on the confinement should be more pronounced at larger .

A model for a scrape-off-layer low-high (L-H) mode transition

Increasing the radial mode number has a stabilizing effect on the conducting-wall and curvature-driven interchange modes in a tokamak scrape-off layer (SOL), arising from the increased polarization response. Such an effect is naturally imposed as the SOL width is decreased, and for a narrow-enough SOL, the stabilizing effect is stronger than the increase in the instability drives. By combining a mixing-length estimate for the thermal diffusivity with energy conservation and heat conduction equations and the condition of continuity of the heat flux at the separatrix, it is found that the resultant turbulence-transport system admits two solutions, one stable and one unstable, at different SOL widths; the inclusion of additional physics can add a second stable root at lower width. These roots are plausibly identified with SOL behavior in low (L) and high (H) modes. Particularly when a model is introduced for finite-β, finite-k∥ effects on the modes, a power threshold for transition to the narrower root is obtained, suggesting a possible L-H transition mechanism. The non-monotonic dependence of the turbulent heat flux vs SOL width and the possibility of multiple solutions for the equilibrium SOL width are verified with nonlinear simulations.

A two-dimensional ion kinetic model of the scrape-off layer of a diverted plasma with a private flux region

Earlier two-dimensional (radial and poloidal angle), analytically tractable ion kinetic models of the scrape-off layer (SOL) in which a steady state is achieved by balancing the streaming loss of ions to the divertor target plates with the radial diffusion of ions from the core are unable to distinguish between limited and diverted plasmas. The model presented here removes this limitation while still remaining amenable to a similar Wiener–Hopf solution procedure. To phenomenologically model ion recycling, the boundary conditions employed at the divertor plates allow for partial reflection. The diffusion into the private flux region and the extended divertor channels (all of normalized length d along the magnetic field), as well as the rest of the SOL, is evaluated. The SOL is shown to be asymmetric about the separatrix because ions from the core must stream by the X point be- fore diffusing into the private flux region. The channel or leg SOL width is of order [LD(1+2d)/vi ‖ln γ‖]1/2, where D, L, vi, and γ are the diffusion coefficient, connection length, ion thermal speed, and reflection coefficient, respectively. The SOL in the private flux region is narrower (by [2d/(1+2d)]1/2) with a lower density (by [2d/(1+2d)]3/4) and a stronger poloidal dependence than the region beyond the separatrix. To equalize the heat load between the private flux region and the leg portions of the target, the legs must be longer than the connection length.

Electron temperature gradient induced instability in tokamak scrape-off layers

An electron temperature instability driven by the Kunkel-Guillory sheath impedance has been applied to the scrape-off layer of tokamaks. The formalism has been generalized in order to more fully account for parallel wavelength dynamics, to differentiate between electromagnetic and electrostatic perturbations and to account for particle recycling effects. It is conjectured that this conducting wall instability leads to edge fluctuations in tokamaks that produce scrape-off layers tens of ion gyroradii thick. The predicted instability characteristics have similarities to experimental edge fluctuation data, and the scrape-off layer width in the DIII-D experiment agrees with theoretical estimates that can be derived from mixing length theory

Resonant helical divertor experiments in ohmic and auxiliary heated JIPP T-IIU plasmas

A series of initial resonant helical divertor (RHD) experiments have been carried out in ohmically and auxiliary heated JIPP T-IIU plasmas. Disruptive and MHD instabilities make the interpretation of the RHD results difficult but an apparent increase in the energy confinement time is observed when the helical magnetic perturbation is applied. This may be due to the suppression of MHD activity or to a reduction in the edge convective heat losses. Magnetic island effects have been observed on the floating potential of a Langmuir probe array and energy scrape-off layer widths have been measured with and without helical perturbations during ICRF operation. Basic pump limiter data is presented including ion temperatures and C 4+ impurity profiles. Energy confinement times are reported in ohmically and NBI heated discharges.