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At least 631 records · Page 35
All sourcesNASA NTRSDOE OSTI
DOE OSTI2013

Particle-in-cell simulation of an electronegative plasma under direct current bias studied in a large range of electronegativity

A one-dimensional electronegative plasma situated between two symmetrical parallel electrodes under DC bias is studied by Particle-In-Cell simulation with Monte Carlo Collisions. By varying the electronegativity {alpha}{identical_to}n{sub -}/n{sub e} from the limit of electron-ion plasmas (negative ion free) to ion-ion plasmas (electron free), the sheaths formation, the negative ion flux flowing towards the electrodes, and the particle velocities at the sheath edges are investigated. Depending on {alpha}, it is shown that the electronegative plasma behavior can be described by four regimes. In the lowest regime of {alpha}, i.e., {alpha} < 50, negative ions are confined by two positive sheaths within the plasma, while in the higher regimes of {alpha}, a negative sheath is formed and the negative ion flux can be extracted from the bulk plasma. In the two intermediate regimes of {alpha}, i.e., 50 < {alpha} < 10{sup 5}, both the electron and the negative ion fluxes are involved in the neutralization of the positive ions flux that leaves the plasma. In particular, we show that the velocity of the negative ions entering the negative sheath is affected by the presence of the electrons, and is not given by the modified Bohm velocity generally accepted for electronegative plasmas. For extremely high electronegativity, i.e., {alpha} > 10{sup 5}, the presence of electrons in the plasma is marginal and the electronegative plasma can be considered as an ion-ion plasma (electron free).

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2013

Multiple ion species plasmas with thermal ions in an oblique magnetic field

Using a three-fluid model, the combined effects of an oblique magnetic field and finite temperature of positive ion species on the characteristics of the sheath region of multi-component plasmas are investigated numerically. It is assumed that the ion species are singly charged and have different masses. In the presence of an external magnetic field, it is shown that the density distribution of positive ion species (especially the lighter ion species) begins to fluctuate and does not decrease monotonically towards the wall. Also, it is shown that by increasing the magnetic field, the amplitude of fluctuation increases and its position moves towards the sheath edge. Moreover, it is illustrated that the presence of the magnetic field affects the sheath width and by increasing the magnetic field, the sheath width decreases. In addition, the results show that in the presence of the magnetic field, the increase of temperature of positive ion species has an infinitesimal effect on the sheath width and density distribution of positive ion species.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2013

Narrow gap electronegative capacitive discharges

Narrow gap electronegative (EN) capacitive discharges are widely used in industry and have unique features not found in conventional discharges. In this paper, plasma parameters are determined over a range of decreasing gap length L from values for which an electropositive (EP) edge exists (2-region case) to smaller L-values for which the EN region connects directly to the sheath (1-region case). Parametric studies are performed at applied voltage V{sub rf}=500 V for pressures of 10, 25, 50, and 100 mTorr, and additionally at 50 mTorr for 1000 and 2000 V. Numerical results are given for a parallel plate oxygen discharge using a planar 1D3v (1 spatial dimension, 3 velocity components) particle-in-cell (PIC) code. New interesting phenomena are found for the case in which an EP edge does not exist. This 1-region case has not previously been investigated in detail, either numerically or analytically. In particular, attachment in the sheaths is important, and the central electron density n{sub e0} is depressed below the density n{sub esh} at the sheath edge. The sheath oscillations also extend into the EN core, creating an edge region lying within the sheath and not characterized by the standard diffusion in an EN plasma. An analytical model is developed using minimal inputs from the PIC results, and compared to the PIC results for a base case at V{sub rf}=500 V and 50 mTorr, showing good agreement. Selected comparisons are made at the other voltages and pressures. A self-consistent model is also developed and compared to the PIC results, giving reasonable agreement.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2016

Kinetic interpretation of resonance phenomena in low pressure capacitively coupled radio frequency plasmas

Low pressure capacitive radio frequency (RF) plasmas are often described by equivalent circuit models based on fluid approaches that predict the self-excitation of resonances, e.g., high frequency oscillations of the total current in asymmetric discharges, but do not provide a kinetic interpretation of these effects. In fact, they leave important questions open: How is current continuity ensured in the presence of energetic electron beams generated by the expanding sheaths that lead to a local enhancement of the conduction current propagating through the bulk? How do the beam electrons interact with cold bulk electrons? What is the kinetic origin of resonance phenomena? Based on kinetic simulations, we find that the energetic beam electrons interact with cold bulk electrons (modulated on a timescale of the inverse local electron plasma frequency) via a time dependent electric field outside the sheaths. This electric field is caused by the electron beam itself, which leaves behind a positive space charge, that attracts cold bulk electrons towards the expanding sheath. The resulting displacement current ensures current continuity by locally compensating the enhancement of the conduction current. The backflow of cold electrons and their interaction with the nonlinear plasma sheath cause the generation of multiple electron beams during one phase of sheath expansion and contribute to a strongly non-sinusoidal RF current. These kinetic mechanisms are the basis for a fundamental understanding of the electron power absorption dynamics and resonance phenomena in such plasmas, which are found to occur in discharges of different symmetries including perfectly symmetric plasmas.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2021

Simulations of ion heating due to ion-acoustic instabilities in presheaths

Particle-in-cell, direct simulation Monte Carlo simulations reveal that ion-acoustic instabilities excited in presheaths can cause significant ion heating. Ion-acoustic instabilities are excited by the ion flow toward a sheath when the neutral gas pressure is small enough and the electron temperature is large enough. A series of 1D simulations were conducted in which neutral plasma (electrons and ions) was uniformly sourced with an ion temperature of 0.026 eV and different electron temperatures (0.1 eV–50 eV). Ion heating was observed when the electron-to-ion temperature ratio exceeded the minimum value predicted by linear response theory to excite ion-acoustic instabilities at the sheath edge (T e /T i ≈ 28). When this threshold was exceeded, the temperature equilibration rate between ions and electrons rapidly increased near the sheath so that the local temperature ratio did not significantly exceed the threshold for instability. This resulted in significant ion heating near the sheath edge, which also extended back into the bulk plasma; presumably due to wave reflection from the sheath. Furthermore, this ion-acoustic wave heating mechanism was found to decrease for higher neutral pressures, where ion-neutral collisions damp the ion-acoustic waves and ion heating is instead dominated by inelastic collisions in the presheath.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2023

Using the Stix finite element RF code to investigate operation optimization of the ICRF antenna on Alcator C-Mod

Abstract As the Ion Cyclotron Radio Frequency range (ICRF) heating becomes more favorable in fusion devices, the urgency of predicting and mitigating impurity generation that arises from it becomes more pressing. In the ICRF regime, rectified Radio Frequency (RF) sheaths are known to form at antenna and material edges that influence negative effects like sputtering and a decrease in heating efficiency. Methods to mitigate the formation of these RF sheaths through RF image currents cancellation have been experimentally studied. A power-phasing scan done on Alcator C-Mod in which the amount of power on the two inner straps ( P in ) versus the total 4 straps ( P tot ) was varied showed a minimization of enhanced potentials between P in / P tot ∼ 0.7–0.9 while impurities were minimized for P in / P tot ∼ 0.5–0.8. New capabilities in the realm of representing the RF sheath numerically now allow for these experiments to be simulated. Given the size of the sheath relative to the scale of the device, it can be approximated as a Boundary Condition (BC). A new parallelized cold-plasma wave equation solver called Stix implements a non-linear sheath impedance model BC formulated by Myra et al (2015 Phys. Plasmas 22 062507) through the method of finite elements using the MFEM library [ http://mfem.org ]. It is seen that Stix shows qualitative agreement with the measured C-Mod enhanced potentials.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2018

Alternative model of space-charge-limited thermionic current flow through a plasma

It is widely assumed that thermionic current flow through a plasma is limited by a “space-charge-limited” (SCL) cathode sheath that consumes the hot cathode's negative bias and accelerates upstream ions into the cathode. In this paper, we formulate a fundamentally different current-limited mode. In the “inverse” mode, the potentials of both electrodes are above the plasma potential, so that the plasma ions are confined. The bias is consumed by the anode sheath. There is no potential gradient in the neutral plasma region from resistivity or presheath. The inverse cathode sheath pulls some thermoelectrons back to the cathode, thereby limiting the circuit current. Thermoelectrons entering the zero-field plasma region that undergo collisions may also be sent back to the cathode, further attenuating the circuit current. In planar geometry, the plasma density is shown to vary linearly across the electrode gap. A continuum kinetic planar plasma diode simulation model is set up to compare the properties of current modes with classical, conventional SCL, and inverse cathode sheaths. SCL modes can exist only if charge-exchange collisions are turned off in the potential well of the virtual cathode to prevent ion trapping. With the collisions, the current-limited equilibrium must be inverse. Inverse operating modes should therefore be present or possible in many plasma devices that rely on hot cathodes. Evidence from past experiments is discussed. Finally, the inverse mode may offer opportunities to minimize sputtering and power consumption that were not previously explored due to the common assumption of SCL sheaths.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2020

Particle-in-cell simulations and passive bulk model of collisional capacitive discharge

Intermediate pressure (0.2–6.0 Torr), radio frequency capacitive discharges are of increasing importance in the thin film processing industry. However, existing low pressure (<0.1 Torr) discharge models are often used beyond their applicability in this pressure range. In this work, the authors performed one-dimensional particle-in-cell (PIC) simulations of a capacitive 2.5 cm gap argon discharge driven at 13.56 MHz with current density amplitude J 0 50 A/m 2 over a wide range of gas pressures p g = 0.04–20 Torr. For intermediate pressures, the PIC results showed that most of the ionization occurs near the plasma-sheath edges with very little occurring within the central bulk region. This led us to develop a “passive bulk” model of the discharge in which bulk electron heating does not contribute to ionization, and all the ionization is due solely to the sheath-heated electrons. The model assumes a constant ion-neutral mean free path λ i in the plasma bulk and either constant λ i or constant ion mobility μ i in the sheaths. The model is solved using an electron temperature iteration scheme. The PIC scalings of the discharge equilibrium parameters (e.g., electron density and temperature, sheath width, and voltage) with the input parameters p g and J 0 showed good agreement with those of the passive bulk model. A constant μ i sheath model showed the best agreement with the PIC results in the intermediate pressure regime of interest, but a constant λ i model is simpler to implement and showed reasonable agreement over a wide pressure range.

36 MATERIALS SCIENCE↗
DOE OSTI2013

Generalized Bohm’s criterion and negative anode voltage fall in electric discharges

The value of the voltage fall across the anode sheath is found as a function of the current density. Analytic solutions are obtained in a wide range of the ratio of the directed velocity of plasma electrons v{sub 0} to their thermal velocity v{sub T}. It is shown that the voltage fall in a one-dimensional collisionless anode sheath is always negative. At the small values of v{sub 0}/v{sub T}, the obtained expression asymptotically transforms into the Langmuir formula. Generalized Bohm’s criterion for an electric discharge with allowance for the space charge density ρ(0), electric field E(0), ion velocity v{sub i}(0), and ratio v{sub 0}/v{sub T} at the plasma-sheath interface is formulated. It is shown that the minimum value of the ion velocity v{sub i}{sup *}(0) corresponds to the vanishing of the electric field at one point inside the sheath. The dependence of v{sub i}{sup *} (0) on ρ(0), E(0), and v{sub 0}/v{sub T} determines the boundary of the existence domain of stationary solutions in the sheath. Using this criterion, the maximum possible degree of contraction of the electron current at the anode is determined for a short high-current vacuum arc discharge.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2018

Floating potential of emitting surfaces in plasmas with respect to the space potential

The potential difference between a floating emitting surface and the plasma surrounding it has been described by several sheath models, including the space-charge-limited sheath, the electron sheath with high emission current, and the inverse sheath produced by charge-exchange ion trapping. Our measurements reveal that each of these models has its own regime of validity. We determine the potential of an emissive filament relative to the plasma potential, emphasizing variations in emitted current density and neutral particle density. The potential of a filament in a diffuse plasma is first shown to vanish, consistent with the electron sheath model and increasing electron emission. In a denser plasma with ample neutral pressure, the floating filament potential is positive, as predicted by a derived ion trapping condition. In conclusion, the filament floated negatively in a third plasma, where flowing ions and electrons and nonnegligible electric fields may have disrupted ion trapping. Depending on the regime chosen, emitting surfaces can float positively or negatively with respect to the plasma potential.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2024

Investigating instabilities in magnetized low-pressure capacitively coupled RF plasma using particle-in-cell (PIC) simulations

The effect of a uniform magnetic field on particle transport in low-pressure radio frequency (RF) capacitively coupled plasma (CCP) has been studied using a particle-in-cell model. Three distinct regimes of plasma behavior can be identified as a function of the magnetic field. In the first regime at low magnetic fields, asymmetric plasma profiles are observed within the CCP chamber due to the effect of $\overrightarrow{E}$ × $\overrightarrow{B}$ drift. As the magnetic field increases, instabilities develop and form self-organized spoke-shaped structures that are distinctly seen within the bulk plasma closer to the sheath. In this second regime, the spoke-shaped coherent structures rotate inside the plasma chamber in the -$\overrightarrow{E}$ × $\overrightarrow{B}$ direction, where $\overrightarrow{E}$ × $\overrightarrow{B}$ are the DC electric and magnetic field vectors, respectively, and the DC electric field exists in the sheath and pre-sheath regions. The spoke rotation frequency is in the megahertz range. As the magnetic field strength increases further, the rotating coherent spokes continue to exist near the sheath. The coherent structures are, however, accompanied by new small-scale incoherent structures originating and moving within the bulk plasma region away from the sheath. This is the third regime of plasma behavior. The threshold values of the magnetic field between these regimes were found not to vary with changing plasma reactor geometry (e.g., area ratio between ground and powered electrodes) or the use of an external capacitor between the RF-powered electrode and the RF source. The threshold values of the magnetic field between these regimes shift toward higher values with increasing gas pressure. Analysis of the results indicates that the rotating structures are due to the lower hybrid instability driven by density gradients and electron-neutral collisions. This paper provides guidance on the upper limit of the magnetic field for instability-free operation in low-pressure CCP-based semiconductor deposition and etch systems that use the external magnetic field for plasma uniformity control.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2026

Understanding carbon sourcing and transport originating from the helicon antenna surfaces during high-power helicon discharge in DIII-D Tokamak

The high-power helicon wave system in the DIII-D tokamak could potentially introduce new plasma–material interaction (PMI) challenges owing to rectified RF sheath potentials that develop near the antenna and surrounding plasma-facing components. We present the first application of the STRIPE (Simulated Transport of RF Impurity Production and Emission) framework to helicon-induced PMIs, extending previous STRIPE studies of ICRH antennas by incorporating net erosion, local re-deposition, and three-dimensional global impurity transport. The integrated workflow couples SOLPS, COMSOL, RustBCA, GITR, and GITRm to simulate carbon erosion, re-deposition, and impurity transport for two experimentally constrained DIII-D H-mode helicon operating scenarios with different antenna–plasma gaps, coupled RF powers, and edge plasma conditions. COMSOL predicts rectified RF sheath potentials of 1–5 kV localized near the lower portion of the antenna, where the magnetic field intersects the surface at grazing incidence. Carbon self-sputtering dominates the erosion source, whereas RF-accelerated D + ions contribute approximately 1% of the total gross erosion. The smaller-gap operating scenario exhibits substantially stronger gross erosion, enhanced local re-deposition (∼12%), and a larger confined carbon inventory owing to increased plasma accessibility and broader RF sheath coverage. Comparison with available DIII-D measurements shows no distinct change in the global carbon signal that correlates with the helicon RF pulse, consistent with the simulations indicating that the helicon-generated carbon source remains small compared with the existing background carbon inventory under the present graphite-wall operating conditions. These results demonstrate the capability of STRIPE to integrate RF sheath modeling, plasma transport, surface interaction physics, and three-dimensional impurity transport for the interpretation of helicon-induced PMIs. The study further identifies the principal sources of modeling uncertainty, including grazing-angle RF sheath physics, slow-wave resolution, plasma-background extrapolation, and trace-impurity transport assumptions, providing a framework for future validation and model development.

Kumar, Atul [Oak Ridge National Laboratory (ORNL),↗
DOE OSTI2014

Image reconstruction of shielded mixed-oxide fuel using a dual-particle imaging system

The dual-particle imaging system being developed at the University of Michigan was used at the Joint Research Centre in Ispra, Italy for measurements on samples of special nuclear material. A 1,150-g mixed-oxide (MOX) fuel sample was measured with various shielding configurations to determine how the presence of lead and/or polyethylene shielding degrades the system's ability to localize a source by simultaneous neutron and photon imaging. Three two-hour measurements were taken with the source shielded by an: a) 8-mm lead sheath and 5.1-cm lead bricks, b) 8-mm lead sheath and 6.5-cm polyethylene bricks, and c) 8-mm lead sheath, 5.1-cm lead bricks, and 6.5-cm polyethylene bricks. The 8-mm lead sheath was used in all cases to reduce the measured photon count rate. A “bare” measurement was also made by using only the 8-mm lead sheath, but the unexpected presence of additional sources has rendered the measurement unsuitable for comparison. Here, the resulting images show that the dual-particle imaging system is able to accurately localize the MOX canister in the presence of intervening material.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
DOE OSTI2010

Three-dimensional tracking of cardiac catheters using an inverse geometry x-ray fluoroscopy system

Purpose: Scanning beam digital x-ray (SBDX) is an inverse geometry fluoroscopic system with high dose efficiency and the ability to perform continuous real-time tomosynthesis at multiple planes. This study describes a tomosynthesis-based method for 3D tracking of high-contrast objects and present the first experimental investigation of cardiac catheter tracking using a prototype SBDX system. Methods: The 3D tracking algorithm utilizes the stack of regularly spaced tomosynthetic planes that are generated by SBDX after each frame period (15 frames/s). Gradient-filtered versions of the image planes are generated, the filtered images are segmented into object regions, and then a 3D coordinate is calculated for each object region. Two phantom studies of tracking performance were conducted. In the first study, an ablation catheter in a chest phantom was imaged as it was pulled along a 3D trajectory defined by a catheter sheath (10, 25, and 50 mm/s pullback speeds). SBDX tip tracking coordinates were compared to the 3D trajectory of the sheath as determined from a CT scan of the phantom after the registration of the SBDX and CT coordinate systems. In the second study, frame-to-frame tracking precision was measured for six different catheter configurations as a function of image noise level (662-7625 photons/mm{sup 2} mean detected x-ray fluence at isocenter). Results: During catheter pullbacks, the 3D distance between the tracked catheter tip and the sheath centerline was 1.0{+-}0.8 mm (mean {+-}one standard deviation). The electrode to centerline distances were comparable to the diameter of the catheter tip (2.3 mm), the confining sheath (4 mm outside diameter), and the estimated SBDX-to-CT registration error ({+-}0.7 mm). The tip position was localized for all 332 image frames analyzed and 83% of tracked positions were inside the 3D sheath volume derived from CT. The pullback speeds derived from the catheter trajectories were within 5% of the programed pullback speeds. The tracking precision of ablation and diagnostic catheter tips ranged from {+-}0.2 mm at the highest image fluence to {+-}0.9 mm at the lowest fluence. Tracking precision depended on image fluence, the size of the tracked catheter electrode, and the contrast of the electrode. Conclusions: High speed multiplanar tomosynthesis with an inverse geometry x-ray fluoroscopy system enables 3D tracking of multiple high-contrast objects at the rate of fluoroscopic imaging. The SBDX system is capable of tracking electrodes in standard cardiac catheters with approximately 1 mm accuracy and precision.

62 RADIOLOGY AND NUCLEAR MEDICINE↗
DOE OSTI2013

High-R Walls for New Construction Structural Performance: Integrated Rim Header Testing

The Building America Program takes two prominent approaches to construct higher R-value walls: larger dimension framing and exterior rigid foam insulation. These have had some success; however, for many production builders the cost of changing framing systems is high, so the changes have been slowly realized. Also, recent building code changes have raised some performance issues for exterior sheathing and raised heel trusses, for example, that indicates a need for continued performance testing of wall systems. Furthermore, some material use survey data have shown that often when builders are switching to 2 × 6 framing members, they commonly use of 16-in. o.c. spacing. The opportunity to (1) encourage the use of thicker framing systems for much higher R-value walls; (2) construct wall systems that optimize the framing use to reduce thermal breaks; and (3) extract opportunities to reduce costs, all remain high priorities for the Building America program, the NAHB Research Center Industry Partnership, and builders. Similarly for the use of exterior rigid sheathing, builders and researchers have investigated alternative bracing techniques to eliminate the use of wood structural sheathing in lieu of foam board sheathing. Structural characteristics, especially in the direction perpendicular to the sheathing, have been reevaluated for the building codes. These include pressure equalization issues across multiple layers of the wall system.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗
DOE OSTI2016

Advanced Extended Plate and Beam Wall System in a Cold-Climate House

This report presents the design and evaluation of an innovative wall system. This highly insulated (high-R) light-frame wall system for use above grade in residential buildings is referred to as Extended Plate & Beam (EP&B). The EP&B design is the first of its kind to be featured in a new construction test house (NCTH) for the DOE Building America program. The EP&B wall design integrates standard building methods and common building products to construct a high-R wall that minimizes transition risks and costs to builders. The EP&B design combines optimized framing with integrated rigid foam sheathing to increase the wall system's R-value and reduce thermal bridging. The foam sheathing is installed between the wall studs and structural wood sheathing. The exterior wood sheathing is attached directly to a framing extension formed by extended top and bottom plates. The exterior wood sheathing can dry to the exterior and provides bracing, a clear drainage plane and flashing surface for window and door openings, and a nailing surface for siding attachment. With support of the DOE Building America program, Home Innovation Research Labs partnered with Lancaster County Career and Technology Center (LCCTC) to build a NCTH in Lancaster, PA to demonstrate the EP&B wall design in a cold climate (IECC climate zone 5A). The results of the study confirmed the benefits of the systems and the viability of its integration into the house construction process.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗
DOE OSTI2017

Thermocouple Errors when Mounted on Cylindrical Surfaces in Abnormal Thermal Environments.

Mineral-insulated, metal-sheathed, Type-K thermocouples are used to measure the temperature of various items in high-temperature environments, often exceeding 1000degC (1273 K). The thermocouple wires (chromel and alumel) are protected from the harsh environments by an Inconel sheath and magnesium oxide (MgO) insulation. The sheath and insulation are required for reliable measurements. Due to the sheath and MgO insulation, the temperature registered by the thermocouple is not the temperature of the surface of interest. In some cases, the error incurred is large enough to be of concern because these data are used for model validation, and thus the uncertainties of the data need to be well documented. This report documents the error using 0.062" and 0.040" diameter Inconel sheathed, Type-K thermocouples mounted on cylindrical surfaces (inside of a shroud, outside and inside of a mock test unit). After an initial transient, the thermocouple bias errors typically range only about +-1-2% of the reading in K. After all of the uncertainty sources have been included, the total uncertainty to 95% confidence, for shroud or test unit TCs in abnormal thermal environments, is about +-2% of the reading in K, lower than the +-3% typically used for flat shrouds. Recommendations are provided in Section 6 to facilitate interpretation and use of the results. .

47 OTHER INSTRUMENTATION↗
NASA NTRS1980

Ion extraction from a plasma

An experimental investigation of the physical processes governing ion extraction from a plasma is presented. The screen hole plasma sheath of a multiaperture ion accelerator system is defined by equipotential plots for a variety of accelerator system geometries and operating conditions. A sheath thickness of at least fifteen Debye lengths is shown to be typical. The electron density variation within the sheath satisfies a Maxwell Boltzmann density distribution at an effective electron temperature dependent on the discharge plasma primary to Maxwellian electron density ratio. Plasma ion flow up to and through the sheath is predominately one dimensional and the ions enter the sheath with a modified Bohm velocity. Low values of the screen grid thickness to screen hole diameter ratio give good ion focusing and high extracted ion currents because of the effect of screen webbing on ion focusing.

Aston, G.↗