Sheath Boundary 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 gyrokinetic simulation model for 2D equilibrium potential in the scrape-off layer of a field-reversed configuration

The equilibrium potential structure in the scrape-off layer (SOL) of the field-reversed configuration (FRC) can be affected by the penetration of edge biasing applied at the divertor ends. The primary focus of the paper is to establish a formulation that accurately captures both parallel and radial variations of the two-dimensional (2D) potential in SOL. The formulation mainly describes a quasi-neutral plasma with a logical sheath boundary. A full-f gyrokinetic ion model and a massless electron model are implemented in the GTC-X code to solve for the self-consistent equilibrium potential, given fixed radial potential profiles at the boundaries. The first essential point of this 2D model lies in its ability to couple radial and parallel dynamics stemming from resistive currents and drag force on ions. The model successfully recovers the fluid force balance and continuity equations. These collisional effects on 2D potential mainly appear through the density profile changes, modifying the potential through electron pressure gradient. This means an accurate prescription of electron density and temperature profiles is important in predicting the potential structure in the FRC SOL. The Debye sheath potential and the potential profiles applied at the boundaries can be additional factors contributing to the 2D variations in SOL. This comprehensive full-f scheme holds promise for future investigations into turbulent transport in the presence of the self-consistent 2D potential together with the non-Maxwellian distributions and open boundary conditions in the FRC SOL.

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.

Influence of radio frequency wave driving frequency on capacitively coupled plasma discharge

A two-dimensional symmetric fluid model is established to study the influence of radio frequency (RF) wave driving frequency on the capacitively coupled plasma discharge. The relationship between the driving frequency and electron density is obtained by solving the electron energy balance equation. The calculation results show that the average electron density first increases rapidly with the increase in driving frequency and then gradually tends to saturation at a threshold frequency. A fluid simulation is also carried out, which provides similar results. Physical studies on this phenomenon are conducted, revealing that the essence of this phenomenon is due to the inability of electrons to quickly respond to potential changes within the boundary sheath when the driving frequency of RF exceeds the plasma frequency. In addition, it is also found that increasing gas pressure can enhance the electron density and the type of gas can also affect the electron density.

Ion flow and dust charging at the sheath boundary in dusty plasma with an electron-emitting surface: applications to laboratory and lunar dusty plasmas

In laboratory and space plasmas, the emission of electrons from the surface significantly affects the characteristics of the plasma sheath that forms at that surface, which is crucial to understanding the overall plasma-wall interaction mechanism. In this work, the collisional fluid model is used for laboratory dusty plasma, whereas the collisionless model is used for lunar dusty plasma. We have extended the Bohm sheath criterion for the formation of the stable plasma sheath due to electron emission from the surface, loss of ion flux, and the gas pressure of the collisional laboratory dusty plasmas. It is found that ion flow at the sheath boundary is considerably influenced by the concentration of electron emission, the ion loss term, and gas pressure. The evolution of the dust charge explicitly determines the magnitude of the ion flow at the sheath boundary. The plasma parameters adopted in the present case are reliable in laboratory and space dusty plasmas, especially the dusty plasma environment on the lunar surface. The lunar surface and dust grains on the Moon become electrically charged as a result of the interaction between solar wind plasma and photoemission electrons emitted from the lunar surface. In addition, the lunar plasma sheath characteristics, dust-charging process, and stable dust levitation in the sheath region have been studied.

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.

Resonant electron confinement and sheath expansion heating in magnetized capacitive oxygen discharges

In weakly magnetized capacitive radio frequency (RF) plasmas electrons accelerated into the plasma bulk by the expanding RF boundary sheath at one electrode can be returned to this electrode due to their gyromotion around an externally applied magnetic field oriented parallel to the electrodes. If the driving frequency and magnetic field are chosen so that the electron cyclotron frequency, ω ce, equals half of the driving RF, ω rf, such energetic beam electrons will be returned to the sheath during its expansion phase and, thus, will be confined and heated resonantly. This magnetized RF sheath resonance (MRSR) effect is studied based on kinetic particle-in-cell simulations in weakly magnetized capacitively coupled oxygen plasmas. In comparison with electropositive argon plasmas, this resonance mechanism is found to be affected strongly by the electronegativity of oxygen discharges. In the unmagnetized case, low-pressure capacitive oxygen discharges operate in an electropositive mode, where nonlinear high-frequency sheath oscillations play an important role similar to previous observations in electropositive discharges with low electron densities. If the resonance condition is fulfilled (), the discharge efficiency is enhanced due to the MRSR effects, resulting in an increase in plasma density. Our numerical results demonstrate that this resonance effect is particularly efficient at low pressure and low electronegativity. However, in strongly electronegative discharges, the time it takes a typical resonant electron to return to the expanding sheath edge is found to be affected by drift and ambipolar electric fields in the plasma bulk, which cause a deviation from the resonance condition, resulting in a reduction of this type of resonance effect.

Hairpin probe assisted saturation current ratio method to determine plasma electronegativity

The saturation current ratio (SCR) method is considered to be one of the simplest methods to determine plasma electronegativity in electronegative discharges using a Langmuir probe (LP). However, its accuracy is susceptible to errors incurred in the estimation of electron and positive ion saturation currents from the ampere–voltage characteristics obtained by a cylindrical LP and partly due to errors in estimating the positive ion flux at the sheath boundary. In spite of its wide use, these underlying limitations and their remedies have not been adequately investigated. In this paper, we address the above problems by involving a DC biased hairpin resonator probe to determine the plasma potential and sheath area correction factor for a cylindrical LP. These measurements are further integrated with the standard SCR method to deduce the plasma electronegativity in an oxygen plasma.

Collisionless dissipation at the boundary sheath of magnetized low temperature plasmas

In partially magnetized technological plasmas like magnetron discharges or Hall-effect thrusters, the interaction of gyrating electrons with the plasma boundary sheath plays an important role. This study shows that the interaction can be described as a dissipative process. It is assumed that the Debye length is much smaller than the electron gyroradius , and in turn much smaller than the mean free path λ and the field gradient length l. Focusing on the scale of the gyroradius, the sheath is assumed as thin (), collisions are neglected (), the magnetic field is taken as homogeneous, and electric fields (= potential gradients) in the bulk are neglected (). The interaction of an electron with the electric field of the plasma boundary sheath is represented by specular reflection, , where v is the electron velocity and n is the sheath normal. A previous study showed that this set-up leads to a scattering process where gyrophase invariant incoming velocity distributions are scattered into outgoing distributions with fractal dependence on the gyrophase (Krüger and Brinkmann 2017 Plasma Sources Sci. Technol. 26 115009). The present research focuses on the subsequent evolution. It is shown that the gyromotion results in fast phase mixing with respect to the gyrophase which quickly restores the gyrophase invariance. In combination, the two phases of the sheath interaction constitute a mapping within the space of gyrophase invariant distributions. This combined process is dissipative and leads to isotropization. As an explicit comparison shows, it acts similarly to elastic electron-neutral collisions and can even dominate the latter in low pressure plasmas. A simplified version of the operator that applies for weakly anisotropic distributions is suited for practical simulation work.

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.

Effects of amplitude modulated discharge on growth of nanoparticles in TEOS/O2/Ar capacitively coupled plasma

We investigate the effects of the amplitude modulation (AM) discharge method on the growth of nanoparticles and the relation between growth of nanoparticles and plasma generation in tetraethylorthosilicate (TEOS)/O2/Ar plasma. The laser-light scattering (LLS) intensity, which is proportional to the density and the sixth power of the size of nanoparticles in the Rayleigh scattering regime, decreases by 18% at an AM level of 10% and by 60% at an AM level of 50%. On the other hand, the ArI emission intensity, which is roughly proportional to plasma density, is higher than that for the continuous wave discharge. Thus, AM discharges suppress growth of nanoparticles in TEOS plasma. We have shown oscillations of the axial electric field Ez with the AM frequency for AM discharge by electric field measurement using an electro-optic probe. We have discussed that these fluctuations of Ez mainly lead to the vertical oscillation of the levitation position of nanoparticles trapped in the plasma sheath boundary region by taking into account the force balance equation in the axial direction on these negatively charged nanoparticles.

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.

Predicting power–voltage characteristics and mode transitions in the COST reference microplasma jet

A 2D cross-field plasma fluid model (CFPM) is applied to He and He/O2 discharges in the CΟoperation in Science and Technology (COST) reference microplasma jet to investigate the operating modes, namely α-, α–γ, and γ-mode. The model not only captures the measured spatiotemporal behavior of He excitation to He metastable but also quantitatively predicts measured power–voltage (PV) characteristics for He/O2 discharges; although not addressed by previous studies, this is a prerequisite for the reliability of the model predictions for the critical-for-applications densities of reactive species. Through a comparison to time-averaged emission profiles and allowed by the dimensionality of the CFPM, the localized, close to the outlet of the discharge channel, onset of γ-mode for He discharges is predicted and justified. Τhe sheath boundary is defined by the maximum of the electron density derivative and the model results compare well to measurements of time-averaged sheath width. Criteria for the transition between the operating modes are formulated. It is considered that when the production rate of He metastable in the sheaths reaches 10% of its total production rate, transition from α- to α–γ mode takes place. When this percentage reaches ∼50%, i.e. α- and γ- modes have an almost equal contribution to the discharge, the electron temperature becomes maximum. Finally, the sensitivity of PV characteristics on the secondary electron emission coefficients, condition of the electrode surface, and fabrication or assembly mishits of the COST jet, is investigated.

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

Validation of the smooth step model by particle-in-cell/Monte Carlo collisions simulations

Bounded plasmas are characterized by a rapid but smooth transition from quasi-neutrality in the volume to electron depletion close to the electrodes and chamber walls. The thin non-neutral region, the boundary sheath, comprises only a small fraction of the discharge domain but controls much of its macroscopic behavior. Insights into the properties of the sheath and its relation to the plasma are of high practical and theoretical interest. The recently proposed smooth step model (SSM) provides a closed analytical expression for the electric field in a planar, radio-frequency modulated sheath. It represents (i) the space charge field in the depletion zone, (ii) the generalized Ohmic and ambipolar field in the quasi-neutral zone, and (iii) a smooth interpolation for the transition in between. This investigation compares the SSM with the predictions of a more fundamental particle-in-cell/Monte Carlo collisions simulation and finds good quantitative agreement when the assumed length and time scale requirements are met. A second simulation case illustrates that the model remains applicable even when the assumptions are only marginally fulfilled.

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.