Magnetic Presheath Research Articles

Plasma dynamics and collisional magnetic presheath structure in unmagnetized divertor plasma in fusion devices

A model of strongly ionized plasma dynamics in a slightly inclined magnetic field with ions, unmagnetized with respect to ion–ion collisions, typical for detached regimes, is presented. It is demonstrated that far from the material surface, the parallel dynamics remains almost the same as in the magnetized plasma. In the wall vicinity, parallel plasma motion is transformed into perpendicular classical diffusion originating from electron–ion collisions, forming a diffusive layer. At a distance of few ion gyroradii from the material surface, a collisional magnetic presheath is formed, where ions move toward the surface with the velocity of the order of the sound speed, in spite of the fact that an ion exhibits many collisions before reaching the surface. For typical inclination angles of magnetic field of the order of few degrees, the electrostatic potential in the diffusive layer and in the presheath deviates considerably from the Boltzmann potential for electrons, which is typical for collisionless magnetic presheath. Moreover, the normal electric field in some regions is directed away from the surface, which is important for impurities to interact with the surface.

Time-dependent collisional radiative modeling of tungsten in the magnetic sheath for erosion diagnosis

Abstract Tungsten is the material of choice for the divertors in ITER, SPARC and future fusion reactors. Accurate diagnosis of tungsten erosion and migration is important for first wall life time, slag production and core performance. The addition of a magnetic presheath requires time-dependent collisional radiative effects to be included for accurate neutral tungsten collisional radiative modeling. Gross erosion measurements could be modified by a factor of 10 due to the inclusion of time-dependent effects for ITER relevant divertor conditions. A simple sputtering model and sheath density model are developed to investigate time-dependent collisional radiative effects. Neutral tungsten spectral lines populated from different metastable levels depend on model parameters leading to potential spectroscopic diagnostics of plasma parameters. Electron temperatures inferred from spectroscopic line ratios are in agreement with Langmuir probe measurements in the Compact Toroidal Hybrid.

Particle-based simulation of atom and ion transport in HiPIMS: effect of the plasma potential distribution on the ionized flux fraction

We present a three-dimensional particle-based computer simulation of high-power impulse magnetron sputtering (HiPIMS) discharges which enables us to simulate the transport of atoms and ions in the discharge and the corresponding plasma parameters. The simulation requires a definition of the plasma potential and electron density distribution (not calculated self-consistently), for which parametric analytical formulae were devised. A numerical algorithm is used to constrain the simulation by an experimental target current waveform, which ensures that the simulation results are closely tied to the experimental discharge conditions. Simulations of a HiPIMS discharge with Ti target show the capability to calculate the spatial distributions of target material atoms and ions and also to quantify the process-gas rarefaction. We evaluated, among others, the ion return probability and the ionized fraction of the target material flux onto the substrate for various values of the potential difference across the magnetic presheath in front of the target racetrack, which is responsible for attracting most of the plasma ions towards the target. It is shown that this parameter of the plasma potential distribution strongly affects the ion return probability and, thus, it must be known quite precisely to reliably predict the ionized flux fraction on the substrate. Other parameters, such as the composition of the ion flux onto the target are less sensitive. The simulation can be run in a reasonably short time and can easily be extended by adding more plasma species (excited states or doubly ionized species) and their interactions.

Determination of the characteristic magnetic pre-sheath length at divertor surfaces using micro-engineered targets on DiMES at DIII-D

The magnetic pre-sheath (MPS) length, L MPS, is a critical parameter to define the sheath potential, which controls the ion trajectory of low-Z species (D, T, He, and C), as well as the prompt re-deposition of high-Z species. To determine L MPS, we fabricated micro-trenches (30 × 30 × 4 μm) via focused ion beam milling on a silicon surface and exposed them to L-mode deuterium plasmas in DIII-D via the divertor material evaluation system (DiMES) removable sample exposure probe. The areal distribution of impurity depositions, mainly consisting of carbon, was measured by energy-dispersive x-ray spectroscopy (EDS) to reveal the deuterium ion shadowing effect on the trench floors. The carbon deposition profiles showed that the erosion was maximized for the azimuthal direction of φ = −40° (referenced to the toroidal magnetic field direction) as well as the polar angle of θ = 80°. A Monte Carlo equation-of-motion (EOM) model, based on a collisionless MPS, was used to calculate the azimuthal and polar deuterium ion angle distributions (IADs) at the surface for a range of L MPS = k × ρ i, where ρ i is the ion gyro radius and k = 0.5–4. Then, gross erosion profiles were calculated by a Monte Carlo micro-patterning and roughness (MPR) code for ion sputtering using as input the calculated azimuthal and polar IADs for each value of k. Good agreement with the experimental C deposition profiles was obtained for the case k = 2.5–3.5. This result is consistent with a previous kinetic modeling prediction of k ∼ 3, as well as previous analytical investigations that predicted the L MPS to be several ion gyro radii. A validation of theoretical sheath models supports its applicability to ITER and pilot plant divertors to successfully predict plasma–materials interactions.

Sheath collapse at critical shallow angle due to kinetic effects

The Debye sheath is known to vanish completely in magnetised plasmas for a sufficiently small electron gyroradius and small angle between the magnetic field and the wall. This angle depends on the current onto the wall. When the Debye sheath vanishes, there is still a potential drop between the wall and the plasma across the magnetic presheath. The magnetic field angle corresponding to the predicted sheath collapse is shown to be much smaller than previous estimates, scaling with the electron-ion mass ratio and not with the square root of the mass ratio. This is shown to be a consequence of the kinetic electron and finite ion orbit width effects, which are not captured by fluid models. The wall potential with respect to the bulk plasma at which the Debye sheath vanishes is calculated. Above this wall potential, it is possible that the Debye sheath will invert.

Influence of magnetic angle on the E × B drift in a magnetic presheath

In this work, we provide experimental measurements of the E×B flow above a non-magnetic, absorbing boundary in a magnetized plasma. Measurements are taken as a function of the angle between the background magnetic field and the boundary normal. The measurements are compared to computational predictions for oblique magnetic fields based on Chodura's model. Ion flow measurements were obtained with laser induced fluorescence and the presheath potential structure was measured with an emissive probe. The ions were found to accelerate to nearly 30% of the sound speed parallel to the boundary at oblique angles of the magnetic field (∼80°) and the ion speed at the electrostatic sheath edge was found to decrease with angle. The edge of the magnetic presheath has been experimentally determined based on the appearance of the E×B drift and is found to be independent of the angle of the magnetic field. We also demonstrate that laser induced fluorescence is suitable as a non-perturbative diagnostic to measure the electric field in a magnetized sheath.

The influence of boundary and edge-plasma modeling in computations of axisymmetric vertical displacement

A number of previously published studies apply extended-magnetohydrodynamics (MHD) computations to model macroscopic dynamics of tokamak vertical displacement events (VDEs). The characteristic plasma-wall contact and resistive-wall diffusion imply sensitivity to boundary conditions in a general sense, but which conditions have significant influence depends on how the plasma is modeled. This work examines these dependencies by comparing results of axisymmetric extended-MHD computations with different sets of boundary conditions, plasma thermal-conduction models, and wall resistivity values. The geometry and plasma parameters of the computations represent a modest-sized tokamak. The forced-displacement scenario and computational setup are similar to those used in previous 3D computations [C. R. Sovinec and K. J. Bunkers, Phys. Plasma Controlled Fusion 61, 024003 (2019)]. The results show that for a given wall resistivity, the VDE time scale is most sensitive to variations in the boundary and thermal-conduction parameters that affect electron thermal transport. The electrical conductivity depends on electron temperature, and the dependence on thermal transport stems from its influence on the electrical circuit that includes the open-field halo current. Conditions that lead to hotter, broader halo regions slow the evolution. Significant sensitivity to the boundary condition on plasma flow-velocity exists when electron thermal conduction is restricted and electron energy loss is convective, which is expected for conditions at the entrance of the magnetic presheath.

Three-dimensional cross-field flows at the plasma-material interface in an oblique magnetic field

This article describes experimental evidence that the magnetic presheath is a fully three-dimensional structure modified by ion–neutral collisions. Velocity distributions of both ions and neutrals, obtained via laser-induced fluorescence, show that cross field ion drifts do not result from entrainment of ions in a flowing neutral background. Ion flows parallel to E×B arise and accelerate to as much as 0.2cs within several ion gyroradii of the boundary surface, where cs is the sound speed. Within measurement resolution, the onset of the E×B aligned flow occurs at the same distance to the surface that ions begin to deflect from travel along magnetic field lines. Collisional fluid and particle-in-cell simulations of the boundary region are compared to the experimental measurements. We find that, in contrast to the classical collisionless Chodura model, collisional effects between the ions and the non-flowing neutral population are essential to quantitatively predict the observed ion drift velocities. No momentum coupling between ions and neutrals, separable from noise and other effects, is observed in either signal. We discuss several explanations and implications of this observation.

An explicit scheme to enforce charge conservation in transient Particle-in-Cell simulations with Maxwell-Boltzmann electrons

The Maxwell-Boltzmann electron model is a very popular approximation of the electronic behavior in electrostatic plasmas, adopted in all cases where the electron dynamics is governed only by a balance between electric and pressure forces. In such a model, the electron dynamics is reduced to solving for a nonlinear Poisson problem together with an additional expression enforcing charge conservation. In this work we derive an expression of charge conservation which can be conveniently applied to explicit schemes to update the reference Boltzmann density, particularly useful when simulating plasma sheaths. The scheme can be equally applied to both steady-state and transient problems. Two examples are shown, a steady-state plasma sheath, and a radio-frequency magnetic presheath. Our proposed scheme allows to enforce global charge conservation locally in time, and can thus be applied to the simulation of transient phenomena.

Dependence on ion temperature of shallow-angle magnetic presheaths with adiabatic electrons

The magnetic presheath is a boundary layer occurring when magnetized plasma is in contact with a wall and the angle $\unicode[STIX]{x1D6FC}$ between the wall and the magnetic field $\boldsymbol{B}$ is oblique. Here, we consider the fusion-relevant case of a shallow-angle, $\unicode[STIX]{x1D6FC}\ll 1$ , electron-repelling sheath, with the electron density given by a Boltzmann distribution, valid for $\unicode[STIX]{x1D6FC}/\sqrt{\unicode[STIX]{x1D70F}+1}\gg \sqrt{m_{\text{e}}/m_{\text{i}}}$ , where $m_{\text{e}}$ is the electron mass, $m_{\text{i}}$ is the ion mass, $\unicode[STIX]{x1D70F}=T_{\text{i}}/ZT_{\text{e}}$ , $T_{\text{e}}$ is the electron temperature, $T_{\text{i}}$ is the ion temperature and $Z$ is the ionic charge state. The thickness of the magnetic presheath is of the order of a few ion sound Larmor radii $\unicode[STIX]{x1D70C}_{\text{s}}=\sqrt{m_{\text{i}}(ZT_{\text{e}}+T_{\text{i}})}/ZeB$ , where e is the proton charge and $B=|\boldsymbol{B}|$ is the magnitude of the magnetic field. We study the dependence on $\unicode[STIX]{x1D70F}$ of the electrostatic potential and ion distribution function in the magnetic presheath by using a set of prescribed ion distribution functions at the magnetic presheath entrance, parameterized by $\unicode[STIX]{x1D70F}$ . The kinetic model is shown to be asymptotically equivalent to Chodura’s fluid model at small ion temperature, $\unicode[STIX]{x1D70F}\ll 1$ , for $|\text{ln}\,\unicode[STIX]{x1D6FC}|>3|\text{ln}\,\unicode[STIX]{x1D70F}|\gg 1$ . In this limit, despite the fact that fluid equations give a reasonable approximation to the potential, ion gyro-orbits acquire a spatial extent that occupies a large portion of the magnetic presheath. At large ion temperature, $\unicode[STIX]{x1D70F}\gg 1$ , relevant because $T_{\text{i}}$ is measured to be a few times larger than $T_{\text{e}}$ near divertor targets of fusion devices, ions reach the Debye sheath entrance (and subsequently the wall) at a shallow angle whose size is given by $\sqrt{\unicode[STIX]{x1D6FC}}$ or $1/\sqrt{\unicode[STIX]{x1D70F}}$ , depending on which is largest.

Numerical model of the radio-frequency magnetic presheath including wall impurities

Here, we present a numerical fluid plasma model able to capture the enhanced sputtering yield from the Faraday Screen and the Plasma-Facing Components of an Ion Cyclotron Resonance Heating antenna in a fusion machine. The model is a one-dimensional phase-resolved representation of a rectified radio frequency sheath in a magnetic field at an angle with respect to the material surface; the momentum transport of both ions and impurities is computed in the model. The sputtering behavior of the impurities coming off from the wall is obtained from the plasma-material interaction code Fractal-Tridyn. This study analyzes a range of magnetic angles and wave frequencies to parametrically investigate their effect on the energy-angle distributions of the impacting ions and sputtered impurities. Finally, an estimate of the impurity fluxes and of the gross-erosion rate is provided and compared with experimental data available in the literature.

On attenuation of electron current of flush-mounted probes and electrodes in magnetised plasmas

The ratio of electron and ion saturation currents measured by probes embedded in the plasma-facing components (PFCs) in magnetised plasmas is typically lower than predicted by Langmuir theory. In the past, several works targeted various effects influencing the ion saturation current, which can be larger than expected, especially if the magnetic field is at a grazing angle with respect to the probe surface. In this contribution, we focus on the electron current, which can be reduced when the magnetic field line intercepting the probe passes through the magnetic pre-sheath of the nearby PFC. In such a case an effective potential well forms and repels a fraction of the electrons incoming from the plasma. Experimental results obtained by a tiltable limiter at the DITE tokamak are revisited and reproduced by means of 2D3V particle-in-cell simulations. The reduction of the electron current is indeed observed both in simulations and in experiment. This mechanism may also explain why some divertor biasing experiments did not produce flows in the divertor region.

Results of Ion Cyclotron Heating Experiments on Proto-MPEX Utilizing a Movable Stainless Steel Target

Ion cyclotron heating (ICH) at a frequency in the 6- to 9-MHz range with electron heating in the 28- to 105-GHz range will be used in the Material Plasma Exposure eXperiment (MPEX) to greatly increase the energy of the plasma stream produced by the helicon plasma source. ICH was chosen over substrate biasing to produce energetic ions because it can more accurately reproduce plasma-material interactions in a fusion device. For instance, when the target is tilted with respect to the background magnetic field during ICH, a magnetic presheath is created so that redeposition phenomena as in a tokamak divertor can be better approximated. ICH experiments were conducted on the Proto-MPEX device, which was developed to provide a physics basis upon which MPEX is designed. In this paper we describe some of these experiments in which the previous fixed graphite target was replaced by a movable stainless steel target. With the new target, the strong, monotonic decrease in ion temperature observed previously as a function of axial distance between the ion cyclotron resonance region and the target was not observed. Instead, only a small drop was seen within ~1 cm of the target. The ion temperatures were determined spectroscopically, utilizing Doppler broadening measurements of an Ar II line, in a plasma that is 90% deuterium and 10% argon. Measurements were obtained using optical fibers at a fixed location, with the target moving perpendicularly relative to the viewing chords. Comparisons with previous results will be discussed, including observed plasma parameters Ti, Te, and ne, and heat flux at the target.

Solution to a collisionless shallow-angle magnetic presheath with kinetic ions

Using a kinetic model for the ions and adiabatic electrons, we solve a steady state, electron-repelling magnetic presheath in which a uniform magnetic field makes a small angle (in radians) with the wall. The presheath characteristic thickness is the typical ion gyroradius . The Debye length and the collisional mean free path of an ion λmfp satisfy the ordering λD ≪ ρi ≪ α λmfp, so a quasineutral and collisionless model is used. We assume that the electrostatic potential is a function only of distance from the wall, and it varies over the scale ρi. Using the expansion in α ≪ 1, we derive an analytical expression for the ion density that only depends on the ion distribution function at the entrance of the magnetic presheath and the electrostatic potential profile. Importantly, we have added the crucial contribution of the orbits in the region near the wall. By imposing the quasineutrality equation, we derive a condition that the ion distribution function must satisfy at the magnetic presheath entrance—the kinetic equivalent of the Chodura condition. Using an ion distribution function at the entrance of the magnetic presheath that satisfies the kinetic Chodura condition, we find numerical solutions for the self-consistent electrostatic potential, ion density and flow across the magnetic presheath for several values of α. Our numerical results also include the distribution of ion velocities at the Debye sheath entrance. We find that at small values of α there are substantially fewer ions travelling with a large normal component of the velocity into the wall.

Measurement and modeling of aluminum sputtering and ionization in the DIII-D divertor including magnetic pre-sheath effects

We present analysis and modeling of Al sputtering and ionization in attached, low-power L-mode plasmas near the outer divertor strike point of the DIII-D tokamak. Al serves as a useful proxy for Be, the low-Z main wall material for ITER and JET that will undergo significant divertor plasma contact upon migrating from the first wall to the divertor. Al is easily distinguishable from background sources in DIII-D (namely C and B), has a high physical sputtering yield similar to Be, and has a long ionization mean free path compared to its gyro radius (). Using neutral Al emission imaging techniques, we measured a toroidal and radial asymmetry in the shape of the photo-emission plumes of sputtered neutral Al that was consistent with previously observed asymmetry in the distribution of redeposited Al in these experiments. We propose that the main cause of the emission and redeposition asymmetry is due to a sputtering anisotropy caused by near-grazing angle incident ions. The observed emission asymmetry was reproduced using a simple emission/ionization model that included full angular distributions of sputtering yield and energy calculated by SDTRIM.SP, but not when symmetric, mono-energetic cosine sputtering distributions were assumed. We used an ion orbit tracking model to calculate the distributions of ion impact energies through the potential gradient in the magnetic pre-sheath and Debye sheath. We found that with the magnetic field pitch angle (1.5°–2° with respect to the surface plane), the majority of ions strike the surface at <15° with respect to the surface plane, leading to angular sputtering yield and energy distributions with significant forward-scattering bias. We also observed surface microstructure consistent with directional sputtering and ion flux shadowing expected from the calculated ion incidence angles.

3D particle-in-cell modeling of Langmuir probe effective collecting area in magnetized plasma

Langmuir probes are a widespread tool for measurement of important plasma parameters such as electron temperature Te, plasma electron density ne, ion saturation current Isat and the floating potential Vfl, which are obtained from a fit to the current–voltage (I–V) characteristic of the probe. In magnetized plasmas, the measurements can be affected by sheath expansion due to large negative bias voltages, which is addressed by the introduction of a fourth parameter to the fitting function correcting the values of all measured quantities. In order to derive the plasma density from Isat, the understanding of probe ion collection is needed. In magnetized plasmas, the collecting area may not correspond to the real geometrical probe surface due to ion finite Larmor effects and so the derivation of Isat (and hence n) can be rather complicated. In this work, the influence of magnetic fields on the probe effective collecting area is studied by the means of fully 3D3V particle-in-cell model SPICE3. A parameter scan based on properties of scrape-off layer plasmas at COMPASS tokamak as well as a particular probe pin used on a horizontal reciprocating manipulator is performed. The results reveal that the presence of the probe head has a substantial effect on the outcome of the measurement as it forms a magnetic presheath at the probe location. An approximate formula for addressing the change of effective collecting area is presented and the data from the simulations are compared to measurements of COMPASS reciprocating probes and lithium beam emission spectroscopy.

HPIC: A scalable electrostatic Particle-in-Cell for Plasma–Material Interactions

The hPIC code is a fully-kinetic electrostatic Particle-in-Cell application targeted at large-scale simulations of Plasma–Material Interactions. The code can simulate multi-component strongly-magnetized plasmas in a region close to the wall, including the magnetic sheath and presheath, plus the first surface layers which release material impurities. The Poisson solver is based on PETSc conjugate gradient with BoomerAMG algebraic multigrid preconditioners. Scaling tests on the Blue Waters supercomputer have demonstrated excellent weak-scaling (tested up to 65,536 cores) and good strong-scaling up to 262,144 cores. In this paper, we will make an overview of the main features of the code and of the scaling performance as measured on the Blue Waters supercomputer at Illinois.

On thermionic emission from plasma-facing components in tokamak-relevant conditions

The first results of particle-in-cell simulations of the electrostatic sheath and magnetic pre-sheath of thermionically emitting planar tungsten surfaces in fusion plasmas are presented. Plasma conditions during edge localized modes (ELMs) and during inter-ELM periods have been considered for various inclinations of the magnetic field and for selected surface temperatures. All runs have been performed under two assumptions for the sheath potential drop; fixed or floating. The primary focus lies on the evaluation of the escaping thermionic current and the quantification of the suppression due to the combined effects of space-charge and Larmor gyration. When applicable, the results are compared with the predictions of analytical models. The heat balance in the presence of thermionic emission as well as the contribution of the escaping thermionic current to surface cooling are also investigated. Regimes are identified where emission needs to be considered in the energy budget.

Advances in understanding of high-Z material erosion and re-deposition in low-Z wall environment in DIII-D

Dedicated DIII-D experiments coupled with modeling reveal that the net erosion rate of high-Z materials, i.e. Mo and W, is strongly affected by carbon concentration in the plasma and the magnetic pre-sheath properties. Different methods such as electrical biasing and local gas injection have been investigated to control high-Z material erosion. The net erosion rate of high-Z materials is significantly reduced due to the high local re-deposition ratio. The ERO modeling shows that the local re-deposition ratio is mainly controlled by the electric field and plasma density within the magnetic pre-sheath. The net erosion can be significantly suppressed by reducing the sheath potential drop. A high carbon impurity concentration in the background plasma is also found to reduce the net erosion rate of high-Z materials. Both DIII-D experiments and modeling show that local 13CH4 injection can create a carbon coating on the metal surface. The profile of 13C deposition provides quantitative information on radial transport due to E × B drift and the cross-field diffusion. The deuterium gas injection upstream of the W sample can reduce W net erosion rate by plasma perturbation. In H-mode plasmas, the measured inter-ELM W erosion rates at different radial locations are well reproduced by ERO modeling taking into account charge-state-resolved carbon ion flux in the background plasma calculated using the OEDGE code.

Gyrokinetic treatment of a grazing angle magnetic presheath

We develop a gyrokinetic treatment for ions in the magnetic presheath, close to the plasma-wall boundary. We focus on magnetic presheaths with a small magnetic field to wall angle, (in radians). Characteristic lengths perpendicular to the wall in such a magnetic presheath scale with the typical ion Larmor orbit size, . The smallest scale length associated with variations parallel to the wall is taken to be across the magnetic field, and ordered , where is assumed. The scale lengths along the magnetic field line are assumed so long that variations associated with this direction are neglected. These orderings are consistent with what we expect close to the divertor target of a tokamak. We allow for a strong component of the electric field in the direction normal to the electron repelling wall, with strong variation in the same direction. The large change of the electric field over an ion Larmor radius distorts the orbit so that it is not circular. We solve for the lowest order orbits by identifying coordinates, which consist of constants of integration, an adiabatic invariant and a gyrophase, associated with periodic ion motion in the system with . By using these new coordinates as variables in the limit , we obtain a generalised ion gyrokinetic equation. We find another quantity that is conserved to first order and use this to simplify the gyrokinetic equation, solving it in the case of a collisionless magnetic presheath. Assuming a Boltzmann response for the electrons, a form of the quasineutrality equation that exploits the change of variables is derived. The gyrokinetic and quasineutrality equations give the ion distribution function and electrostatic potential in the magnetic presheath if the entrance boundary condition is specified.