Volume 25, Issue 8, 01 August 1954

A Theorem Concerning Noise in Electron Streams
View Description Hide DescriptionIt is proposed that if I _{max} and I _{min} are the maximum and minimum noise currents in a noise standing wave on an electron stream, then the product of their magnitudes cannot be smaller than .Various assumptions lead to a factor α ranging between 0.8 and 1. I _{0} is beam current, B is band width, ω is frequency, ω_{ q } is effective plasma frequency, T_{c} is cathodetemperature, and V _{0} is the voltage specifying the velocity of the electrons.

The Transfer Function as a Tool in the Analysis of a Resistance‐Capacitance Coupled Voltage Amplifier
View Description Hide DescriptionThe frequency response of a typical resistance‐capacitance coupled voltage amplifier has been theoretically analyzed and the result compared with that given by Terman. The advantages and disadvantages of the two methods have been illustrated both mathematically and graphically. A solution to the phase‐shift problem at any frequency considered has been included.

Geometrical Acoustics. I. The Theory of Weak Shock Waves
View Description Hide DescriptionIn the first part the discontinuity conditions in an arbitrary continuous material are deduced for a general (i.e., possibly curved) discontinuity surface. It is then shown that only three types of discontinuities are possible—shocks, contact discontinuities, and phase‐change fronts. In the second part the acoustic discontinuity conditions are deduced and specialized to a perfect fluid without heat conduction. Then a first‐order partial differential equation is obtained for the location of an acoustic shock front. This equation can be solved, as in optics, by means of rays. The variation of shock strength along a ray is then determined (this is one main result of this paper). Coefficients of reflection and transmission for an acoustic shock at a contact discontinuity in the basic flow are also obtained. Finally, the results are exemplified by an analysis of the shock tube.

Transient Wave Analysis in a Linear Time‐Dependent Material
View Description Hide DescriptionWe consider a body which under stress exhibits an elastic, a viscous, and a retarded elastic response. For the particular case of a constant velocity applied at the end of a semi‐infinite bar, the transient stresses, strains and velocities are found by the method of characteristics. From this solution can also be obtained the stresses for the case of a constant stress applied at the end of a semi‐infinite bar. By superposition we can also solve problems involving finite bars. For a constant velocity applied at the end of the bar an integral expression is derived for the stress at that end as a function of time.

Thermionic Emission and Electron Diffraction from Thin Films of Barium Oxide
View Description Hide DescriptionA high‐vacuum, sealed‐off glass, electron diffraction tube was developed for observing the physical structure of evaporated BaO films on a nickel substrate. Simultaneously, measurements of thermionic emission could be made. The thermionic activity of the deposited film increased until approximately 20 monolayers (measured using a radioactive tracer technique) had been laid down, and no further increase was found up to 50 monolayers. This emission density (0.4A/cm^{2} at 1000°K) is comparable with that obtainable from sprayed oxide coatings. With the receiver at less than 450°K the oxide film showed an amorphous structure. With the receiver at 800°K the film was crystalline and was believed to exist in clumps. This crystalline structure became amorphous if the films were heated to 1070°K and this form persisted as the oxide film was removed by evaporation. The relation of the thermionic emission from thin BaO films to that from sprayed oxide cathodes is discussed.

On the Nature of Radiation Damage in Metals
View Description Hide DescriptionThe nature of the permanent damage retained in metals from irradiation has been investigated in somewhat greater detail than has been done in the past. The usual assumption has been that the damage in all metals consists chiefly of interstitial‐vacancy pairs. The model presented in this paper reduces to this picture for the light elements but introduces a new concept in the case of damage in the heavy metals, called a displacement spike. Calculations are made from which one can estimate the relationship between the density of interstitial‐vacancy pairs and the temperature of the associated thermal spike. An assumption regarding the extent to which interstitial‐vacancy pairs persist throughout the duration of the thermal spike has been made, based upon these calculations. The number of interstitial‐vacancy pairs predicted in the heavy elements is considerably smaller than that predicted by the former model. A mechanism is proposed by which small dislocation loops can be produced in the heavier metals by irradiation.
This article is based upon studies conducted for the U. S. Atomic Energy Commission under Contract AT‐11–1‐GEN‐8.

A Capillary Viscometer with Continuously Varying Pressure Head
View Description Hide DescriptionA new capillary viscometer has been designed to study the flow behavior of non‐Newtonian fluids. The instrument is convenient, absolute, and accurate, and covers continuously a wide shearing stress range in a single determination. A falling mercury column forces the sample through the capillary. Measurement of the column height as a function of time gives both pressure drop and flow rate. Provision is also made for the use of driving fluids less dense than mercury for measurements at lower shearing stresses. The density of the sample need not be determined. Methods and illustrations are given of the application of the new instrument to the determination of the absolute viscosities of Newtonian liquids, and the flow curves of non‐Newtonian fluids.

Physical Theory of New Circuit Representation for Junction Transistors
View Description Hide DescriptionA circuit representation for a junction transistor is derived which places the mechanism of transistor action in evidence. The circuit is a direct interpretation of the diffusion equation and the boundary conditions which include the effects of base width modulation. It is found that the active part of the circuit is independent of frequency. A modification of the circuit for common emitter operation is shown and experimental results are given.

Experimental Procedures for Determining the Efficiency of Four‐Terminal Networks
View Description Hide DescriptionFive experimental procedures which may be used for determining the efficiency of four‐terminal networks, by means of circular loci plotted in the impedance or reflection coefficient planes, are presented.

On the Chromatic Field Aberration of the Magnetic Electron Lens in the Electron Microscope
View Description Hide DescriptionThe chromatic field aberration of the magnetic lens in the electron microscope is theoretically studied.
Good results are obtained for the coefficient of the chromatic difference in magnification of the objective, taking into account the inclination of the principal illuminating rays. The same coefficient of the intermediate lens increases rapidly as the magnification is reduced by the intermediate lens. The calculated results agree well with experimental results.
Calculated results are given for the coefficients of chromatic difference in rotation of all lenses as well as for the coefficient of chromatic difference in magnification of the projection lens.

Statistical Hydrodynamics in Porous Media
View Description Hide DescriptionThe statistics of disordered phenomena as exemplified by Einstein's theory of the Brownian motion is applied to the flow of fluids through porous media.
It is shown that such a statistical treatment of the hydrodynamics in porous media automatically explains some well‐known phenomena in a more satisfactory manner than do capillaric models. The statistical theory leads to a differential equation of motion of the fluid which is a modification of that of Darcy; notably a new macroscopic quantity is introduced which is termed ``dispersivity.'' This quantity is indicative of the sideways dispersion which a stream of fluid undergoes when it is passing through the porous medium. Under certain statistical assumptions outlined in the paper, the dispersivity becomes a constant of the porous medium.
The new differential equation of motion of the fluid is discussed in detail and some indications about applications are given.

Coincidence of Pulse Trains
View Description Hide DescriptionNew methods for determining the time fraction of coincidence of separate periodic pulse trains are considered. The analysis applies solely to pulse trains whose fundamental periods are commensurable. For two pulse trains, the coincidence fraction is easily determined. For three or more pulse trains, a method for determining the largest possible error resulting from direct use of elementary probability theory is developed. Hence the question: ``When does probability theory provide a close approximation to the coincidence fraction?'' is to some degree answered.

The Joint Distribution of n Successive Outputs of a Linear Detector
View Description Hide DescriptionThe joint probability density function of n successive outputs of a linear detector is derived for the case of dependent Gaussian inputs.

Application of Ideal Gas Theory to the Gaseous Expansion from an Electric Spark
View Description Hide DescriptionThe gaseous expansion from an electric spark is described in this paper in terms of ideal gas theory. The assumption is made that a quantity of energy is injected into a small gas volume in an infinitesimally short time and that the initial volume of gas then expands until it reaches the pre‐spark pressure at an elevated temperature. Experimental results are given for a condenserdischarge illustrating the dependence of the pressure equilibrated gas volume upon initial pressure and condenser energy. These results are interpreted using the ideal gas model presented. The significance of this expansion to the problem of spark ignition in combustible gases is discussed.

Factors Determining the Permanent Magnet Properties of Single Crystals of Fe_{2}NiAl
View Description Hide DescriptionIt is shown that fine precipitated particles present in single crystals of Fe_{2}NiAl are elongated and that the shape anisotropy of these particles is a major factor in determining the coercive force of Fe_{2}NiAl. For fields of less than 7000 oersteds, 〈111〉 directions are the directions of easy magnetization in the (110) plane of the crystal; this is due to the effect of the shape of the precipitated particles, which are oriented in three mutually perpendicular directions. In higher fields, the torque due to this effect decreases and then the [001] direction is the direction of easy magnetization because of intrinsic crystal anisotropy. These conclusions are based on an analysis, and on measurements, of the torque on three mutually perpendicular rods of magnetic material. These rods simulate the preciptated particles in the actual crystal.

An Electrodynamic Perturbation Theorem, with Application to Nonreciprocal Systems
View Description Hide DescriptionBy means of a slight modification of the macroscopic electrodynamic reciprocity theorem it is possible to obtain the perturbation of the admittance matrix of an electrodynamic device due to a suitable perturbation of the dielectricsusceptibility, conductivity, and magnetic susceptibilitytensors in the device. The theory is applicable to nonreciprocal systems, but in practice can be used to obtain only the first‐order perturbation of the admittance matrix. An expression relating the current induced in part of a system due to the motion of current in another part of the system is similarly obtained. Dc and microwave gyrators are treated, and the connection is pointed out between Faraday rotation in a transmission cavity and the magnetic energy splitting of its circularly polarized normal modes.

Short‐Time Frequency Measurement of Narrow‐Band Random Signals in the Presence of Wide‐Band Noise
View Description Hide DescriptionIn certain applications it is necessary to measure the center frequency of a symmetrical power spectrum in the shortest possible time. Two instrumentations for short‐time frequency measurement, the autocorrelator and the frequency discriminator, are examined for their ability to accomplish this task. The analysis compares the performance of the two systems and indicates the effect of such factors as signal‐to‐noise ratio and filter adjustment.

On the Distributions of Signals and Noise after Rectification and Filtering
View Description Hide DescriptionThe probability distributions for broad‐ and narrow‐band signals and normal random noise, following a square‐law rectifier and a video (or audio) filter of arbitrary width, are examined. The present approach is based on a method originally used by Kac and Seigert [J. Appl. Phys. 18, 383 (1949)] for noise alone (after quadratic rectification but no filter) in the case of the nth‐order distribution (n≥2). The procedure requires an appropriate transformation to express the output waveform in terms of the input disturbance; the statistics of the output are now determined by a suitable transformation with respect to the original, normal statistics. Explicit solutions are obtained for an integral equation involving the autocorrelation function of the noise, the weighting function of the video (or audio) filter, and an orthonormal set of eigenfunctions. For noise alone only the eigenvalues need be determined, but for a signal and noise it is necessary to know the eigenfunctions as well. Among the new results are (1), the calculation of the general, nth‐order characteristic function for the filtered output following quadratic rectification for an input noise and a signal andnoise; (2), a discussion of the second‐order probability densityW _{2} in this case; (3), some examples of practical interest; and (4), the limiting cases of broad and narrow post‐detection filters (vis‐à‐vis the predetection filter), with particular attention to approximations to W _{2} for signal and noise for narrow videos and an improved approximation for W _{1} for noise alone, as well.
 LETTERS TO THE EDITOR


Diffraction of Electromagnetic Waves by an Aperture in a Large Screen
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The Electron Atmosphere in Dielectrics
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