Sheath Boundary Conditions Research Articles

Electromagnetic effects on dynamics of high-beta filamentary structures

The impacts of the electromagnetic effects on blob dynamics are considered. Electromagnetic BOUT++ simulations on seeded high-beta blobs demonstrate that inhomogeneity of magnetic curvature or plasma pressure along the filament leads to bending of the blob filaments and the magnetic field lines due to increased propagation time of plasma current (Alfvén time). The bending motion can enhance heat exchange between the plasma facing materials and the inner scrape-off layer (SOL) region. The effects of sheath boundary conditions on the part of the blob away from the boundary are also diminished by the increased Alfvén time. Using linear analysis and BOUT++ simulations, it is found that electromagnetic effects in high temperature and high density plasmas reduce the growth rate of resistive drift wave instability when resistivity drops below a certain value. The blobs temperature decreases in the course of its motion through the SOL and so the blob can switch from the electromagnetic to the electrostatic regime where resistive drift waves become important again.

Benchmarking sheath subgrid boundary conditions for macroscopic-scale simulations

The formation of sheaths near metallic or dielectric-coated wall materials in contact with a plasma is ubiquitous, often giving rise to physical phenomena (sputtering, secondary electron emission, etc) which influence plasma properties and dynamics both near and far from the material interface. In this paper, we use first-principles PIC simulations of such interfaces to formulate a subgrid sheath boundary condition which encapsulates fundamental aspects of the sheath behavior at the interface. Such a boundary condition, based on the capacitive behavior of the sheath, is shown to be useful in fluid simulations wherein sheath scale lengths are substantially smaller than scale lengths for other relevant physical processes (e.g. radiofrequency wavelengths), in that it enables kinetic processes associated with the presence of the sheath to be numerically modeled without explicit resolution of spatial and temporal sheath scales such as electron Debye length or plasma frequency.

Intrinsic instabilities in X-point geometry: A tool to understand and predict the Scrape Off Layer transport in standard and advanced divertors

Intrinsic Scrape Off Layer (SOL) instabilities are studied using flute approximation and incorporating the appropriate sheath boundary conditions at the target. The linear growth rate and the structure of the modes are obtained. The associated diffusion is estimated using a γ/k⊥2 approach for the fastest growing modes. The model used includes curvature and sheath drives, finite Larmor radius effects and partial line tying at the target. The magnetic geometry is obtained using current carrying wires, representing the plasma current and the divertor coils, and naturally generates X-point geometry and magnetic shear effects. The calculation is performed for ITER relevant parameters and scans in SOL width and distance from the separatrix are presented. In addition to a standard Lower Single Null, Super-X and Snowflake configurations are examined in order to assess the importance of the geometry on the stability of the boundary plasma.

Mitigating impact of thermal and rectified radio-frequency sheath potentials on edge localized modes

The mitigating impact of thermal and rectified radio frequency (RF) sheath potentials on the peeling-ballooning modes is studied non-linearly by employing a two-fluid three-field simulation model based on the BOUT++ framework. Additional shear flow and the Kelvin-Helmholtz effect due to the thermal and rectified RF sheath potential are induced. It is found that the shear flow increases the growth rate while the K-H effect decreases the growth rate slightly when there is a density gradient, but the energy loss of these cases is suppressed in the nonlinear phase. The stronger external electrostatic field due to the sheaths has a more significant effect on the energy loss suppression. From this study, it is found the growth rate in the linear phase mainly determines the onset of edge-localized modes, while the mode spectrum width in the nonlinear phase has an important impact on the turbulent transport. The wider mode spectrum leads to weaker turbulent transport and results in a smaller energy loss. Due to the thermal sheath and rectified RF sheath potential in the scrape-off-layer, the modified shear flow tears apart the peeling-ballooning filament and makes the mode spectrum wider, resulting in less energy loss. The perturbed electric potential and the parallel current near the sheath region is also suppressed locally due to the sheath boundary condition.

Electromagnetic effects on plasma blob-filament transport

Both microscopic and macroscopic impacts of the electromagnetic effects on blob dynamics are considered. Linear stability analysis and nonlinear BOUT++ simulations demonstrate that electromagnetic effects in high temperature or high beta plasmas suppress the resistive drift wave turbulence in the blob when resistivity drops below a certain value. In the course of blob’s motion in the SOL its temperature is reduced, which leads to enhancement of resistive effects, so the blob can switch from electromagnetic to electrostatic regime, where resistive drift wave turbulence become important. It is found that inhomogeneity of magnetic curvature or plasma pressure along the filament length leads to bending of the high-beta blob filaments. This is caused by the increase of the propagation time of plasma current (Alfvén time) in higher-density plasma. The effects of sheath boundary conditions on the part of the blob away from the boundary are also diminished by the increased Alfvén time.

Effect of boundary conditions on the heat flux to the wall in two-temperature modeling of ‘thermal’ plasmas

In this paper we propose new boundary conditions at floating and biased walls for two-temperature thermal arc models. In the derived boundary conditions the walls are assumed to be cold and therefore there is no thermionic electron emission and erosion of the wall. The boundary conditions previously used in modeling high-pressure thermal arcs ignore the formation of a plasma sheath at floating walls. As shown in the paper, using the sheath boundary conditions lead to a drastic increase in the heat flux to the wall that has to be taken into account in modeling thermal arcs and heat transfer.

Benchmarks of KIPP: Vlasov‐Fokker‐Planck Code for Parallel Plasma Transport in the SOL and Divertor

AbstractBenchmarks of the new 1D2V kinetic code KIPP (KInetic code for Plasma Periphery) for parallel plasma transport in the scrape‐off layer (SOL) and divertor of magnetic confinement fusion devices are presented. The code is based on the continuum discretisation scheme for the Vlasov‐Fokker‐Planck equation. It assumes plasma quasi‐neutrality, maintained by the electron parallel momentum balance, and uses a logical sheath boundary condition for the Debye potential drop at material surfaces. The code is parallelized under the MPI environment, with the most time consuming part, Coulomb collisions, being calculated simultaneously for all spatial locations by separate processors using a sparse matrix solver for the full non‐linear collision operator in two velocity variables: parallel and gyro‐averaged perpendicular velocities. KIPP is being developed with the aim of integrating it into SOLPS (B2‐Eirene), to replace fluid treatment of parallel plasma transport with the kinetic one. Benchmark results for parallel electron heat conduction and electron‐ion thermoforce for highly collisional plasmas are presented, as well as some results for less collisional plasmas. This paper focuses on the 1d2v features of the code, with the 0d2v features presented earlier in [1, 2]. (© 2014 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Study of wave propagation in various kinds of plasmas using adapted simulation methods, with illustrations on possible future applications

Abstract The understanding of wave propagation in turbulent magnetized plasmas can be rather complex, particularly if they are inhomogeneous and time-dependent. Simulation can be a useful tool for wave propagation studies, provided that the “model” equations take into account the characteristics of the medium relevant for the studied problem and that the numerical scheme including boundary conditions is stable and accurate enough. The choices for the model equations and the corresponding schemes are analyzed and discussed as a function of various parameters, such as the order of the numerical scheme and the number of grid points per wavelength. A quick review of the up-to-date numerical developments is given on the sheath boundary conditions and on the perfect matching layer in anisotropic media. Possible developments of plasma diagnostics conclude this state-of-the-art of simulations of electromagnetic waves in plasmas.

2D simulations of transport dynamics during tokamak fuelling by supersonic molecular beam injection

Time-dependent transport of both plasma and neutrals is simulated during supersonic molecular beam injection (SMBI) yielding the evolution of edge plasma and neutral profiles. The SMBI model is included as a module, called trans-neut, within the original BOUT++ boundary plasma turbulence code. Results of calculations are reported for the realistic divertor geometry of the HL-2A tokamak. The model can also be used to study the effect of gas puffing. A seven-field fluid model couples plasma density, heat, and momentum transport equations together with neutral density and momentum transport equations for both molecules and atoms. Collisional interactions between molecules, atoms, and plasma include dissociation, ionization, recombination and charge-exchange effects. Sheath boundary conditions and particle recycling are applied at both the wall and the divertor plates. A localized boundary condition of constant molecular flux (product of density times speed) is applied at the outermost flux surface to model the SMBI. Steady state profiles with and without particle recycling are achieved before SMBI. During SMBI, the simulation shows that neutrals can penetrate several centimetres inside the last closed (magnetic) flux surface (LCFS). Along the SMBI path, plasma density increases while plasma temperature decreases. The molecule penetration depth depends on both the SMBI flux and the initial plasma density and temperature along its path. As the local plasma density increases substantially, molecule and atom penetration depths decrease due to their higher dissociation and ionization rates if the electron temperature does not drop too low. Dynamic poloidal spreading of the enhanced plasma density region is observed due to rapid ion flow along the magnetic field (parallel) driven by a parallel pressure asymmetry during SMBI. Profile relaxation in the radial and poloidal directions is simulated after SMBI termination, showing that the plasma returns to pre-SMBI conditions on a time scale of 60 ms.

Velocity boundary conditions at a tokamak resistive wall

Velocity boundary conditions appropriate for magnetohydrodynamic simulations have been controversial recently. A comparison of numerical simulations of sideways wall force in disruptions is presented for Dirichlet, Neumann, Robin, and DEBS boundary conditions. It is shown that all the boundary conditions give qualitatively similar results. It is shown that Dirichlet boundary conditions are valid in the small Larmor radius limit of electromagnetic sheath boundary conditions.

VINETA II: A linear magnetic reconnection experiment

A linear experiment dedicated to the study of driven magnetic reconnection is presented. The new device (VINETA II) is suitable for investigating both collisional and near collisionless reconnection. Reconnection is achieved by externally driving magnetic field lines towards an X-point, inducing a current in the background plasma which consequently modifies the magnetic field topology. Owing to the open field line configuration of the experiment, the current is limited by the axial sheath boundary conditions. A plasma gun is used as an additional electron source in order to counterbalance the charge separation effects and supply the required current. Two drive methods are used in the device. First, an oscillating current through two parallel conductors drive the reconnection. Second, a stationary X-point topology is formed by the parallel conductors, and the drive is achieved by an oscillating current through a third conductor. In the first setup, the magnetic field of the axial plasma current dominates the field topology near the X-point throughout most of the drive. The second setup allows for the amplitude of the plasma current as well as the motion of the flux to be set independently of the X-point topology of the parallel conductors.

CSF outflow along spinal nerves – A neuroradiological documentation

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.

Connection coefficients for cold plasma wave propagation near metallic surfaces

Sheaths tend to form when immersing metallic objects in plasmas. As it avoids the need to capture the sheath details, which occur on the Debye length scale while antennas are typically various orders of magnitude larger, the sheath boundary condition due to D'Ippolito and Myra (2006 Phys. Plasmas 13 102508, 2008 Phys. Plasmas 15 102501) offers antenna designers a major reduction in the numerical problem size they face. The sheath boundary condition was derived by making a number of simplifying assumptions to enable finding an analytical approximation of the conditions rapidly oscillating waves have to satisfy beyond the sheath that forms close to such objects. This paper discusses the solution of the cold plasma wave equation for sheath relevant density profiles, e.g. highlighting the role of the orientation of the static magnetic field and of oblique incidence, and underlining the impact the density profile has on the wave physics. It illustrates that the cross-talk between the waves impinging on and those excited at the wall and in the sheath sensitively depends on a number of parameters. The 2 × 2 connection coefficient matrix that is numerically obtained captures the sheath region fast time scale wave physics for a given density profile. When supplemented with a satisfactory model for the slow time scale variation it is a numerical tool that permits upgrading the realism of the fast time scale wave physics contained in the sheath boundary condition and that can help delimiting the range of applicability of simplified models, and assessing if a sufficiently general set of boundary conditions to describe the effect of the sheath can at all be constructed.

Properties of a warm plasma collisional sheath in an oblique magnetic field

The properties of a warm plasma collisional sheath in an oblique magnetic field and the associated sheath criterion are investigated with a two-fluid model. In the fluid framework, a sheath criterion including effects of the magnetic field and collision is established theoretically for a wide range of ion temperature. With the sheath criterion as the plasma-sheath boundary condition, different plasma parameters including potential, electron and ion densities, and ion velocity are calculated for various ion temperatures and ion thermal motions. It is shown that the properties of the sheath depend not only on the plasma balance equations but also on the sheath boundary conditions. In addition, effects of the directions and magnitudes of the magnetic field on the plasma sheath are also discussed under different ion temperatures.

Self consistent radio-frequency wave propagation and peripheral direct current plasma biasing: Simplified three dimensional non-linear treatment in the “wide sheath” asymptotic regime

A minimal two-field fluid approach is followed to describe the radio-frequency (RF) wave propagation in the bounded scrape-off layer plasma of magnetic fusion devices self-consistently with direct current (DC) biasing of this plasma. The RF and DC parts are coupled by non-linear RF and DC sheath boundary conditions at both ends of open magnetic field lines. The physical model is studied within a simplified framework featuring slow wave (SW) only and lateral walls normal to the straight confinement magnetic field. The possibility is however kept to excite the system by any realistic 2D RF field map imposed at the outer boundary of the simulation domain. The self-consistent RF + DC system is solved explicitly in the asymptotic limit when the width of the sheaths gets very large, for several configurations of the RF excitation and of the target plasma. In the case of 3D parallelepipedic geometry, semi-analytical results are proposed in terms of asymptotic waveguide eigenmodes that can easily be implemented numerically. The validity of the asymptotic treatment is discussed and is illustrated by numerical tests against a quantitative criterion expressed from the simulation parameters. Iterative improvement of the solution from the asymptotic result is also outlined. Throughout the resolution, key physical properties of the solution are presented. The radial penetration of the RF sheath voltages along lateral walls at both ends of the open magnetic field lines can be far deeper than the skin depth characteristic of the SW evanescence. This is interpreted in terms of sheath-plasma wave excitation. Therefore, the proper choice of the inner boundary location is discussed as well as the appropriate boundary conditions to apply there. The asymptotic scaling of various quantities with the amplitude of the input RF excitation is established.

A finite element procedure for radio-frequency sheath–plasma interactions in the ion cyclotron range of frequencies

A numerical code that solves self-consistent radio-frequency (RF) sheath–plasma interactions in the ion cyclotron range of frequencies is developed based on a nonlinear finite element technique. The present code solves for plasma waves based on the cold plasma model subject to a sheath boundary condition. The finite element procedure has been implemented for one- and two-dimensional analyses using simplified models for the poloidal plane of a tokamak. The results show good accuracy and generalize previous analytical calculations. The present algorithmic approach shows promise for developing a code to predict RF sheath potentials in the scrape-off layer of RF-heated fusion experiments.

A sheath boundary condition for fast wave propagation near conducting surfaces

Radiofrequency (rf) waves can accelerate electrons into material boundaries, so that electron confinement requires rf sheath potentials that are significantly larger than the thermal Bohm sheath. The condition for rf sheaths to occur is that the rf electric field has a component E|| parallel to the equilibrium magnetic field. Thus, a proper treatment of rf wave propagation requires an accurate description of the geometry of the magnetic field and of the bounding surfaces, and a boundary condition (BC) that includes the effect on the waves of the electron-poor sheath. When the static magnetic field has a component at an angle to the sheath, the propagating fast wave (with E||=0) is coupled to a slow wave (with E||≠0) in order to satisfy the boundary condition at the metal wall, and the time-averaged sheath potential has a strong component from rectification of the rf sheath. In this brief communication, a previously derived sheath BC is reformulated to treat the coupling of the fast wave to the slow wave analytically, thereby greatly reducing the necessary numerical resolution required for calculation of fast wave propagation.

Numerical analysis of radio-frequency sheath-plasma interactions in the ion cyclotron range of frequencies

A new finite element numerical scheme for analyzing self-consistent radio-frequency (RF) sheath-plasma interaction problems in the ion cyclotron range of frequencies is applied to various problems represented by simplified models for the tokamak scrape-off layer. The present code incorporates a modified boundary condition, which is called a sheath boundary condition, that couples the radio-frequency waves and sheaths at the material boundaries by treating the sheath as a thin vacuum layer. A series of numerical analyses in one- and two-dimensional domains show several important physical properties, such as the existence of multiple roots, hysteresis effects, presence and characteristics of the sheath-plasma waves, and the phase shift of a reflected slow wave, some of which are newly identified by introducing a spatially varying plasma density and background magnetic field.

Blob current structures in TORPEX plasmas: experimental measurements and numerical simulations

In the simple magnetized torus TORPEX, field-aligned blobs originate from ideal interchange waves and propagate radially outward due to ∇B and curvature induced drifts. Time-resolved two-dimensional measurements of the field-aligned current density J∥ associated with blobs are obtained from conditionally sampled data from a single-sided Langmuir probe and a specially designed current probe. The profile of J∥ exhibits an asymmetric dipolar structure, which originates from the polarization of the blob and is consistent with sheath boundary conditions. The asymmetry results from the non-linear dependence of J∥ at the sheath edge upon the floating potential. Using internal measurements, we directly confirm the existence of two regimes, in which parallel currents to the sheath do or do not significantly damp charge separation and thus blob radial velocity. To investigate the effect of the observed asymmetry of J∥ on the blob motion, we carried out numerical simulations of seeded blobs, using a two-field fluid model, which evolves electron density and vorticity. Simulations are performed spanning a wide range of blob sizes covering both regimes. We use either the complete or a linearized form for the sheath dissipation term in the vorticity equation. The structure of the parallel current density and plasma potential is found to be different in the two cases. Asymmetric profiles are observed in simulations with the complete form, while symmetric profiles are obtained when a linearized form is used. Negligible effects are, however, observed in terms of blob radial velocity. The relevance of the present results for fusion devices is also discussed.

Direct Two-Dimensional Measurements of the Field-Aligned Current Associated with Plasma Blobs

In simple magnetized toroidal plasmas, field-aligned blobs originate from ideal interchange waves and propagate radially outward under the effect of ∇B and curvature induced E×B drifts. We report on the first experimental two-dimensional measurements of the field-aligned current associated with blobs, whose ends terminate on a conducting limiter. A dipolar structure of the current density is measured, which originates from ∇B and curvature induced polarization of the blob and is consistent with sheath boundary conditions. The dipole is strongly asymmetric due to the nonlinear dependence of the current density at the sheath edge upon the floating potential. Furthermore, we directly demonstrate the existence of two regimes, in which parallel currents to the sheath do or do not significantly damp charge separation and thus blob radial velocity.