Volume 41, Issue 4, 15 March 1970

Acoustoelectric Amplification in a Many‐Carrier System
View Description Hide DescriptionAcoustoelectric amplification, in the linear approximation, is considered for a system containing several types of carriers in the two limiting cases of fast and slow carrier equilibration. The pertinent expressions are first derived for a piezoelectricsemiconductor and then expanded to the more practical case of a layered system containing one or more semiconducting layers coupled to a piezoelectric element. An experimental example is given in the form of a guided elastic plate wave in lead zirconate titanate coupled to a plate of near‐intrinsic Ge.

Raman Scattering in ZnTe
View Description Hide DescriptionThe Raman spectrum of ZnTe has been investigated. The fundamental frequencies have been found to be v̄ _{LO}=208.3±0.5 cm^{−1} and v̄ _{TO}= 177.5±0.5 cm^{−1}. The temperature variation of v̄ _{LO} has been examined between room temperature and 4°K. The zone boundary frequencies at the critical pointsX, L, and W have been estimated from the second‐order Raman spectrum. In determining these frequencies a theoretical model was used to assist in the assignment of the frequencies and as a check on the consistency of the results. The values obtained were further checked using regularities previously observed in the phonon spectra of zinc‐blende semiconductors.

X‐Ray Investigation of Solid Helium
View Description Hide DescriptionSpecimens of hcp ^{4}He used for thermal conductivity measurements have been examined by an x‐ray method. This method is described and several Laue photographs are shown. These photographs are an excellent test of specimen quality. The number of reflections observed for high‐quality crystals is sufficient for orientation determinations.

Etching of Submicron Pores in Irradiated Mica
View Description Hide DescriptionAs discovered by Price and Walker, small uniform pores may be created in muscovite by etching in HF thin samples that have been subjected to fission particle irradiation. The process of pore growth is followed by monitoring the conductance across a thin sample as the etching proceeds. For irradiation with ^{252}Cf the tracks quickly etch to a radius of 33 Å‐the region of primary damage. Further radial etching in the undamaged material is slow but increases to a fixed rate as the radius increases. This radius dependence of etching is interpreted by a kinetic analog of the Kelvin equation for vapor pressure over curved surfaces. With suitable assumptions on the mechanism of attack, the surface energy of the muscovite‐solution interface is calculated to be about 300 ergs/cm^{2}.

Excess Velocity Potential of the Needle Crystal
View Description Hide DescriptionStarting with the traditional time‐invariant paraboloidal model to represent the diffusion‐controlled growth of a needle‐shaped crystal in a pure supercooled melt, the effect of thermal imbalance at the solid‐liquidinterface is calculated. In particular, the diffusion field equations are solved for the initial excess velocity distribution at the interface, on the assumption that the shape constraint is suddenly replaced by the constraint of heat conservation. The computed results show that the hypothetical paraboloid tends to bulge everywhere behind the tip, with a pronounced circumferential peak bulge at one radius from the tip of the needle. The analytical result correlates well with the observed shape of dendritic needle crystals whose side branches protrude from (rather than oscillate about) the paraboloidal root shape. The paper concludes with the suggestion that the formation of side branches may be usefully regarded as the self‐induced oscillation of a nonlinear system. To minimize deviations from the law of heat conservation, the analytic model should include traveling interface waves.

Thermodynamics of Crystalline Elastic‐Visco‐Plastic Materials
View Description Hide DescriptionThe basic objective is the presentation of a description of rate‐sensitive plastic materials which agrees with events on the microscopic level and with macroscopic experiments and which is internally consistent. We utilize the framework of the thermodynamics with internal state variables formulated recently by Coleman and Gurtin. The internal state variables in the present theory are considered to be average quantities related to properties of the crystal defects in the material. Rate‐dependent phenomena, (e.g., a time‐dependent stress‐strain relation, creep, etc.) are studied in detail. The theory is illustrated with a simple example.

Diffusion of Cobalt in Beta‐Uranium
View Description Hide DescriptionThe solute diffusion of cobalt in beta‐uranium was measured using the thin‐layer sectioning technique. The results can be expressed by D= 1.54×10^{−2} exp(−27 450/RT) cm^{2}/sec. The diffusivities of cobalt are higher by about three orders of magnitude than the self‐diffusion coefficients in beta‐uranium. The possibility of cobalt diffusing by means of the combined substitutional‐interstitial mechanism has been examined.

Interdiffusion in Lead Selenide
View Description Hide DescriptionA theoretical model has been developed to explain the movement of a p‐n junction in PbSe by the interdiffusion process. This model, which is a modification of an interdiffusion theory due to Brebrick, has one value for the diffusion coefficient in p‐type material and another value in n‐type material. Solutions to the diffusionequation for this model are obtained and compared to experimental interdiffusion data for PbSe at 400°C obtained by the p‐n junction method. The significance of the results to device fabrication and annealing is discussed.

Mechanism of Secondary Emission and Single‐Particle Statistics from Low‐Density Films of Alkali Halides
View Description Hide DescriptionThe mechanism of field‐enhanced secondary emission has been studied experimentally in detail for KCl low‐density transmission dynodes transferred in a dry nitrogen atmosphere. By means of a Kelvin probe located at the center of a collector, dynode surface potentials and their relationship with collector potential, secondary yield, primary energy, and current density have been studied. A unique relationship between yield and surface potential has been found, independent of all other parameters for current densities between 1 and 10 nA/cm^{2}. This study clearly shows that an avalanche process, together with an increase in escape length, is responsible for the high yields obtainable. A study of transient effects reveals that the high surface potential needed for high yield decays rapidly after the primary beam is turned off. A smaller surface potential, with a long decay time constant, can be expected to provide slight field enhancement for single particle bombardment at low rates. The statistical distributions of the number of emitted secondary electrons per primary incident at high (1‐MeV) and low (9.5‐keV) energies have been measured for low‐density films of CsI and KCl at low count rates. The results do not differ very much from those obtained previously from normal density films except that the yields are somewhat higher, particularly after the film has been charged with a dense primary beam. The distributions obtained are non‐Poissonian in nature (more nearly exponential), and this is explained by their similarity to normal density films.

Mass Spectrometer Ion Source with High Yield
View Description Hide DescriptionAn electron impact ion source suitable for use with a quadrupole mass filter is described. Ion formation occurs throughout a relatively large volume since no magnetic fieldcollimation of the ionization electron stream is used. A sensitivity of 8 Torr^{−1} was obtained for an ion energy of 50 eV rising to a constant sensitivity of 12 Torr^{−1} for ion energies in excess of 250 eV. Trajectory tracing has been used to give some insight into the efficient operation of the ion source.

Experimental Investigation of the Relative Light Distribution in a High‐Pressure Rapidly Alternating dc Glow Discharge
View Description Hide DescriptionMeasurements have been made of the relative light intensity distribution in an rf glow discharge (exhibiting the characteristics of a rapidly alternating dc glow discharge) maintained between copperelectrodes in air at atmospheric pressure. Both the spatial distribution and the dependence on time of the light intensity were examined. The face diameter of each electrode was 3 mm and the electrode separation was 0.5 mm± 0.025 mm. All data were taken with a discharge frequency of 0.2 MHz and a discharge current of 0.6 A. Image converter data are presented as well as photomultiplier tube data. The experimental data presented verify that the cathodeglow does definitely shift position from one electrode to the other in alternating half‐cycles and that essentially a total light turn‐off occurs prior to reignition in the next half‐cycle.

Reignition Voltage in a High‐Pressure rf Discharge
View Description Hide Descriptionrf glow discharges at high pressure are quenched after every half‐cycle and must be reignited in the following half‐cycle. The reignition voltage V_{i} was investigated experimentally in the frequency range 0.15–1 MHz. It was found that V_{i} grows with electrode distance d up to a certain value d _{max}. At d _{max}, V_{i} decreases distinctly and stays low for a further increase of d. The explanation given for this effect is that at relatively small electrode distances all charge carriers can be removed from the discharge gap before reignition and breakdown must take place without support from space charges. For large d, however, the charge carriers cannot travel through the whole gap in the given time. Some remain in the gap and facilitate breakdown. Therefore a smaller value of V_{i} can reignite a long gap. The measured frequency response of V_{i} supports this explanation. A theoretical estimate of values of d _{max} is within a factor of 1.6 of experimental values.

Charge Separation in a Quasineutral Plasma by Application of an External Voltage
View Description Hide DescriptionThe application of an electric voltage to two electrodes between which a quasineutral plasma is contained results in chargetransport and charge separation in the plasma. In this paper, the charge distribution, field distribution, and current density in the plasma resulting from the application of a monotonously increasing voltage are computed. The solution is derived under the assumption that the current in the plasma is essentially ion and electron current, and that displacement current can be neglected.

Correlation of the Electron‐Emitting Properties of Cathodes in Vacuum and in Gas Discharges
View Description Hide DescriptionExperimentation involving the transients of the starting behavior of gas discharges reveals that this proceeds, in general, in three distinct stages: (1) a time lag for breakdown, termed plateau A, (2) a period of transition due to interaction between discharge and cathode, termed plateau B, and (3) the establishment of a final steady state for both discharge and cathode, termed plateau C. The initial state of plateau B is identified as a state of cathode and discharge that would constitute a steady state if the effects of ionic bombardment and Joule heating were absent. This state is found to obey the following relation, which is analogous to the Schottky equation for cathodes in vacuum:where I _{θ}=AT ^{2} exp (−∈φ/kT), the Richardson‐Dushman thermionic emission;V _{θ} is constant with a value near the ionization potential of the gas in the diode, and the voltage at which occurs a readily determined rearrangement of the cathodic sheath; the slope d(lnI)/d(V ^{1/2}) is a constant dependent on cathode material and the atomic number of the gas in the diode. It is shown that the extrapolated linear dependence of Eq. (1) intersects the ordinate (V=0) at a singular point I_{R} , independent of the atmosphere of the diode (vacuum, gas or type of gas) and identical with the zero‐field current of the cathode in vacuum. All experimental observations appear consistent with a theoretical model postulating a Schottky effect at the cathode. A consequence of these results is a firm correlation of cathode behavior in vacuum and in gas discharges.

Analysis of Thermal Induction Plasmas Dominated by Radial Conduction Losses
View Description Hide DescriptionThe energy balance equation is applied to induction plasmas in thermal equilibrium. Approximate, iteration‐type, solutions are obtained for cases where heat losses by radiation, axial conduction, and convection can be disregarded. It is assumed that the electric conductivity rises in proportion to the heat conduction potential and that the radial distribution of the induced electric field can be represented by a power law. Under these conditions, the equation can be transformed into Bessel's equation and solved for the heat conduction potential. With a uniform field, the solution reduces to that for a dc arc. The condition of vanishing temperature at the enclosing wall establishes an eigenvalue for the induced electric field at the circumference. Absolute temperature distributions can be calculated as a function of gas properties and applied conditions. It is shown that the latter are given by the time rate of change of primary magnetic flux through the discharge section. The method is applied to argon plasmas at atmospheric pressure. For these plasmas, optimum conversion of magnetic energy into heat should occur at a primary flux rate of 48 V. This value is lowered by the secondary current in the plasma to an actual burning voltage of 32 V. Both values are independent of driving frequency and plasma radius. Skin depth ratio and conversion efficiency at the optimum point agree closely with the values known from induction heating of metals. Experimental data indicate that the discharge has a tendency to operate near this point. Comparison of temperature distributions obtained by this method with exact computer solutions show that the axis temperature is over‐estimated by about 15%, but the general shape of the profile is well approximated.

Analytical Treatment of Radiation and Conduction Losses in Thermal Induction Plasmas
View Description Hide DescriptionApproximate solutions have been obtained of the Elenbaas‐Heller equation for a two‐zone model of thermal induction plasmas. Most of the heat production takes place in the external zone, where it is kept in balance by conduction losses. The major portion is lost to the wall, the minor transferred to the internal zone. This heat supply accounts for most of the radiation losses, which are confined to the internal zone. A small fraction of radiation is balanced by direct dissipation. Under these conditions, the distribution of the heat conduction potential assumes a parabolic shape for the inner zone, whereas it is described by Bessel functions in the external zone. A coordinate transformation in this zone accounts for the nonuniformity of the induced electric field and explicitly shows the effect of skin depth upon the profile shape. Matching of the zonewise solutions yields temperature distributions that are continuous to the first derivative and display the characteristic minimum at the axis known from experimental work. Generalized charts are presented by which a particular profile can be calculated from the gas transport properties and the time rate of change of primary magnetic flux. The method is applied to argon plasmas at atmospheric pressure with radiationproperties calculated from atomic theory. Simple expressions are derived for the total radiated power and the radiation efficiency of the discharge by a further idealization of the model. They indicate that, at most, 50% of the input power can be converted into radiation as long as the discharge remains attached to the tube wall. It is also shown that large field penetration depth improves the efficiency. The results are in qualitative agreement with available experimental data. A quantitative check will require more complete experiments.

End‐Region Analysis for Stress and Optical Pathlength Change in Composite Laser Rods
View Description Hide DescriptionA general solution is presented for the end‐region stress in a composite cylindrical rod where differential thermal expansion or contraction occurs between the core and cladding. Results describe local conditions set up in the ends of clad laser rods during manufacture and permit an analytical assessment of the optical path distortion which can arise in this geometry from residual strain. The formulations are obtained by superposition of the infinite rod solution and a solution to the boundary value problem posed by an axial force distribution, of equal but opposite magnitude to the infinite rod stress, applied to the surface of a stress‐free cylinder. Expressing the applied tractions as a Fourier‐Dini expansion at the axial boundary and the radial stress as a Fourier expansion at the radial boundary leads to a double infinite series form for the principal stresses. Implementation of Fejer's theorem was helpful in smoothing the numerical results; however, summing as many as 100 series terms with the computer was necessary to gain satisfactory convergence. Principal stress‐strain distributions are presented for a typical glass rod with a core‐cladding diameter ratio of 0.7 to 1 and contraction ratio below the transformation temperature of 0.95 to 1. Results show the end‐region domian extends less than 1 rod diameter. Optical pathlength variation across the core aperture for radial and tangential beampolarizations was computed to be 0.58 and 0.51 μ, respectively.

Mechanism of Undamped Output Pulsations in Maser Oscillators
View Description Hide DescriptionA mechanism has been proposed to explain the undamped spiking of the output power occurring in some multilevel maseroscillators. The phenomenon is explained in terms of the coupling between the signal frequency energy storage and the circuit properties at the pump frequency induced by the dependence of the pump level populations on the former. Approximate numerical calculations have shown that the coupling may be strong enough to render the operation of the oscillator unstable. Theoretical results obtained are in qualitative agreement with some of the observed properties of the spiking phenomenon.

Fast Modulator for Extraction of Internal Laser Power
View Description Hide DescriptionGeneral design considerations for internal laser acousto‐opticmodulators are given. Calculations are carried out for the time dependence of the power within the cavity and of the external pulsed power. Based on these calculations, acousto‐opticquartzmodulators were designed to be inserted inside He–Ne and argon folded cavities. Light pulses, with duration continuously variable from 15 nsec to cw and with repetition rate variable from single pulses to a few MHz have been extracted from the cavities. After dumping out most of the cavity energy, the time required for the internal power to rise from 10% to 90% of its steady‐state value is of the order of 3 μsec. With a pulse repetition rate of 1 MHz, the average light power was essentially the same as of the cw power capability of the lasers. The peak power intensity of the scattered light could reach the value of more than 50 times the cw power which was about 5 W for a 100mW He–Ne laser and 100 W for a 2‐W argon laser. The ability to pulse modulate the laser power at high repetition rates with negligible sacrifice in average power is important in many applications, including optical memories and laser machining.

Intensity Correlation Functions of a Non‐Q‐Switched Laser, Measured by Second‐Harmonic Generation
View Description Hide DescriptionThe intensity correlation function of the light from a non‐Q‐switched Nd:glass laser has been measured, using an optical gate (OG) to produce second‐harmonic light. The resolution time of this optical gate depends on the differences of the group velocities involved and the crystal length of the optical gate; in the described experimental arrangement a time resolution of about 10^{−13} sec is achieved. The effect of thick crystals on the time dependence of the second‐harmonic light intensity is discussed for some special cases. The experimental results are in agreement with the freerunning laser model, namely that a non‐Q‐switched Nd:glass laser has intensity fluctuations similar to thermal light. These results confirm some earlier results which have been achieved by a different technique.