Volume 26, Issue 5, 01 May 1955

``Gate Modulation'' of Electromagnetic Radiation
View Description Hide DescriptionThe space‐charge layer at a p‐njunction is a region of low concentration of electrons and holes, and therefore exhibits less absorption than the bulk of the semiconductor for radiation of sufficiently long wavelengths. Thus the space‐charge region of a p‐njunction provides an optical window of a width which can be modulated by an applied field. A quantitative estimate of this effect is given. Because of an obvious relation to unipolar transistors, the name ``gate modulation'' is proposed, as opposed to the ``injection modulation'' discussed previously.

Note on the Kramers‐Kronig Relations
View Description Hide DescriptionThe explicit form of the relationship between the real and imaginary parts of a physically realizable network function is correlated with the alternate conventions available for such problems. The transformation from a linear frequency scale to a logarithmic one is simply effected by considering the Mellin transforms of the appropriate functions.

Diffusion, Static Charges, and the Conduction of Electricity in Nonmetallic Solids by a Single Charge Carrier. I. Electric Charges in Plastics and Insulating Materials
View Description Hide DescriptionThe dynamic equilibrium of space charge in insulators such as ceramics, molecular crystals, or high polymers, is considered from the thermodynamic point of view with quantum‐mechanical boundary conditions. The treatment constitutes the opposite extreme from the usual ohmic conduction equations; in the first paper, only the zero‐current equilibrium of charge is considered. Applications are made to the observed charging of high polymers during molding.

Diffusion, Static Charges, and the Conduction of Electricity in Nonmetallic Solids by a Single Charge Carrier. II. Solution of the Rectifier Equations for Insulating Layers
View Description Hide DescriptionThe discussion of the thermodynamic equilibrium of an electron atmosphere in a dielectric is extended to the current‐carrying steady state. Under the assumption that the experimental behavior at zero current is continuous with that when there are finite electrical currents, it is found that forward and reverse currents show distinct behavior. Expressions are developed for the electrostatic potential, field, charge density, the current‐applied voltage relation, and the capacity and rectifying behavior of dielectric layers. The non‐ohmic conduction exhibits rectification, and departures from the Wagner relation are predicted, of the type observed experimentally, including turnover voltages. The contact charging of a dielectric is the zero‐current limit of the non‐ohmic behavior which causes rectification.

Small Particle X‐Ray Scattering by Fibers, Size and Shape of Microcrystallites
View Description Hide DescriptionA theoretical and experimental analysis is given of small particle x‐ray scattering by fibers.
The scattering by different fibers of high orientation is compared with the theoreticalscattering curves derived for independent scattering by an assemblage of parallel cylinders. Under certain conditions of swelling, excellent agreement is obtained between experimental and theoretical curves. From this agreement it is concluded that under these conditions, independent particle scattering is realized and that interparticle interference and multiple scattering do not play a part.
Under all other conditions (dry fiber and other conditions of swelling) interparticle interference plays an important role in the scattering by these ``densely packed'' materials as can be concluded from the different distributions of intensity. The swelling method offers a means for separating independent and nonindependent scattering.
An analysis of the influence of various conditions of swelling is made, and the correct experimental conditions for obtaining independent scattering are derived from the results.
From the scattering under such conditions, the particle size in different fibers is determined on the basis of the theoretical formulas for independent scattering.

Čerenkov Radiation of Electrons Moving Parallel to a Dielectric Boundary
View Description Hide DescriptionThe phenomenon of Čerenkov radiations of electrons moving parallel to a dielectric boundary is investigated, using an eigenfunction expansion of the electromagnetic field. It is shown that the Čerenkov effect is similar to the excitation of surface waves in traveling wave tubes.

Silicon Solar Energy Converters
View Description Hide DescriptionTheory is given for the design of siliconsolar energy converters commonly known as the Bell Solar Battery. Values are given for the various parameters in the design theory. Experimental data are presented and compared with the theoretical relations based on a simple model.
It is found that with present techniques, units can be made with up to 6 percent efficiency in the conversion of solar radiant energy to electrical energy. An important factor in obtaining such high efficiencies is the reduction of the series resistance of the cell to as low a value as possible.

Effect of Air Damping on Transverse Vibrations of Stretched Filaments
View Description Hide DescriptionThe effect of air damping on the resonant frequencies of forced vibration of stretched filaments is studied by observing the shift in frequency when the surrounding medium is changed from air at atmospheric pressure to hydrogen at the same pressure, or to air at reduced pressures. For fibers of linear density less than about 10 micrograms per centimeter, the shift between atmospheric air and vacuum exceeds one cycle per second, becoming greater as the fibers become finer. The frequency shifts observed experimentally are compared with those predicted by certain formulas of Stokes. It is found that the theory works well enough to allow the effect of air damping to be taken into account in measurements of linear density by means of the vibroscope. However, the observed shift seems to be about one or two cycles per second higher than that calculated in the case of small shifts, and about 20 or 30 percent higher in the case of large shifts. A rigorous evaluation of the applicability of Stokes' theory would require further investigation.

Plasma Ion Oscillations in Electron Beams
View Description Hide DescriptionThe frequency of the oscillations observed in ion‐neutralized electron streams such as that of an ion‐trapping gun or of a tetrode has been shown to agree well with the Langmuir‐Tonks theory for plasma ion oscillations. The existence of a dipole mode of oscillation in addition to the longitudinal mode has been observed for a plasma column. A mechanism is proposed for the excitation of these self‐sustained oscillations by which the secondary electron current from electrodes bounding the plasma is modulated by the vibration of the ions in such a way as to deliverenergy to the ac field associated with the ion oscillations. Experimental observations verify this picture as far as the source of energy is concerned.

Anisotropic Diffusion Lengths in Diffusion Theory
View Description Hide DescriptionA set of formulas defining diffusion lengths in heterogeneous assemblies is presented. Even in the homogeneous limit, these formulas lead to anisotropicdiffusion lengths for systems such as rod or slab assemblies which are microscopically anisotropic.

Asymptotic Spherical Shock Decay
View Description Hide DescriptionIt is shown that the description of viscous and heat conductiveeffects in asymptotic spherical shock decay can be reduced to the solution of an ordinary first‐order differential equation relating shock strength and radius. The derivation of this equation is based, to a considerable extent, on a well‐justified quasi‐stationary approximation. Computational work required for handling specific situations is outlined.

Propagation of Shock Waves in Aluminum
View Description Hide DescriptionThe velocity of shock waves in aluminum and the associated translational motions, produced by metal‐metal impact, have been determined by an electrical contact technique. The results obtained have been used to evaluate an equation of state for the metal.

Noise in One‐Dimensional Electron Beams
View Description Hide DescriptionA generalized theory of noise in one‐dimensional electron beams is developed with the aid of the theory of four‐terminal networks. No specific assumptions are made as to the input noise velocity and current modulations and their correlation at the potential minimum. The ensuing theory is simpler and more general than the corresponding theories used in the past. Transformations are discussed of the standing wave of the mean‐square noise current in drift regions by means of ``lossless beam transducers.'' It is shown that such transformations can be reduced to the formalism of conventional impedance transformations. Expressions are derived for the minimum obtainable noise figures of a velocity‐jump amplifier, a klystron, and a traveling‐wave tube. It is proved that these expressions present an ultimate limit for the noise figures of the respective tubes with regard to transformations by beam transducers with and without loss.

Arcing at Electrical Contacts on Closure. Part VI. The Anode Mechanism of Extremely Short Arcs
View Description Hide DescriptionThe erosion at the anode of a short arc has been studied as a function of the arc duration and the magnitude of the arc current. With the current maintained at a constant value the anode pit grows continuously in diameter up to a critical value of the order of 10 microns; when this size is reached, a new arc is initiated and a new pit starts to develop. The process may be repeated. Consideration of the heat loss from the anode shows that for a constant arc power the pressure of metal vapor between the electrodes is very sensitive to the area covered by the arc. An order of magnitude estimate of the minimum metal vapor pressure required to maintain the arc (∼100 atmospheres) yields a value of the maximum pit diameter in good agreement with the experimental observations. It is evident that the steady‐state short arc does not exist, and quantities such as the metal transfer, ion to electron current ratio, and pressure in the arc are dependent on the time since the initiation of the arc.

Multiple Coincidence Magnetic Storage Systems
View Description Hide DescriptionIn existing magnetic matrix storage systems a given location is selected by applying to two intersecting wires a current equivalent to one‐half of the selecting field. This situation is generalized so that any core is selected by energizing p wires each with a current equivalent to 1/p of the selecting field. The advantages gained are in the correspondingly smaller fields applied to the nonselected cores, or alternatively, in the faster switching times obtainable by applying a total field greater than the coercive force to the selected core. To obtain the increased selection ratio p—2, additional sets of wires must be introduced into the matrix. Methods for accomplishing this are developed with the aid of a system analogous to plane analytic geometry for a finite set of points. Utilizing the increased selection ratio new fabrication techniques may be employed. Specifically, a storage matrix is illustrated in which the cores are toroids etched from a continuous sheet of magnetic material.

Nucleation of Ammonium Iodide Crystals from Aqueous Solutions
View Description Hide DescriptionAmmonium iodide crystals nucleate at a sensible rate in small drops (10–50 micron diameter) of solution only if the supersaturation ratio S equals or exceeds a value of 1.21. This critical supersaturation ratio corresponds to an interfacial energy σ between ammonium iodide crystals and solution equal to or greater than 15.4 ergs/cm^{2}. However, for sensible nucleation of NH_{4}I on a freshly cleaved surface of one of the mica minerals, S is related to the disregistry δ between atom sites on the mica surface and the atom sites on a {111} plane of NH_{4}I. This dependence can be described by the equation lnS=3.8δ^{2}+0.0059. This equation is in agreement with the theory of Turnbull and Vonnegut relating disregistry to the potency of nucleation catalysts. However, the coefficient of δ^{2} is about 1 to 2 orders of magnitude smaller than the theoretical expectation.
Our results are consistent with Bradley's hypothesis that S, for sensible 2‐dimensional nucleation of NH_{4}I on its own perfect {111} planes, is remarkably small, viz. S≃1.01.

Self‐Propagating Intermittent Discharge
View Description Hide DescriptionWhen a constant current pulse is applied to a pair of electrodes at small separations in air a series of electrical discharges takes place. These are characterized by a fixed distance between successive discharges. The intermittent nature of the discharge is determined by the local circuit and the spatial distribution of a series of discharges results from the blast wave which is propagated from each discharge. Measurements of the propagation distance as a function of the time interval between discharges and the energy released in each discharge are in qualitative agreement with those predicted from the theory of an intense explosion. The voltage transients across the electrodes show that during a series of discharges the breakdown voltages remain substantially constant and equal to the minimum breakdown voltage in air. This is attributed to the fact that the discharge can always find a low‐density region which is quite near the front of the blast wave where the conditions for minimum breakdown voltage can be satisfied.

Signal‐to‐Noise Improvement and the Statistics of Track Populations
View Description Hide DescriptionA treatment of the population statistics of signal and of noise patterns, or tracks, is given in this paper. Some idealized and abstract models of tracking procedures are studied; the models are intended to represent the processes encountered in radar tracking and in scanning nuclear emulsions for tracks. The equilibrium track population, the age distribution of the population at equilibrium, and a signal‐to‐noise improvement factor are obtained for each of the models considered. It is shown that the equilibrium population can be kept to reasonably small values, and the signal‐to‐noise ratio improved, if effective methods are used to eliminate deteriorating tracks.

Role of Positive Ions in High‐Voltage Breakdown in Vacuum
View Description Hide DescriptionMeasurements were made of the electron emission from targets of magnesium,aluminum, steel, copper,gold, and lead when bombarded by ions from hydrogen, helium, nitrogen, xenon, and mercury. The ions, whose energy was varied over the range from 10 to 140 kilovolts, were produced by ionization of the residual gas in the anode electrode and emerged through a small opening into an essentially uniform accelerating field. An initial rapid rise of electron emission with ion energy was followed in all cases by a slow linear increase. The emission ratio varied from 2 to 20 and was maximum for nitrogen ions on steel. The effect of extractive gradient at the bombarded metal surface was slight and no simple dependence on the nature of the ion or of the bombarded metal was observed. The significance of these measurements on the electronion interaction theory of high‐voltage breakdown in vacuum is discussed.

Nyquist's and Thevenin's Theorems Generalized for Nonreciprocal Linear Networks
View Description Hide DescriptionIt is shown that an N‐node nonreciprocal linear network, with a system of internal thermal noise generators at temperature T, is equivalent to the source‐free network together with a set of correlated nodal current generators, with infinite internal impedance, such that where y_{rs} is an element of the network admittance matrix and i_{r} is the rth nodal noise current with frequency v. The noise sources can also be represented by a system of nodal voltage generators, with infinite internal admittance, such that .
The application of these results to a system of coupled antennas in an equi‐thermal enclosure is noted and necessary conditions for the realizability of passive nonreciprocal networks are derived.