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Volume 67, Issue 10, 15 May 1990

A theoretical study of the hyperbolic electron mirror as a correcting element for spherical and chromatic aberration in electron optics
View Description Hide DescriptionThe spherical and chromatic aberrations of a converging electron mirror are of opposite sign from those of electron lenses. This important property makes it possible in principle to compensate the aberrations of electron lenses by means of an electron mirror and to design electron microscopes based on a corrected optics system incorporating an electron mirror. In this paper the properties of the hyperbolic electron mirror are calculated, and the conditions for simultaneous correction of spherical and chromatic aberrations are worked out for several types of electron microscopes. The hyperbolic mirror field is a rotationally symmetric potential field between two electrodes. The electrodes are shaped as equipotential surfaces of the hyperbolic field, except for an aperture on the axis of the positive electrode for entrance and exit of electrons. The effect of the aperture is to create a thin diverging aperture lens at the termination of the hyperbolic field. The properties of the mirror are calculated analytically. The problem of separating the electron beam incident on the mirror from the beam returning from the mirror without impairing the image quality is solved by means of magnetic deflecting fields located at image planes. The mirror corrections can be applied to either magnetic or electrostatic lenses. The parameters for correction of aberrations are calculated for systems using electrostatic lenses. With appropriate polarity of the accelerating voltage and the lens and mirror voltages the calculations apply to ion imaging systems as well.

Charge‐transfer collisions between He^{+} _{2} ions and N_{2}: Branching ratio into vibrational states
View Description Hide DescriptionA plasma‐mixing device in which a helium plasma beam is crossed with a molecular nitrogen beam was used to measure the branching ratio of the excitation of individual vibrational levels of the B ^{2}Σ electronic state of the molecular nitrogen ion in charge‐transfer collisions between He^{+} _{2}ions and ground‐state N_{2} molecules. The branching ratio of the excitation of individual vibrational levels of the C ^{3}Π electronic state of the neutral nitrogen molecule due to the resonant energy‐transfer collisions between argon metastables and ground‐state nitrogen molecules was also measured using a plasma beam of a mixture of argon and helium. These results allow comparison of our measurements with results obtained using other techniques.

Electronic stopping‐power calculations for heavy ions in semiconductors
View Description Hide DescriptionA model for ion stopping in semiconductors, which considers separate stopping contributions from valence and core electrons, and explicitly includes the effect of the gap, has been used to calculate the electronic stopping power of energetic B, P, and As in Si, Ge,GaAs, and CdTe for projectile energies 10 keV–100 MeV. Account was taken of the partially stripped incident ions by means of the effective charge. There is good agreement at low ion velocity with Lindhard and Scharff’s [J. Lindhard and M. Scharff, Phys. Rev. 1 2 4, 128 (1961)] values which for heavy ions do not depend on effective charge theory, as well as with the semiempirical curves at energies E≥0.2 MeV/nucleon where they can be compared.

Simple analytic potentials for linear ion traps
View Description Hide DescriptionWe have developed a simple analytical model for the electric and ponderomotive (trapping) potentials in linear ion traps. We have used this model to calculate the required voltage drive to our mercury trap, and the result compares well with our experiments. The model gives a detailed picture of the geometric shape of the trapping potential and allows an accurate calculation of the well depth. The simplicity of the model allowed us to investigate related, more exotic trap designs which may have advantages in light‐collection efficiency.

Effects of finite radial geometry on free‐electron‐laser instability with a longitudinal wiggler field
View Description Hide DescriptionThe theory of free‐electron‐laser instability for a tenuous relativistic electron beam propagating parallel to a longitudinal wiggler field has been extended to include the influence of finite radial geometry on its stability properties. The growth rate of the instability shows a sensitive dependence on (ν/γ)^{1} ^{/} ^{3}, where ν is the Budker parameter and γ is the beam energy. The growth rate increases with increasing beam intensity. However, the instability bandwidth with respect to the beam location inside the waveguide decreases for beams with somewhat higher ν/γ values. The instability is broadband for several harmonics excited.

Solving electromagnetic scattering problems at resonance frequencies
View Description Hide DescriptionThe ‘‘resonance problem’’ is that at certain values of the wave number k (the resonant k’s), the second‐kind integral equation for solving scattering problems can become extremely ill‐conditioned. This adversely affects both the accuracy and speed of numerical solutions. We consider transverse‐magnetic scattering from a conductor (Dirichlet problem). The integral equation (derived using double‐layer potentials) is discretized using approximately fourth‐order convergent quadrature formulas. At resonant k’s for circular and elliptical scatterers, we find very large condition numbers for the discrete matrices [up to O(10^{7}) ], generally leading to poor solutions. We apply two approaches to alleviate the resonance problem. The first is to use a different integral equation, based on both single‐ and double‐layer potentials. This leads to low condition numbers and good solutions at resonant k. The second method is to use the original second‐kind integral equation, introduce a small imaginary part in k, and extrapolate back to the real axis. Solutions obtained by the two methods are in excellent agreement. The extrapolation technique will be particularly useful in the case of the exterior Neumann problem, when the application of the first technique will be numerically more difficult. By solving the resonance problem, we ensure that fast and accurate solutions are obtainable at any arbitrary wave number.

Thermally induced optical bistability and self‐oscillation in a nonlinear etalon filled with optical adhesive
View Description Hide DescriptionWe report the optical bistability and the self‐oscillation of a nonlinear Fabry–Perot etalon filled with Norland optical adhesive 81. A normal and an inverted bistable loop were observed for a short (80msec) and a long (1.2sec) input optical pulse duration, respectively. The self‐oscillation properties depended sensitively on the substrate and the spacer thicknesses. The measured self‐oscillation period became longer with an increase of the spacer thickness and was in the range o 0.2 to 3 seconds. The inversion of the bistable loop, and the self‐oscillation in this experiment can be explained by the competition between the fast thermal refractive index change and the slow linear thermal expansion of the etalon.

Evanescent wave absorption spectroscopy using multimode fibers
View Description Hide DescriptionEvanescent waveabsorption in an aqueous dye solution has been performed using multimode fused silica fiber which was unclad at the sensing region. Evanescent absorbance values for methylene blue in a concentration range 3×10^{−8} to 5×10^{−6} M are reported. In order to produce modes close to cutoff in the sensing region, tunneling modes were launched into the clad fiber. Spatial filtering was used to restrict the light launched to those modes which have substantial power in their evanescent field in the unclad region. The measured evanescent absorbance of the dye solution was found to vary linearly with the exposed core length and to exhibit a square root dependence on concentration. The former effect is predicted from standard theory while the latter is attributed to adsorption on the core surface which obeys a Debye–Huckel‐type concentration dependence. In addition, a concentration enhancement of two orders of magnitude was observed due to this surface adsorption. While this effect limits the use of the technique for a reversible sensor it may be exploited in disposable probes.

Comparison of infrared upconversion methods for photon‐limited imaging
View Description Hide DescriptionInfrared upconversion offers advantages over direct detection of thermal imagery, but has been of limited use because of low upconversion efficiencies and because of the complexity of the upconversion systems. Photon‐limited imaging techniques can overcome the disadvantages of upconversion. The low‐power levels required by photon‐counting detectors make large upconversion efficiencies unnecessary. At the same time, photon‐limited imaging offers advantages in speed of operation and ease of implementation. We investigate the application of photon‐limited imaging to sum‐frequency upconverters, infrared quantum counters in alkali‐metal vapor, and a recently reported infrared phosphor. Upconversion efficiencies and noise effects associated with the different upconversion methods are derived. Two figures of merit are used to compare the upconversion methods. One figure of merit is the conventional noise equivalent differential temperature (NEΔT). The other is a criterion based on the statistics of photon‐limited images applied to scene matching. We find that the sum‐frequency upconverter and the phosphor require fewer detectedphotons than the infrared quantum counter to achieve the same values for the figures of merit. We also find that reliable scene matching can be performed with fewer detectedphotons than would be expected from the NEΔT figure of merit.

Steady‐state temperature of an evaporating water droplet with a monolayer coating
View Description Hide DescriptionA mathematical model is derived for the steady‐state temperature of an evaporating water droplet with a monolayer coating. The model uses the flux‐matching arguments of Fuchs to describe the concentration and temperature fields outside the evaporating droplet. Assuming the mean molecular speed, the gas‐phase diffusion coefficient, and the gas thermal conductivity to be temperature independent, a closed‐form expression is derived for the steady‐state temperature of the droplet as a function of the monolayer accommodation coefficient. Comparison between model predictions and recent fluorescence thermometry experiments shows good agreement.

Bounds on the effective properties of polydispersed suspensions of spheres: An evaluation of two relevant morphological parameters
View Description Hide DescriptionExpressions for the two microstructural parameters that appear in the variational third‐order bounds [G. W. Milton, Phys. Rev. Lett. 4 6, 542 (1981)] for the effective conductivity and elastic moduli of composite media are derived analytically to first order in the sphere concentration c for random well‐mixed dispersions of impenetrable spheres with an arbitrary size distribution. These relations lead to rigorous bounds on the effective properties which are exactly valid to order c ^{2} for such models. The apparent l i n e a r behavior of the microstructural parameters up to moderately high c enables one to apply the bounds beyond second‐order in c, however. Employing these results, the effect of polydispersivity on the effective properties is examined. It is worth noting that, under some conditions, polydispersivity can actually lead to a slight decrease of the shear modulus, whereas, for highly conducting particles, polydispersivity always increases the effective conductivity.

Theoretical model of gravitational perturbation of current collector axisymmetric flow field
View Description Hide DescriptionSome designs of liquid‐metal current collectors in homopolar motors and generators are essentially rotating liquid‐metal fluids in cylindrical channels with free surfaces and will, at critical rotational speeds, become unstable. An investigation at David Taylor Research Center is being performed to understand the role of gravity in modifying this ejection instability. Some gravitational effects can be theoretically treated by perturbation techniques on the axisymmetric base flow of the liquid metal. This leads to a modification of previously calculated critical‐current‐collector ejection values neglecting gravity effects. The purpose of this paper is to document the derivation of the mathematical model which determines the perturbation of the liquid‐metal base flow due to gravitational effects. Since gravity is a small force compared with the centrifugal effects, the base flowsolutions can be expanded in inverse powers of the Froude number and modified liquid‐flow profiles can be determined as a function of the azimuthal angle. This model will be used in later work to theoretically study the effects of gravity on the ejection point of the current collector.

Unsteady adiabatic isentropic expansion of gas into vacuum from a toroidal puff valve
View Description Hide DescriptionObservations were made on the expansion of polyatomic (CF_{4}) and diatomic (O_{2}) gases into vacuum from a toroidal puff valve. Fast ionization gauge measurements have been compared with an unsteady adiabatic isentropic model. Observed temporal and spatial gas density profiles closely followed model predictions until the arrival of gas reflected from the upstream wall of the vacuum vessel.

Control of plasma parameters and electric fields in a microwave‐rf hybrid plasma
View Description Hide DescriptionControl of electron energy and electric field in a low‐pressure argon plasma produced by a hybrid (2.45 GHz microwave and 13.56 MHz rf) discharge was studied for thin‐film preparation. The hybrid plasma was found to be useful over a wide range of magnetic field strengths, unlike conventional microwave plasma. A novel probe measurement revealed that the electron temperature and density were effectively controllable by the microwave power and the magnetic field strength, rather than the rf power, and the potential profile describing the electric field was controllable by the magnetic field strength. The control of an ion beam injected from the microwave into the rf plasma is described.

A theory of weak transient electrical discharges on dielectric surfaces
View Description Hide DescriptionThe nonlinear evolution of transient electrical discharges initiated from a small charge spot on dielectricsurfaces is analyzed with a transmission line model. The relation between the resistance per unit length, R̂, and the current,I, is assumed to be given by a local Arc Welder’s Ansatz: R̂‖I‖=E*, where E* is a positive constant. Comparison is made with a similar study of discharges initiated from a large charge spot. While both studies predict conditions under which charge is, or is not, transported to a dielectric edge, significant differences in the two cases are revealed. For example, if charge is not transported to an edge, current reversal is possible if the charge spot is small, but can only be unidirectional if the spot is large.

Interaction between a sheet source and a moving compressible plasma
View Description Hide DescriptionThe problem of radiation from a sheet current source in a moving compressible plasma is treated. In order to know the interaction between the sheet source and the moving plasma, first the sign of the radial component of the propagation constant is determined accurately on the basis of the radiation condition. Then the radiation power is investigated numerically for various sets of the direction of the source and that of the moving plasma. In particular, it is found that the source is given an energy by the surrounding plasma medium under certain conditions.

Probe determination of the electron energy distribution in a Hg‐Ar low‐pressure positive column
View Description Hide DescriptionThe electron energy distribution function in a mercury‐argon low‐pressure positive column was determined from the second derivative of voltage‐current characteristics of a single probe. The probe signals were analyzed with a digital signal processing technique. The high‐energy tail of the distribution functions ( f∼10^{−5}) was obtained at mercury coldest spot temperature of 20, 42, and 60 °C (mercury density ratio of 4.8×10^{−4}, 2.8×10^{−3}, and 1.0×10^{−2} ), and discharge current of 0.2, 0.4, and 0.6 A for a 24‐mm‐diam tube. The electron density and electric field strength were measured at the same time, and used as input to a Boltzmann equation analysis code. General agreement was found between the experimental and theoretical results for the distribution function.

Role of recoil implanted oxygen in determining boron diffusion in silicon
View Description Hide DescriptionAnnealing of silicon implanted with boron through a surface oxide results in an enhanced diffusion of boron. This enhanced diffusion is suppressed during an initial incubation period. An activation energy of 2 eV is associated with the enhanced diffusion, indicating excess silicon interstitials may be involved. On the other hand, the process leading to the onset of enhanced diffusion possesses an apparent activation energy of 3.7 eV. Two‐step annealing reduces the latter value to 2.6 eV, the activation energy for interstitial oxygen diffusion. The different activation energies evaluated for the saturation process will be discussed. Transmission electron microscopy shows that the coalescence of dislocations, as well as the growth of faulted loops, proceeds rapidly after the incubation period for enhance diffusion. Precipitates along small dislocation loops are also observed after the incubation period. It is proposed that oxygen precipitation, with emission of silicon interstitials, predominates for annealing beyond the incubation period and is therefore responsible for the enhanced diffusion of boron. The enhanced diffusion sequence is initially incubated by trapping oxygen at dislocations. The real onset of the enhanced diffusion occurs when the dislocations are saturated and the oxide precipitation at the dislocations commences.

Spin‐polarized scanning tunneling microscope: Concept, design, and preliminary results from a prototype operated in air
View Description Hide DescriptionWe describe the concept of the spin‐polarized scanning tunneling microscope. It consists of a ferromagnetic tip with saturated magnetization from which spin‐polarized electrons tunnel into a ferromagnetic sample which has its axis of magnetization aligned with that of the tip. When the magnetization of the sample is alternated periodically from parallel to antiparallel, a portion of the tunnel current is predicted to oscillate at the same frequency, with an amplitude linearly proportional to the average tunnel current. The construction of a prototype microscope, operated in air, is described. When the sample magnetization is alternated, a modulation of the tunnel current is observed at the same frequency. This signal satisfies criteria developed to characterize spin‐polarized tunneling. Spurious signals are also observed and their probable origins identified. A number of improvements are suggested that should eliminate the spurious effects.

Vacancy‐type defects in Si^{+} ‐implanted GaAs and its effects on electrical activation by rapid thermal annealing
View Description Hide DescriptionThe depth distributions of vacancy‐type defects in Si^{+} ‐implanted and thermally activated GaAs were studied by a slow positron beam technique and were compared with the results observed with a transmission electron microscope. In as‐implanted GaAs, the concentration of vacancy‐type defects decreased monotonically with increasing depth below the surface and the generation of point defects was demonstrated by the lattice image of transmission electron microscopy. The vacancy concentration is not dependent upon activation conditions; however, the electrical activation coefficiency obtained from Hall measurements is enhanced with increasing activation annealing time. This indicates that the electrical activation of Si^{+} ‐implanted GaAs is proceeding by the exchange of interstitial Si with substitutional Ga rather than the recombination of interstitial Si into Ga‐related vacancies. The maximum number of extrinsic‐type stacking faults was observed at 70–80 nm below the surface after the activation annealing, which is compared with that of vacancy‐type defects, at 25–35 nm, obtained by the slow positron beam technique. This discrepancy in both of the damage distributions could originate in different types of defects existing along the depth below the surface, which was discussed with the high‐energy recoil theory.