Concentric Spherical Electrodes Research Articles

A systematic approach to the modelling and comparison of the geometries of spherical electrodes in inertial electrostatic confinement fusion devices

Inertial electrostatic confinement fusion (IECF) devices often use two concentric spherical electrodes to converge ions in a plasma electrostatically. Using a highly transparent inner cathode, the ions can move through the cathode and collide at the center to undergo fusion reactions. This is a simple method to build a neutron source. Past research has focused chiefly on cathode “grids” manufactured by joining metal wire loops or disc-shaped elements via spot welding. There are two common geometries: “Globe” grids with a distinct latitude-longitude structure and “symmetric” grids with even-sized triangular-shaped apertures. Recent advances in additive manufacturing have opened the way to manufacturing a third class of grids in which the apertures are evenly distributed over the grid surface and have either circular or polygonal shaped apertures - here called “regular” grids. These three types are analyzed and compared based on a set of metrics, including transparency, homogeneity of aperture size, and the regularity of aperture distribution. It is shown that every type of grid comes with different advantages and disadvantages. The analysis focuses on grid geometries with 6 to 120 apertures.

Curvature affects electrolyte relaxation: Studies of spherical and cylindrical electrodes.

With two minimal models, I study how electrode curvature affects the response of electrolytes to applied electrostatic potentials. For flat electrodes, Bazant etal. [Phys. Rev. E 70, 021506 (2004)PLEEE81539-375510.1103/PhysRevE.70.021506] popularized the RC timescale λ_{D}L/D, with λ_{D} being the Debye length, 2L the electrode separation, and D the ionic diffusivity. For thin electric double layers near concentric spherical and coaxial cylindrical electrodes, I show here that equivalent circuit models again predict the correct ionic relaxation timescales. Importantly, these timescales explicitly depend on both electrode radii, not simply on their difference.

Evidence for surface fusion in inertial electrostatic confinement devices

Inertial electrostatic confinement is a method of producing nuclear fusion in which concentric spherical electrodes are used to accelerate ions to fusion relevant energies. Fusion events are generally attributed to collisions between accelerated ions and neutral gas molecules in the centre of the device, with ion–grid collisions considered detrimental. In this paper, we present data that indicate that collisions between ions and neutral gas molecules adsorbed on the grid surface may, in fact, contribute significantly to the observed fusion rate in deuterium fuelled systems. When operating in the 1 × 10−4–1 × 10−3 Torr, V ≤ 40 kV regime, fusion on the grid surface is found to contribute up to 80% of the measured fusion rate, as determined from hysteresis effects between the fusion rate and system pressure. Surface fusion measurements were also carried out for a selection of cathode materials, with graphite found to produce a fusion rate that is an order of magnitude greater than the highest performing metal targets.

Ion Fluxes and Electro-osmotic Fluid Flow in Electrolytes around a Metallic Nanowire Tip under Large Applied ac Voltage

Motivated by the analysis of electrochemical growth of metallic nanowires from solution, we studied ion fluxes near nanoelectrodes in a binary symmetric electrolyte on the basis of the modified Poisson-Nernst-Planck equations in the strongly nonlinear region at large applied ac voltage. For an approximate calculation of the electric field near the nanowire tip, concentric spherical blocking electrodes were considered with radius of the inner electrode being of typically a few ten nanometers. The spatiotemporal evolution of the ion concentrations within this spherical model was calculated numerically by using the finite element method. The potential drop at the electric double layer, the electric field enhancement at the electrode surface, and the field screening in the bulk solution were determined for different bulk concentrations, ac voltages, and frequencies. The appearance of ac electro-osmotic fluid flow at the tip of a growing metallic nanowire is discussed, based on an estimation of the body force in the liquid near the nanowire tip, which was modeled by a cylinder with hemispherical cap. Electric field components tangential to the electrode surface exist near the contact between cylinder and hemisphere. Our analysis suggests that ac electro-osmotic flow causes an additional convective transport of metal complexes to the tip of the growing metal nanowire and thus affects the nanowire growth velocity.

Thermo-charged capacitors and the Second Law of Thermodynamics

In this Letter we describe a vacuum spherical capacitor that generates a macroscopic voltage between its spheres harnessing the heat from a single thermal reservoir at room temperature. The basic idea is trivial and it makes use of two concentric spherical electrodes with different work functions. We provide a mathematical analysis of the underlying physical process and discuss its connections with the Second Law of Thermodynamics.

Electrochemistry in Nanometer-Wide Electrochemical Cells

The electrochemical properties of an electrochemical cell defined by two concentric spherical electrodes, separated by a 1 to 20-nm-wide gap, and a freely diffusing electrochemically active molecule (e.g., ferrocene) have been investigated by coupling of Brownian dynamics simulations with long-range electron-transfer probability values. The simulation creates a trajectory of a single molecule and calculates the likelihood that the molecule undergoes a redox reaction during each time interval based on a probability-distance function derived from literature first-order kinetic data for a surface-bound ferrocene. Steady-state voltammograms for the single-molecule concentric spherical electrochemical cell are computed and are used to extract a heterogeneous electron-transfer rate for the freely diffusing molecule redox reaction. The Brownian dynamics simulations also indicate that long-range electron transfer, between the redox molecule and electrode, leads to nonsigmoidal-shaped i-E characteristics when the distance between electrodes approaches the characteristic redox tunneling decay length. The long-range electron transfer generates a "tunneling depletion layer" that results in a potential-dependent diffusion-limited current.

Nonthermal Atmospheric RF Plasma in 1-D Spherical Coordinates: A Parametric Study

We present 1-D simulations of atmospheric-pressure RF-excited plasma with two concentric spherical electrodes and the inner electrode powered. The gap distance between the inner and outer electrodes is 1 mm. The gas used is helium with a small amount of nitrogen as an impurity. The coupled continuity equations and electron energy equation are solved with Poisson's equation using the finite element method. In this paper, we particularly focus on the influence of a blocking capacitor, nitrogen concentration, and secondary electrons. In the presence of a blocking capacitor, the self-bias voltage alters sign from negative to positive as the power increases. Reduction of relative nitrogen concentration from 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-3</sup> to 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-6</sup> leads to significant changes in the gas-phase chemistry as well as species flux impacting the outer electrode. Secondary electrons turned out to play a minor role in the transition from the corona to glow modes. We also show that the directed ion kinetic energy distribution to the outer electrode largely depends on the discharge mode.

Nonthermal atmospheric rf plasma in one-dimensional spherical coordinates: Asymmetric sheath structure and the discharge mechanism

We present one-dimensional simulations of atmospheric pressure rf-excited plasma with two concentric spherical electrodes and the inner electrode powered. The gas used is helium with 0.1% nitrogen addition. The gap distance between the inner and outer electrodes is 1mm. The coupled continuity equations and electron energy equation are solved with Poisson’s equation using the finite element method. A mode transition is observed in the discharge power-voltage curve between 1 and 1000mW. In the low power mode, ionization rate peaks only near the inner electrode. The electron-impact excitation and ionization rates peak in the local cathodic phase. In the high power mode, the rate of ionization peaks near the outer electrode as well as the inner electrode. The inner sheath significantly shrinks and the direct electron-impact ionization is the primary ionization reaction near the inner electrode. The ionization rate near the outer electrode is due to Ohmic sheath oscillation heating of electrons, resulting in a peak in metastable helium creation. Penning ionization is the major ionization reaction near the outer electrode. Thus, two different ionization mechanisms coexist near the inner and outer electrodes. Electron heating near the outer electrode may have implications for surface processing in atmospheric pressure microdischarges. The local field approximation (LFA) in high power mode fails to predict the ionization rate peak near the outer electrode due to its inability to properly account for electron diffusion in the presence of both a strong electric field and electron density gradient. However, use of the LFA is adequate to model the low power mode and it correctly predicts the existence of the mode transition.

Double Potential Well Regimes in Collisionless Spherical Discharges

The study of potential profiles in glow discharges initiated between concentric spherical electrodes is motivated by the experimental investigations of inertial electrostatic confinement devices, which have the potential to be used as compact neutron generators. Here, we explore double potential well regimes within the cathode of such devices, utilizing a previously developed collisionless model. This is accomplished in an efficient manner by creating contour plots of the double well depth (DWD) and the double well radius, width, with respect to the spreads in angular energy of electrons and ions, and with respect to the ion perveance and ratio of ion to electron perveance. These plots expand our knowledge of the DWD behavior beyond the previous understandings, both qualitatively and quantitatively. In addition, we consider the relationship of these results with the experimental results of Gu and Miley and the theoretical results of Matsuura in an effort to better understand the results of Gu and Miley

Space Charge Limited Currents from a Strip Shaped Emitter in a Parallel Plate Geometry

Microscopic electrical defects in the photoreceptor termed Charge Deficient Spots (CDSs) can give rise to objectionable print defects in xerographic systems such as laser printers. Theoretical calculations of Space Charge Limited Currents (SCLC) between concentric cylindrical and spherical electrodes show that a finite SCLC can be sustained, for a finite applied voltage, even as the radius of the emitting electrode goes to zero. Numerical simulations of the SCLC in a model system consisting of a ground plane with a finite circular emitting region and a parallel collector kept at constant applied potential have shown that the SCLC varies linearly with emitter radius for small radii. In this paper we consider the emitting region to be an infinitely long strip of finite width, which may be termed a Charge Deficient Line (CDL). Using the same numerical technique, we address the following questions: i) does the current vanish as the width of the CDL vanishes and ii) what is dependence of the current on the width? Finite element methods were used to calculate the SCLC consistent with Maxwell's equations and the correct boundary conditions. Our results show that, for a fixed applied voltage, the SCLC varies linearly with emitter width for large width and becomes independent of width for small width.

Intense Ion Beam Flux of Adsorbed Gases and Metallic Anode Materials in the “Point Pinch Diode” Measured with Thomson-Parabola Ion Spectrometer

An intense flux of ion beams was observed in a “Point Pinch Diode” which consists of concentric elliptic or spherical electrodes and a slender magnetically insulated transmission line. The ion beam had an energy of about 380 keV, which was equivalent to the supplied diode voltage. The peak current density of the ion beam ranged from 5 to 7.5 kA/cm2 in spite of a small input energy (less than about 1 kJ). Measurements with a Thomson-parabola ion spectrometer show that the major components were hydrogen, carbon, and oxygen, the origins of which were oil and water adsorbed on the surface of the metallic anodes. A significant flux of the metallic ion beams was also detected in the cases of aluminium, copper and gold anodes.

Characteristics of secondary-emission detectors under gamma irradiation

Impulsive radiation from nuclear reactors and strong-current accelerators in the dosage range up to 1 x 10/sup 13/ rad/sec (a rad = 0.01 Gy) is recorded using secondary-emission detectors (SED) with systems of axicylindrical, plane-parallel, and concentric spherical electrodes. In this paper they present the results of investigations of the characteristics of SED with plane-parallel stainless steel electrodes, and the design with a system of congruent spherical electrodes is described and its advantages for the determination of the dosage of ..gamma.. radiation with uncertain spatial-angular and energy distributions are demonstrated.

Variational formulation for the equilibrium condition of a conducting fluid in an electric field

In this paper the variational formalism is used to derive a set of equations describing the equilibrium configuration of a conducting fluid in an applied electric field. The validity of the variational equations is confirmed by application to the well-defined problem of concentric spherical electrodes. It is further shown that a cone, including the so-called Taylor cone used to model the equilibrium configuration of liquid metal ion sources, is inconsistent with the general equations. An analysis of the Taylor derivation suggests that reasons for the disagreement are the omission of the pressure difference term in the Laplace formula and use of only an approximate solution to the electrostatic cone problem. Finally a quasi-empirical method is suggested for the self-consistent solution of the variational equations.

Space-charge-limited bipolar current flow between concentric spherical electrodes

Poisson&apos;s equation in spherical symmetry is solved numerically assuming that at each electrode there is an unlimited supply of charges of zero energy; positive charges at the positive electrode and negative charges at the negative electrode. A solution is obtained corresponding to zero electric field at each electrode surface, this defines the maximum possible current flow of each charge polarity. The numerical technique is based on a perturbation of the solution appropriate to parallel plane geometry and is carried out for a ratio of electrode radii ranging from 1 to 400. In the case of the external emitter configuration the increase in charged-particle current afforded by bipolar flow, in comparison to unipolar flow, can be several orders of magnitude. Application to fusion fuel-pellet compression, field-emission microscopy and thermionic-energy conversion is briefly discussed.

Measurements of a spherical potential profile produced by electrostatically focused ions

An electrostatic potential well was produced by injecting positive zinc ions into a hollow cathode. The apparatus consisted of two concentric spherical electrodes with the inner wire-mesh electrode being 91% transparent. Ion current pulses as high as 40 mA were injected by a vacuum-arc source located between the spheres. The outer sphere was biased at 4 kV and the inner sphere from 0 to −1.5 kV so that the ions would circulate between the spheres and be drawn toward the inner sphere. Current pulses lasted up to 20 μs and during the current pulses, potential wells of up to 200 V were formed by the accumulation of ions within the inner electrode. The well profile was computed from the deflection of a 2-nA swept electron beam. The deflection was measured with a many-slotted circumferential detector which intercepted the beam after it traversed the space-charge region. Each profile was calculated from data recorded during a single 2-μs sweep of the probing beam.

Transient Drift Dominated Conduction in Dielectrics

A generalized transient analysis has been developed using a drift dominated conduction model to solve for the electric field and space charge distributions in a dielectric for any initial and boundary conditions as well as for any type of terminal excitation or constraint. Past results for parallel plate electrodes were extended to lossy dielectrics with ohmic conductivity. Analogous methods were developed for concentric cylindrical and spherical electrodes. The case of bipolar conduction including charge recombination is also treated. The method of characteristics was used throughout this study so that the governing partial differential equations were converted into a set of first order ordinary differential equations. For current excitations, these equations are easily integrated while for voltage excitations the equations are in the correct form for Runge-Kutta numerical integration. Special cases examined include the charging transients to a step voltage or current from rest or from a pre-stressed level and the discharging transients for systems in the dc steady state which are instantaneously opened or short circuited.

Transient Drift-Dominated Unipolar Conduction between Concentric Cylinders and Spheres

A new analysis analogous to recent work for parallel-plateelectrodes is presented using a unipolar ion-mobility conduction modelbetween concentric cylindrical or spherical electrodes. Exact solutionsare obtained for the transient behavior of the bulk electric-field andspace-charge density distributions and for the terminal current-voltage(I-V) time dependence. The analysis is generalized to handle any initialand boundary conditions for any terminal constraints or excitations.Using the method of characteristics, the governing first-orderchargeconservation quasi-linear partial differential equation is converted into aset of first-order ordinary differential equations. It is shown that forcurrent source excitations these equations can be easily integrated,while for voltage-source excitations the equations are in the correctform for the Runge-Kutta method of numerical integration. Thecoaxial cylindrical geometry is emphasized, treating the special cases ofthe charging transients to a step voltage or current from rest underspace-charge limited conditions and the discharging transients ofsystems which are in the dc steady state and instantaneously open- orshort-circuited. The solutions are computer drawn in three dimensionsusing a recently available graphics package.

Étude expérimentale de la polarisation d'une électrode en milieu résistant

Measurements of the polarization of a plane platinum electrode in nitrobenzene solutions are presented and discussed. The supporting electrolyte concentration is made to vary between 10 −1 M and a value lower than 10 −6 M; the highest resistivity value (2×10 8 Ω cm) of the studied solutions was imposed by the experimental procedure. Concentric spherical electrodes have also been studied. The polarization-current density curves do not vary with the electrolyte concentration or nitrobenzene resistivity. The electron-transfer mechanism is not modified in high resistive media. The influence of spacing on the polarizations of two plane parallel electrodes set very close to each other is investigated, too. The polarizations are found nearly constant and thus independent of the amount of free ions in the volume of liquid between the electrodes, even when it is theoretically too low to establish the voltage drop at the interface. The results indicate a strong interaction of the electrode reactions at such low spacings and the formation of ions from the weakly ionized impurities of nitrobenzene.

Beam formation in a triode ion gun

Beam formation in a triode ion gun has been investigated. The gun consisted of a plasma ion source operated with argon, a low-potential cup extractor and an acceleration tube (diameter D). The ion optics of the system were studied by recording the current density profile of focussed 40 keV beams with the beam current as a parameter. Currents up to about 200 μA were obtained by increasing the plasma density in the ion source. Focussing was achieved by suitably adjusting the extractor potential. To get a comprehensive view of beam formation the following gun parameters were varied: extraction-gap distance (0.5⩽d⩽7 mm, adjustable in situ), extractor length (0.59≤LD≤1.65), acceleration-gap distance (0.05≤gD≤0.8), length of ion-source outlet (0.1≤l≤1 mm), diameter of extractor entrance opening (2.5≤b≤5 mm) and monitor position (z = 28 and 70 cm from the midplane between the electrodes). The focussing extractor voltage was found to increase linearly with increasing extractor length for LD⪰1. A minimum extractor voltage of only 150 V was observed at LD = 0.7. The beam profiles at z = 70 cm were found to be broadened markedly by space-charge expansion in the field-free drift region. The influence of extraction-gap distance and extractor length was much less pronounced. Profile distortions observed under well-defined conditions at either low or high beam currents were found to be due to a particular shape of the plasma boundary or strong beam divergence in the extraction region, respectively. The divergence of beams from convex plasma boundaries could be described quantitatively by applying the space-charge law between concentric spherical electrodes. The width of the profiles at z = 28 cm could be interpreted using standard beam-transport theory. Combined profile measurements at either monitor position provided an estimate of the beam emittance. Using recently reported properties of a two-tube electrostatic lens a self-consistent picture of beam formation in the triode ion gun could finally be obtained.

Theoretical analysis of a time-of-flight mass spectrometer with spherical electrodes and radial ion paths

A general expression for the total ion flight time is derived for a time-of-flight mass spectrometer having four concentric spherical electrodes which bound two accelerating regions and a drift region. The special case of negligible initial velocity is then considered, and it is shown that the spherical geometry gives space-time focusing characteristics which are at least as good as those of instruments having similarly spaced cylindrical or planar electrodes. The use of spherical electrodes also offers a large entrance area into which ions can be drawn from a surrounding plasma, provides equal sensitivity for ions entering from all directions, and allows the use of a very small ion collector such as a channel electron multiplier. It follows that this type of mass spectrometer may be a particularly attractive choice for applications requiring unusually high sensitivity.