Sheath Boundary Conditions Research Articles

Self-consistent modelling of radio frequency sheath in 3D with realistic ICRF antennas

Abstract Ion Cyclotron Resonant Frequency (ICRF) induced impurity production has raised many concerns since ITER proposed to change the first wall material from beryllium to tungsten. Enhanced DC plasma potential (VDC) due to RF sheath rectification is well known as one of the most important mechanisms behind the RF induced impurities. Our previous work (L. Lu et.al, Plasma Phys. Control. Fusion 60 (2018) 035003) considered the impact of both the slow wave and the fast wave on the RF sheath rectification in a 2D geometry. It can barely recover the double-hump structure of the VDC poloidal distribution observed in various machines when only the slow wave is modelled using the multi-2D approach which intrinsically assumes the poloidal wavenumber kz is zero. The fast wave on the other hand is found to be more sensitive to a finite kz and may need to be tackled in 3D. This work reports our recent progress on the 3D RF sheath modelling. In this new code, the latest RF sheath boundary conditions (J. R. Myra, J. Plasma Phys. 87 (2021) 905870504) and the realistic 3D ICRF antennas are implemented. Compared to the 2D results, the 3D code could well recover the double-hump poloidal distribution of VDC even with the fast wave included, which confirms our speculation on the necessity of treating the fast wave in 3D. While the double-hump pattern is robust in the simulation, the amplitude of VDC is found to be affected by the magnetic tilt angle and the antenna geometry. This emphasizes the importance of adopting a realistic antenna geometry in the RF sheath modelling. The double-hump VDC poloidal structure breaks as the magnetic tilt angle increases. This is explained by the gyrotropic property of the cold plasma dielectric tensor. The spatial proximity effect we identified in the previous 2D simulations is still valid in 3D. Finally, simulation shows the slow wave dominates the RF sheath excitation in the private SOL, while the fast wave gradually takes over when moving to the far SOL region. This code could be a new tool to provide numerical support for ITER impurity assessment and ICRF antenna design.

A non-neutral 1D fluid model of hall thruster discharges: full electron inertia and anode sheath reversal

A non-neutral model (NNM) of the axial plasma discharge in a Hall thruster, including full electron inertia, is presented. In the finite-volume formulation, two types of sheath boundary conditions previously used in the literature are tested and proven to behave practically identically in this model. Both normal and reversed (i.e. electron repelling and attracting, respectively) anode sheaths are admitted. This model is compared with the quasineutral model developed in a previous work, which includes only azimuthal electron inertia and normal anode sheaths. Both models agree excellently within the parametric region where steady-state solutions with a normal anode sheath exist. The NNM shows the absence of steady-state solutions with a reversed anode sheath. Nonetheless, a reversed sheath can appear during the transient to a steady-state solution with a normal sheath and the periodic transition from a normal to a reversed sheath can be observed in the presence of breathing-mode oscillations. In other cases, the reversed sheath leads to the discharge shut-off. Full electron inertia is always important in the presence of a reversed sheath. The parametric threshold of the wall accommodation parameter from a stationary solution to a breathing mode one differs slightly between the non-neutral and the quasi-neutral model.

Full-F turbulent simulation in a linear plasma device using a gyro-moment approach

Simulations of plasma turbulence in a linear plasma device configuration are presented. These simulations are based on a simplified version of the gyrokinetic (GK) model proposed by Frei et al. [J. Plasma Phys. 86, 905860205 (2020)], where the full-F distribution function is expanded on a velocity-space polynomial basis allowing us to reduce its evolution to the solution of an arbitrary number of fluid-like equations for the expansion coefficients, denoted as the gyro-moments (GM). By focusing on the electrostatic and neglecting finite Larmor radius effects, a full-F GM hierarchy equation is derived to evolve the ion dynamics, which includes a nonlinear Dougherty collision operator, localized sources, and Bohm sheath boundary conditions. An electron fluid Braginskii model is used to evolve the electron dynamics, coupled to the full-F ion GM hierarchy equation via a vorticity equation where the Boussinesq approximation is used. A set of full-F turbulent simulations are then performed using the parameters of the LArge Plasma Device (LAPD) experiments with different numbers of ion GMs and different values of collisionality. The ion distribution function is analyzed illustrating the convergence properties of the GM approach. In particular, we show that higher-order GMs are damped by collisions in the high-collisional regime relevant to LAPD experiments. The GM results are then compared with those from two-fluid Braginskii simulations, finding qualitative agreement in the time-averaged profiles and statistical turbulent properties.

Effect of electromagnetic wave reflection from conducting surfaces on blob dynamics in the tokamak scrape-off layer

Electromagnetic dynamics of blobs in hot scrape-off-layer plasmas of the tokamak are affected by excitation of the Alfvén waves and their subsequent propagation to the machine first wall along open magnetic field lines. In this study, the interaction of electromagnetic perturbations with the conducting tokamak wall and the resulting impact of these perturbations on the motion of filaments at the tokamak edge are analyzed. The model describing blob dynamics is presented. To describe the reflection of the Alfvén waves from the tokamak wall, the new form of sheath boundary conditions for the parallel current and electrostatic potential at the plasma–sheath interface is proposed. It is demonstrated that depending on the wall resistivity, the waves can be either absorbed or reflected by the wall, influencing the excitation of electromagnetic fluctuations inside the filament plasma. The theoretical conclusions of the study are supported with the BOUT++ numerical modeling of blob dynamics at the edge of the DIII-D and NSTX tokamaks. It is shown that taking the reflective boundary conditions into account leads to the excitation of the standing Alfvén waves in the filament, periodically canceling the electrostatic currents inside the blob.

Magnetic potential based formulation for linear and non-linear 3D RF sheath simulation

This paper reports a new numerical scheme to simulate the radio-frequency (RF) induced RF sheath, which is suitable for a large 3D simulation. In the RF sheath boundary model, the tangential component of the electric field () is given by the gradient of a scalar electric field potential. We introduce two additional scalar potentials for the tangential components of the magnetic field, which effectively impose the normal electric displacement (D n ) on the plasma sheath boundary condition via in-homogeneous Neumann boundary condition and constrain the tangential electric field on the surface as curl-free (). In our approach, the non-linear sheath impedance is formulated as a natural extension of the large thickness (or asymptotic) sheath limit (), allowing for handling both asymptotic and non-linear regimes seamlessly. The new scheme is implemented using the Petra-M finite element method analysis framework and is verified with simulations in the literature. The significance of non-linearity is discussed in various plasma conditions. An application of this scheme to asymptotic RF sheath simulation on the WEST ICRF antenna side limiters is also discussed.

Validation of edge turbulence codes against the TCV-X21 diverted L-mode reference case

Self-consistent full-size turbulent-transport simulations of the divertor and scrape-off-layer (SOL) of existing tokamaks have recently become feasible. This enables the direct comparison of turbulence simulations against experimental measurements. In this work, we perform a series of diverted ohmic L-mode discharges on the tokamak à configuration variable (TCV) tokamak, building a first-of-a-kind dataset for the validation of edge turbulence models. This dataset, referred to as TCV-X21, contains measurements from five diagnostic systems from the outboard midplane (OMP) to the divertor targets—giving a total of 45 one- and two-dimensional comparison observables in two toroidal magnetic field directions. The experimental dataset is used to validate three flux-driven 3D fluid-turbulence models—GBS, GRILLIX and TOKAM3X. With each model, we perform simulations of the TCV-X21 scenario, individually tuning the particle and power source rates to achieve a reasonable match of the upstream separatrix value of density and electron temperature. We find that the simulations match the experimental profiles for most observables at the OMP—both in terms of profile shape and absolute magnitude—while a comparatively poorer agreement is found towards the divertor targets. The match between simulation and experiment is seen to be sensitive to the value of the resistivity, the heat conductivities, the power injection rate and the choice of sheath boundary conditions. Additionally, despite targeting a sheath-limited regime, the discrepancy between simulations and experiment also suggests that the neutral dynamics should be included. The results of this validation show that turbulence models are able to perform simulations of existing devices and achieve reasonable agreement with experimental measurements. Where disagreement is found, the validation helps to identify how the models can be improved. By publicly releasing the experimental dataset and validation analysis, this work should help to guide and accelerate the development of predictive turbulence simulations of the edge and SOL.

Impact of Generalized Sheath Boundary Conditions on Dynamics of Plasma Filaments at the Tokamak Edge

Impact of Generalized Sheath Boundary Conditions on Dynamics of Plasma Filaments at the Tokamak Edge

Turbulent broadening of electron heat-flux width in electromagnetic gyrokinetic simulations of a helical scrape-off layer model

We demonstrate that cross field transport in the scrape-off layer (SOL) can be moderately increased by electromagnetic effects in high-beta regimes, resulting in broadening of the electron heat-flux width on the endplates. This conclusion is taken from full-f electromagnetic gyrokinetic simulations of a helical SOL model that roughly approximates the SOL of the National Spherical Torus Experiment. The simulations have been performed with the Gkeyll code, which recently became the first code to demonstrate the capability to simulate electromagnetic gyrokinetic turbulence on open magnetic field lines with sheath boundary conditions. We scan the source rate and thus β, so that the normalized pressure gradient (the MHD ballooning parameter α∝∂β/∂r∝β/Lp) is scanned over an experimentally relevant range, α=0.3−1.5. While there is little change in the pressure gradient scale length Lp near the midplane as beta is increased, a 10% increase in cross field transport near the midplane results in an increase in the electron heat-flux width λq and a 25% reduction of the peak electron heat flux to the endplates.

Characteristics of double-peaked particle deposition at divertor target plates in the EAST tokamak

Increasing the heat and particle deposition on the divertor target plates is an effective approach for reducing the extremely high heat load. Future tokamak fusion devices are expected to have a deposition width on the order of a millimeter. Recently, a double-peaked distribution (DPD) pattern of particle deposition at the divertor target plates has been observed in both deuterium and helium plasma discharges in the Experimental Advanced Superconducting Tokamak, which can significantly spread the deposition width of heat and particle fluxes, and clearly shows a toroidal symmetric distribution. It has been found that the DPD behavior occurs not only in plasma discharges with lower hybrid wave (LHW) heating, but also with electron cyclotron resonance heating or neutral beam injection (NBI) heating alone. In addition, the DPD shows an obvious in–out asymmetry between the divertor target plates, which strongly depends on the toroidal field direction, i.e. it distinctly appears on the outer divertor plate in unfavorable B t conditions, while shifting to the inner divertor plate under favorable B t conditions. Meanwhile, the transition between the single-peaked distribution and the DPD is normally correlated with the line-averaged plasma density and the auxiliary heating power. The statistical results for the pure LHW heating discharge scheme show that the DPD behavior is significantly affected by both the plasma density and the heating power, i.e. the lower the ratio of the plasma density to the heating power, the more likely it is that DPD behavior will occur. The critical boundary lines between the DPD and non-DPD patterns are obtained with the line expressions ∼ 2P LHW,abs + 1.4 and ∼ 3.33P LHW,abs + 1 for the unfavorable and favorable B t cases, respectively. Finally, the underlying physics is also discussed, suggesting that the electric field drifts and the local sheath boundary condition may exert a strong influence on the DPD.

Effects of divertor electrical drifts on particle distribution and detachment near the divertor target plate in DIII-D

Strong impacts of drifts on the divertor plasma in–out asymmetry and detachment are demonstrated in DIII-D with an open divertor configuration. For forward toroidal field, BT, i.e., with the ion B × ∇B drift toward the divertor, the particle flux to the inner divertor, as represented by the Langmuir probe measured ion saturation current (Jsat), exhibits a double peak structure, with electron temperature, lower at the inner target. Reversing the BT direction reverses both the radial and poloidal E × B flows, leading to a broad particle flux profile in the outboard scrape-off layer (SOL) with a similar double-peak structure to that observed at the inner target with forward BT. The correlation of a double peak structure with divertor temperature profiles confirms physical coupling between the drift flow and sheath boundary condition and their strong impact on divertor profiles. In addition, under reversed BT conditions, increasing the density flattens the target temperature profile. However, Jsat remains high away from the strike point, rendering it difficult to achieve an “effective” detached plasma, i.e., with effective reduction in both peak heat flux and peak temperature (in the far SOL). In contrast, divertor detachment with a cold and flat temperature profile can be achieved at both target plates with the forward BT.

Simulations of COMPASS vertical displacement events with a self-consistent model for halo currents including neutrals and sheath boundary conditions

The understanding of the halo current properties during disruptions is key to design and operate large scale tokamaks in view of the large thermal and electromagnetic loads that they entail. For the first time, we present a fully self-consistent model for halo current simulations including neutral particles and sheath boundary conditions. The model is used to simulate vertical displacement events (VDEs) occurring in the COMPASS tokamak. Recent COMPASS experiments have shown that the parallel halo current density at the plasma-wall interface is limited by the ion saturation current during VDE-induced disruptions. We show that usual magneto-hydrodynamic boundary conditions can lead to the violation of this physical limit and we implement this current density limitation through a boundary condition for the electrostatic potential. Sheath boundary conditions for the density, the heat flux, the parallel velocity and a realistic parameter choice (e.g. Spitzer’s resistivity and Spitzer–Härm parallel thermal conductivity) extend present VDE simulations beyond the state of the art. Experimental measurements of the current density, temperature and heat flux profiles at the COMPASS divertor are compared with the results obtained from axisymmetric simulations. Since the ion saturation current density () is shown to be essential to determine the halo current profile, parametric scans are performed to study its dependence on different quantities such as the plasma resistivity and the particle and heat diffusion coefficients. In this respect, the plasma resistivity in the halo region broadens significantly the profile, increasing the halo width at a similar total halo current.

Plasma edge simulations including realistic wall geometry with SOLPS-ITER

Abstract In plasma edge simulations using the SOLPS-ITER code, the simulated Scrape-Off Layer plasma domain has historically been restricted to magnetic flux surfaces contacting divertor targets at both ends. We present here a newly developed numerical solver for the B2.5 plasma solver in SOLPS-ITER, allowing the numerical grid to be extended to the true vessel boundaries. The new, unstructured Finite Volume scheme can deal with arbitrary grids and magnetic topologies in the 2D poloidal plane. It includes a correct numerical treatment of possibly misaligned faces and cells w.r.t. the magnetic field to cope with, for example, strong divertor target shaping. The solver combines the benefits of an accurate numerical separation of fast parallel and slow radial transport, with a realistic description of the wall geometry, and the possibility of local grid refinement to capture sharp features in the Scrape-Off Layer flows. Generalized sheath boundary conditions are presented that can be imposed at all vessel boundaries, removing an important modeling uncertainty related to the specification of ad hoc decay length boundary conditions at the outer flux surfaces. The resulting model is applied to an AUG single-null case, a standard benchmark case for SOLPS-ITER. We analyze in particular the impact of the extended plasma model on upstream and divertor plasma conditions, and the improved predictions of heat and particle loads to the main chamber wall. The extended solver also allows for a much improved qualitative agreement between fluid and kinetic neutral simulations, because the fluid neutral solution, which is obtained on the plasma grid, now also extends to the true main chamber and divertor vessel boundaries.

Fluid and gyrokinetic turbulence in open field-line, helical plasmas

Two-fluid Braginskii codes have simulated open-field line turbulence for over a decade, and only recently, it has become possible to study these systems with continuum gyrokinetic codes. This work presents a first-of-its-kind comparison between fluid and (long-wavelength) gyrokinetic models in open field-lines, using the GDB and Gkeyll codes to simulate interchange turbulence in the Helimak device at the University of Texas [T. N. Bernard et al., Phys. Plasmas 26, 042301 (2019)]. Partial agreement is attained in a number of diagnostic channels when the GDB sources and sheath boundary conditions (BCs) are selected carefully, especially the heat-flux BCs that can drastically alter the temperature. The radial profile of the fluctuation levels is qualitatively similar and quantitatively comparable on the low-field side, although statistics such as moments of the probability density function and the high-frequency spectrum show greater differences. This comparison indicates areas for future improvement in both simulations, such as sheath BCs, and improvements in GDB like particle conservation and spatially varying thermal conductivity, in order to achieve better fluid-gyrokinetic agreement and increase fidelity when simulating experiments.

Dynamics of scrape-off layer filaments in high β plasmas

The role of magnetic perturbations generated by filaments in the scrape-off layer is investigated by performing simulations of 3D seeded filaments with an electromagnetic numerical code which includes sheath boundary conditions. Depending on the plasma β, three smoothly connecting regimes were identified: an electrostatic regime where the magnetic field is substantially unaffected by the motion of the filament, an intermediate regime where the magnetic field is excited but relaxes within the filament’s lifetime and an electromagnetic regime where the frozen-in condition is well satisfied. The electromagnetic effects are found to have a significant impact on the filament dynamics at values of β relevant for fusion devices, including increased midplane radial velocity, bending of the filament and braiding of magnetic field lines. Importantly, a finite Alfvén speed can allow electrical disconnection of the target and the upstream part of the filament, thus removing the slowing down effect associated with the sheath and producing faster filaments and more intense cross-field transport in perturbations that were affected by the sheath in the β = 0 limit.

Numerical solutions of Maxwell's equations in 3D in frequency domain with linear sheath boundary conditions

In this paper, we construct a numerical technique capable of solving Maxwell's equations in the frequency domain, both in vacuum and in cold magnetized plasma, with a boundary condition that guarantees the existence of a potential associated with the radio frequency electric fields tangential to certain surfaces. This potential is of interest to nonlinear sheath physics, since it enables the calculation of the time-dependent sheath current excited by a single-frequency electromagnetic wave and thereby the associated DC sheath current and sheath potential.

Calculation of RF sheath properties from surface wave-fields: a post-processing method

In ion cyclotron range of frequency (ICRF) experiments in fusion research devices, radio frequency (RF) sheaths form where plasma, strong RF wave fields and material surfaces coexist. These RF sheaths affect plasma material interactions such as sputtering and localized power deposition, as well as the global RF wave fields themselves. RF sheaths may be modeled by employing a sheath boundary condition (BC) in place of the more customary conducting wall (CW) BC; however, there are still many ICRF computer codes that do not implement the sheath BC. In this paper we present a method for post-processing results obtained with the CW-BC. The post-processing method produces results that are equivalent to those that would have been obtained with the RF sheath BC, under certain assumptions. The post-processing method is also useful for verification of sheath BC implementations and as a guide to interpretation and understanding of the role of RF sheaths and their interactions with the waves that drive them.

Impact of Sheath Boundary Conditions and Magnetic Flutter on Evolution and Distribution of Transient Particle and Heat Fluxes in the Edge-Localized Mode Burst by Experimental Advanced Superconducting Tokamak Simulation**Supported by the National Key R&D Program of China under Grant Nos 2017YFE0301100, 2017YFE0301101, 2017YFE0301104 and 2014GB106001, the National Natural Science Foundation of China under Grant Nos 11275047, 11675217, 11505236 and 11405215,

To study the evolution and distribution of the transient particle and heat fluxes during the edge-localized modes (ELMs) burst on the experimental advanced superconducting tokamak (EAST), the BOUT++ six-field two-fluid model with sheath boundary conditions (SBCs) and magnetic flutter terms in the parallel thermal conduction is used to simulate the evolution of the profiles and growing process of the fluxes at divertor targets. Although SBCs hardly play a role in the linear phase, in the nonlinear phase both SBCs and magnetic flutter can change the dominant toroidal mode. SBCs are able to broaden the frequency distribution of the turbulence. The magnetic flutter increases the ELM size from 2.8% to 8.4%, and it doubles the amplitudes of the radial heat and particle transport coefficients at outer midplane (OMP), at around 1.0m2s−1. It is then able to increase the particle and heat flux at the divertor targets and to broaden the radial distribution of the parallel heat flux towards the targets.

Gyrokinetic continuum simulations of plasma turbulence in the Texas Helimak

The first gyrokinetic simulations of plasma turbulence in the Texas Helimak device, a simple magnetized torus, are presented. The device has features similar to the scrape-off layer region of tokamaks, such as bad-curvature-driven instabilities and sheath boundary conditions on the end plates, which are included in these simulations. Comparisons between simulations and measurements from the experiment show not only similarities, including equilibrium profiles and fluctuation amplitudes that approach experimental values, but also some important quantitative differences. Both experimental and simulation results exhibit turbulence statistics that are characteristic of blob transport.

Radio-frequency wave interactions with a plasma sheath in oblique-angle magnetic fields using a sheath impedance model

The physics of interactions between waves in plasmas and sheaths for background magnetic fields which make oblique angles with sheath surfaces is studied with the use of the self-consistent finite element code rfSOL incorporating the recently developed sheath impedance model [J. R. Myra, Phys. Plasmas 24, 072507 (2017)]. The calculation based on this model employs the generalized sheath boundary condition (sheath BC), which surpasses the previously used capacitive sheath BC in reliability by taking into account the contributions of the ion and electron currents in the sheath and the displacement current. A series of numerical simulations is carried out in two-dimensional slab geometry with a flat or curved sheath surface as part of the boundary. It is shown that the sheath–plasma wave appears when the equilibrium magnetic field line angle with respect to the sheath surface is small, the absolute value of the radio-frequency (RF) sheath voltage is large, and the plasma density is slightly higher than the lower hybrid resonance density (LHR density), all of which bring the sheath property closer to being capacitive. It is also shown that the sharp variation of the magnetic field line angle along the sheath surface can sensitively affect the maximum absolute value of the RF sheath voltage at a plasma density slightly lower than the LHR density.

An ERP study of inhibitory control in adults with developmental coordination disorder

The steady state radial electric field (Er) is calculated by coupling a plasma transport model with the quasi-neutrality constraint and the vorticity equation within the BOUT++ framework. Based on the experimentally measured plasma density and temperature profiles in Alcator C-Mod discharges, the effective radial particle and heat diffusivities are inferred from the set of plasma transport equations. The effective diffusivities are then extended into the scrape-off layer (SOL) to calculate the plasma density, temperature and flow profiles across the separatrix into the SOL with the electrostatic sheath boundary conditions (SBC) applied on the divertor plates. Given these diffusivities, the electric field can be calculated self-consistently across the separatrix from the vorticity equation with SBC coupled to the plasma transport equations. The sheath boundary conditions act to generate a large and positive Er in the SOL, which is consistent with experimental measurements. The effect of magnetic particle drifts is shown to play a significant role on local particle transport and Er by inducing a net particle flow in both the edge and SOL regions.