Sheath Boundary Conditions Research Articles

Fluid simulations of conducting-wall-driven turbulence in boundary plasmas

It is clear that the edge plasma plays a crucial role in global tokamak confinement. This paper is a report on simulations of a new drift wave type instability driven by conducting wall (also originally named as a ∇Te instability) [Phys. Fluids B 3, 1364 (1991)]. A 2d(x,y) fluid code has been developed in order to explore the anomalous transport in the boundary plasmas. The simulation consists of a set of fluid equations (in the electrostatic limit) for the vorticity ∇⊥2φ, and the temperature Te in a shearless plasma slab confined by a uniform, straight magnetic field Bz with two divertor (or limiter) plates intercepting the magnetic field. The model has two regions separated by a magnetic separatrix: In the edge region inside the separatrix, the model is periodic along the magnetic field while in the scrapeoff layer (SOL) region outside the separatrix, the magnetic field is taken to be of finite length with model (logical sheath) boundary conditions at diverter (or limiter) plates. The simulation results show that the observed linear instability agrees well with theory, and that a saturated state of turbulence is reached. In saturated turbulence, clear evidence of the expected long-wavelength mode penetration into the edge is seen, an inverse cascade of wave energy (toward both long wavelengths and low frequencies) is observed. The simulation results also show that amplitudes of potential and the electron temperature fluctuations are somewhat above and the heat flux are somewhat below those of the simplest mixing-length estimates. A full inverse cascade of the turbulence indicates that the cross-field transport is not diffusive. A self-consistent simulation to determine the microturbulent SOL electron temperature profile has been done, the results of which reasonably agree with the experimental measurements.

A Suitable Boundary Condition for Bounded Plasma Simulation without Sheath Resolution

We have developed a technique that allows for a sheath boundary layer without having to resolve the inherently small space and time scales of the sheath region. We refer to this technique as the logical sheath boundary condition. This boundary condition, when incorporated into a direct-implicit particle code, permits large space- and time-scale simulations of bounded systems, which would otherwise be impractical on current supercomputers. The lack of resolution of the collector sheath potential drop obtained from conventional implicit simulations at moderate values of ωpe Δt and Δ z/ λDe provides the motivation for the development of the logical sheath boundary condition. The algorithm for use of the logical sheath boundary condition in a particle simulation is presented. Results from simulations which use the logical sheath boundary condition are shown to compare reasonably well with those from an analytic theory and simulations in which the sheath is resolved.

Multidimensional and Multifluid Plasma Edge Modelling: Status and New Directions

AbstractThe plasma boundary in magnetic confinement devices is observed in experiments and in computations to contain radial and poloidal variations in plasma potential, strong radial electric fields and large poloidal drift flows in addition to the parallel flow toward the plasma sheath boundaries and the particle recycling from the walls. The global power balence is largely influenced by impurity radiation and thus by impurity transport in the edge region. The behavior of the edge region is related to global confinement in ways not yet fully known and motivates further improvements in edge plasma modelling.General multifluid transport equations are reviewed in the context of the current status of plasma edge modelling. It is assumed that the macroscopic transport in the plasma edge region is suitable for a moments description, or fluid model. Progress is well established in computational treatments of the standard paradigm including classical parallel and anomalous cross‐field flux coupled to neutrals in analytic or Monte Carlo steady state computations. Formulation of momentum diffusivities and curvature drift in toroidal coordinates are considered. New directions include defining the dominant influence of drifts and non‐ambipolar flows, improving coupled plasma‐neutral transport calculations, and treating impurity flow in full multifluid models. Calculation of the plasma potential driving the E × B drift in the scrape‐off layer can be extended inside the last closed flux surface by conserving the divergence of the plasma currents. Coupled plasma‐neutral fluids using a neutral diffusion approximation show promise for recycling calculations. Impurity transport based on full multifluid treatment along the field lines has shown good agreement with divertor experiments.Advanced topics for the near future include plasma core‐edge transport coupling and eventually the direct solution of coupled momentum equations rather than the presently assumed cross‐field ‘anomalous’ flux functions. In the edge region, plasma sheath boundary conditions are a significant sink for plasma particles and heat; a small coupling between the momentum components in the plasma edge can be sufficient to drive an ‘anomalously’ large efflux from the core plasma.

Non‐Local Sheath Boundary Conditions for Fluid Equations

Non‐Local Sheath Boundary Conditions for Fluid Equations

Use of the two-ion hybrid as an impurity diagnostic

In a plasma containing more than one ion species, the frequencies of the ion–ion hybrid resonances can be a sensitive measure of the densities of the minor species, but only if the frequency shifts caused by electron motions are small, as experimental observations suggest. By calculating the eigenfrequencies for ion–ion hybrid waves taking into account collisions, Landau damping, electron inertia, electromagnetic effects, and density gradients, it is found that the frequency shifts are not negligible unless k∥ is extremely small. Treatment of the sheath boundary conditions at the ends of a plasma column shows that the effective value of k∥ can indeed be sufficiently small, and that the uncorrected resonance frequency is surprisingly accurate over a wide parameter range. Data from an Ar–Xe discharge demonstrate the usefulness of this technique for measuring impurity concentrations.

Laminar Stagnation-Point Heat Transfer for a Two-Temperature Argon Plasma

A theory for the heat transfer to the stagnation-point boundary layer of an axisymmetric blunt body in a subsonic two-temperature argon plasma flow was developed. Two-temperature transport properties were calculated from the rigorous kinetic theory and are employed in solving the multifluid problem formulated with a wall sheath boundary condition. The system of equations is solved numerically for various problem parameters. The effects of parameters on thermal nonequilibrium characteristics of the boundary layer are discussed. Also shown are the variations in the transport properties across the boundary layer.

Modelling of the boundary plasma of large tokamaks

Fluid models developed at Culham for the boundary plasma of tokamaks are surveyed and their application to devices such as INTOR or NET is described. The simplest model is based upon transport of a single fluid and considers parallel conduction along the scrape-off layer with a convective sheath boundary condition: its versatility is demonstrated in a comparison of the INTOR divertor and limiter. A two-fluid, one-dimensional model has been critically compared with the simple model; it has also been used in a study of impurity transport, and predictions for a highly recycling plasma are described. A two-fluid two-dimensional model of the plasma is presented: it has provided predictions for the thermal load on the INTOR divertor plate. We conclude by showing the need for a careful physical description of a two-dimensional plasma boundary.

Parallel Current and Sheath Effects on Collisional Drift Waves in an Axially Symmetric Device with End Plates

A theoretical calculation is made of the normal mode structure of collisional drift waves in Q machines, due to the presence of end plates. The two fluid equations for electrons and ions are employed, including the effects of electron temperature perturbations and electron heat flow. Particular emphasis is placed on how a direct electron current along the magnetic field alters this structure. The dispersion relation and the sheath boundary condition resulting from both particle and heat flows are obtained. A slab plasma model is adopted, with a uniform magnetic field perpendicular to both the density gradient and the end plates. The case where the electron flow velocity is comparable to the ion acoustic wave velocity is studied in detail. The dispersion relation indicates that the wave frequency and the temporal growth rate change only very little for devices with end plates. The normal model consists of two oppositely directed traveling drift waves and two small amplitude oppositely directed traveling entropy waves. The drift waves grow spatially in the direction of electron flow and have a small axial phase shift, which varies linearly along the same direction. Good agreement is obtained with recent experimental results.

Electron thermochemical nonequilibrium effects in re-entry boundary layers

Results of calculated nonequilibrium electron temperature and concentration characteristics in boundary layers are presented for re-entry conditions: Um = 27,500-34,000 fps and altitude 110,000-150,000 ft. These results show the effects of reactions, collisions, electrical current, and electron reflection on the electron heat transfer and temperature. The electron conservation equations in boundary-layer form were solved in the quasi-neutral region with collisionless sheath boundary conditions or approximate boundary conditions derived from the collisionless sheath expressions and valid with collisions in the sheath. A numerical solution was obtained by a finite difference technique after a similarity transformation arid quasilinearization of the equations. The solutions show significant temperature nonequilibrium. Electron current and reflection, combined into a single parameter, reduces electron temperature and increases conduction of energy but does not explicitly affect electron concentration or diffusion of ionization energy.