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Volume 22, Issue 9, 01 September 1951

Axially Symmetric Systems for Generating and Measuring Magnetic Fields. Part I
View Description Hide DescriptionThis is Part I of a systematic discussion of axially symmetric magnetic fields, both central and remote from the origin, search coils reporting the field or gradient at a single point, and mutual inductances. Here the central uniformity of symmetrical fields and gradients is analyzed by zonal harmonic expansion. Laplace's equation and symmetry restrict these fields to a few types, regardless of the detailed geometry of the generating system. Universal error‐contour maps are derived for the central field or gradient in systems having errors of second, fourth, or sixth order, and for hybrid types combining second and fourth. One hybrid has an oblate error field suitable for cloud‐chamber and orbital applications.
Source systems include circular filaments, cylindrical or plane circular current sheets, and thick solenoids of rectangular or notched section. Each type of source may be designed to produce any of the field patterns. To this end, source constants derived for the particular source type are combined into a set of over‐all coefficients that express the field constants for a complete system. Rapid methods are given for computing the source constants and from them all the field derivatives, using recurrence relations or tables of Legendre functions. In particular, computing time for thick‐solenoid fields or gradients is greatly reduced, using a new series with a recurrence formula. The text includes tabular aids and reference formulas, and discusses the rate of convergence of series for central and remote fields, and for mutual inductances.
Special systems briefly described include several infinite series of systems like that which starts with Ampere's loop, the Helm‐holtz pair, and Maxwell's three‐loop system. These have integral numbers of circular filaments from two to infinity. More practical are the thin solenoids. Those that produce a fourth‐order (Helm‐holtz) field by omission of central turns are fully tabulated for all lengths. A short solenoid with double‐wound ends and sixth‐order error may realize greater uniformity in actual practice than any previously described system. Still greater (theoretical) uniformity is achieved in two eighth‐order combinations of a short solenoid with a loop pair; these are described and depicted, with error limits.

Information Theory and Most Efficient Codings for Communication or Memory Devices
View Description Hide DescriptionShannon's theorem about the capacity of a channel is discussed, and it is shown that the most efficient coding is the one yielding the most probable distribution of the code symbols. A specific rule is obtained for this most probable distribution. Most efficient coding is essential for communication channels or memory devices in large scale computers.

Theory of V‐Antennas
View Description Hide DescriptionAn integral equation for the current in an apex‐driven symmetrical V‐antenna is derived and solved by successive approximations. General formulas for the distribution of current and the impedance are obtained. The zeroth‐order impedance is evaluated for a leg‐length h=λ_{0}/4 as a function of the enclosed angle and used to estimate experimental results.

On the Stress‐Function Approaches of Boussinesq and Timpe to the Axisymmetric Problem of Elasticity Theory
View Description Hide DescriptionIn the first part of this note the stress‐function approaches of Boussinesq and Timpe to the rotationally symmetric problem in the classical theory of elasticity are referred to general orthogonal axisymmetric curvilinear co‐ordinates. Although the underlying computations are of a routine character, it is felt that the presentation of the final results may serve a useful purpose. In the second part of the note, a connection between the two stress‐function approaches is established.

The Offset Wave‐Guide Junction as a Reactive Element
View Description Hide DescriptionA new type of wave‐guide circuit element has been described that has a number of desirable electrical and mechanical properties. These include ease and accuracy of adjustment, and simple analytical expressions for some of the more important properties.
The capacitive junction allows the practical construction of capacitively coupled resonant cavities. Such cavities have a relatively constant band width over their tuning range, as compared with the more commonly used inductively coupled cavities.

Mathematical Data for Electron Drain on Positive Ion Sources
View Description Hide DescriptionA study of the motion of electrons moving in the presence of crossed electric and magnetic fields is presented. Special electromagnetic regions are selected for discussion which assist in the controlling of electron discharge on positive ion sources when used with large mass‐spectrograph units. The article compares the components of motion parallel and perpendicular to the magnetic field in the following regions: uniform crossed electric and magnetic fields;electric field produced by nonparallel plane condenser plates, uniform H parallel to one plate; electric field produced by coaxial circular cylindrical condensers, uniform magnetic field normal to axis of cylinders; uniform electric field, circularly bowed magnetic field. The components of motion are expressed in terms of mathematical functions, and where it is deemed useful, additional results are presented in graphical form so that the conclusions can be applied with a minimum of calculations.

Arcing at Electrical Contacts on Closure. Part II. The Initiation of an Arc
View Description Hide DescriptionThe capacity of the plates of an oscilloscope charged to 35 or 40 volts is discharged repeatedly by approaching electrodes of carbon, active silver, and inactive silver. Facts about the discharges, which are arcs of very short duration, are inferred from resulting open circuit potentials and calculated electrode separations.
The separation at the first arc varies in different experiments but corresponds on the average to a nominal electric field of 0.6×10^{6} volts/cm for carbon or active silver and to 2×10^{6} volts/cm for inactive silver. Each arc is initiated by a very small number of field emission electrons. The hypothesis that a single electron may perhaps be sufficient is consistent with observations at later stages of each closure when the electrodes are closer and the field much higher.
The earlier observation, that the potential across a short arc is constant and independent of current, is not true if the arc time is sufficiently short. For active silver a time comparable with 2×10^{−8} sec is required to establish the steady arc voltage characteristic of later stages of arcs which last longer than this. The initial time during which the potential is decreasing toward its final steady value is 100 times the transit time of a silver ion across the gap.

X‐Ray Absorption in a Crystal Set at the Bragg Angle
View Description Hide DescriptionWhereas extinction effects would be expected to decrease the x‐ray transmission through a crystal when it is set at a reflecting angle, it is shown experimentally that in many cases the transmission increases at the Bragg angle.
This is believed to be due to the fact that the decrease in the effective absorption coefficient overshadows the losses due to reflection.
A reconsideration of Darwin's presentation of extinction allowing for variable μ shows that the transmission may increase or decrease depending on the values of μ and p. Thus the earlier observations of Bragg and co‐workers are reconciled with the observations reported here.
The importance, to crystal structure workers, of determining how μ varies with direction in periodic media is obvious.

On the Theory of Random Noise. Phenomenological Models. I
View Description Hide DescriptionThree phenomenological models are considered from which can be constructed a macroscopic statistical description of varieties of electronic noise, of which shot, thermal, and Barkhausen noise, electron multiplier and precipitationnoise, clutter, ignition, and impulsive random noise in general are representative examples. The models examined are (I) non‐overlapping, periodic noise waves, common in pulse‐time modulation and other communication schemes, where the amplitude, phase, duration, and epoch in a period interval are subject to statistical variations; (II), non‐overlapping, nonperiodic disturbances, encountered in servo‐mechanism operation and keyed‐carrier communication techniques, for instance, which are like (I), but lack the basic periodic structure; and (III), poissonnoise, consisting of the superposition of independent, randomly occurring elementary impulses. Much of the electronic noise mentioned above belongs to this more comprehensive type, where overlapping of the basic pulses is the characteristic feature. Because all (second‐order) moments are required in general for the analysis of noise in nonlinear systems, the attempt is made here to determine explicitly on the basis of the appropriate model the second‐order probability densityW _{2} in the important stationary cases. For noise of types (I) and (II) this appears impractical except in the simplest cases: only the lower order moments prove tractable. However, for poissonnoise (III) an explicit treatment is possible for impulsive random noise, nearly normal random noise, and for the limiting, normal random cases (of which shot and thermal noise are examples). In Part I the main features of the models (I–III) are discussed, and the general probability densityW_{l} (X _{1}, t _{1}; …; X_{s}, t_{s} ) in the nonstationary instances is formally constructed. In Part II, the distribution density for nearly normal random noise is given, the first and second (second‐order) moments of the various distributions are determined, and from these in turn are found the spectral distribution of the energy in the random waves.

On the Theory of Random Noise. Phenomenological Models. II
View Description Hide DescriptionPart II is devoted to the detailed evaluation of the first and second (second‐order) moments, namely, average values and the cross‐ and autocorrelation functions for stationary random noise waves for models I–III, whose statistical description is given in Part I. From these in turn are determined the cross‐ and auto‐spectral intensities governing the distribution of energy in the random disturbances. Finally, the asymptotically normal distributions characteristic of the high density poisson noise (III) are evaluated, together with higher order correction terms and their associated characteristic functions.

Emission of Radiation from Diatomic Gases. II. Experimental Determination of Effective Average Absorption Coefficients of CO
View Description Hide DescriptionEmpirical evidence obtained for CO at room temperature, which supports the use of average absorption coefficients for entire vibration‐rotation bands, is examined. In Sec. II the existence of an average apparent absorption coefficient for data obtained with inadequate spectral resolution is demonstrated. In Sec. III semiquantitative evidence at elevated total pressures and small optical densities for the use of a constant absorption coefficient equal to the ratio of integrated absorption to effective band width is described. These results serve as direct support for a proposed simplified method for radiant‐heat‐transfer calculations.

The Evaporation Products of Barium Oxide from Various Base Metals and of Strontium Oxide from Platinum
View Description Hide DescriptionThe evaporation products of BaO heated on ribbon filaments of Pt, Ta,Ni,Mo, and W, and of SrO on Pt have been studied using a high resolution mass spectrometer for positive ion analyses. The ratio Ba^{+}/BaO^{+}, was measured for each base material as a function of temperature and of the energy of the ionizing electrons to determine the origin of each ion peak observed. The results indicate: (a) Only on systems BaO on Pt and BaO on Ni, and SrO on Pt were the evaporation processes reproducible without particular attention to procedure. (b) The two systems BaO on Pt and SrO on Pt differ markedly in their evaporation mechanisms. (c) At high temperatures peaks are found due to Ba_{2}O^{++}, Ba_{2}O^{+}, Ba_{2}O_{2} ^{+}, and other barium compounds depending on the base metals used. (d) A measurable ion current was found due to Sr^{+} ions evaporated from Pt.

The Allotropic Transformation of Hafnium
View Description Hide DescriptionThe existence of an allotropic transformation in hafnium, suggested by Zwikker in 1926, has been confirmed. The transformation temperature is 1310±10°C. The high temperature beta‐form is probably body‐centered cubic.

Electrical Charge Storage in Polystyrene Capacitors
View Description Hide DescriptionMeasurements on charge storage in polystyrene capacitors over a period of months indicate that exceptionally fine capacitors may be made of polystyrene film when sufficient care is taken. Very small charge ``soakage'' occurs in such a capacitor, and charges may be retained for times of the order of one hundred years and possibly longer. The specific resistance approaches 10^{22} ohm cm when measured over a period of months. The power factor of polystyrene is about 10^{−4} for frequencies of 10^{−1} to 10^{−6} cycle per sec with a tendency to increase at the lowest frequencies and with a possible peak at still lower frequencies. The difference between charge soakage during charging and the charge recovery after shorting indicates some nonreversible current flow when measurements are made over several months' time.

Some Experimental Indications of the Stresses Produced in a Body by an Exploding Charge
View Description Hide DescriptionThe effects produced by small cylindrical charges that were detonated on the surfaces of heavy steel plates are discussed. Particular attention is paid to (a) shapes of crater, (b) changes in hardness, (c) flow patterns, (d) fractures, and (e) changes in microstructure. The distribution of stress appears in some respects to correspond to that which might be set up by a static load. The mechanisms of the inelastic deformation, however, differ very greatly between the static case and the dynamic case. Dynamic loading produces numerous shock twins and fractures that undoubtedly occur because of the very high strain rates involved.

A Reinterpretation of Experiments on Intermetallic Diffusion
View Description Hide DescriptionReported values for the heat of activation, H, for volume chemical diffusion, as obtained from the slope of the best straight line in a semilogarithmic plot of diffusion data against T ^{−1}, may often be greatly in error. These values will be too low whenever diffusion along internal surfaces plays a significant role at the lower temperatures of measurement. A method is presented which attempts to avoid such errors in H by using the calculated values of Zener for the intercept of the straight line. When the data is reconsidered in the light of this method, the widely accepted belief that H for chemical diffusion in dilute solid solutions is generally considerably less than H for self‐diffusion of the solvent is brought to question. In fact, it is found that the chemical diffusionactivation energy is generally within 15 percent of that for self‐diffusion. It is further concluded that the process of diffusion under a chemical gradient may itself produce internal surfaces which act as short‐circuiting diffusion paths.

The Generation and Measurement of Low Frequency Random Noise
View Description Hide DescriptionJudgment of the performance of automatic control systems often involves a consideration of the behavior of such systems in the presence of random noise. The noise may be of an undesirable nature, such as receiver noise, or it may represent an ensemble of statistical inputs which the system is to follow. Analytical techniques exist for determining the response of linear systems to noise inputs. However, no general methods are available for analyzingnonlinear systems subject to noise inputs. An electric analog computer, together with a suitable source of noise, may be used to study nonlinear systems. This paper describes an electronic noise generator designed for analog computer or simulator use. Methods are discussed for measuring the important characteristics of low frequency noise, such as the mean value, spectral density, amplitude distribution, and autocorrelation. Particular attention is devoted to the length of time necessary to establish satisfactory estimates of the properties of low frequency noise.

Carbon, Oxygen, and Sulfur Content of Chilean Coppers as Related to Cuprous‐Oxide Rectifiers
View Description Hide DescriptionSeveral Chilean coppers used in cuprous‐oxide rectifier work have been analyzed for carbon, oxygen, and sulfur. The carbon determinations were in agreement with published solubility data. Large differences were found in the oxygen and sulfur content which could be correlated with the refining data of the copper and the reverse leakage currents of the rectifiers. The change in sulfur content caused by various heat treatment also was investigated.

Enhanced Emission from Magnetron Cathodes
View Description Hide DescriptionExisting theories of the static magnetron do not predict violation of the Hull cut‐off condition or cathode bombardment. Measurements made at anode voltages and magnetic fields much larger than those used by earlier investigators revealed violations of the Hull cut‐off condition considerably more pronounced than those previously reported, and much greater amounts of cathode bombardment. When sufficient cathode bombardment takes place, emission may be enhanced (through secondary emission) by a factor of ∼10^{3} over the thermionic value. When enhanced emission occurs in magnetrons employing pure metalcathodes, it is found that maximum current limits exist for each magnetic field. These limits form a maximum current boundary on a voltage‐current plot. The maximum current boundary depends on secondary emissionproperties of the cathode surface and on geometry. Experimental observations on enhanced emission, cathode bombardment, the maximum current boundary, and flow of anodecurrent in violation of the Hull cut‐off condition are combined into a self‐consistent picture in static magnetrons employing pure metalcathodes. Although cathode bombardment and flow of anodecurrent are still unexplained, their existence can account for the observed enhanced emission and maximum current boundary. In this it is unnecessary to endow the cathodes with anomalous thermionic or secondary emissionproperties.
The process causing cathode bombardment, enhanced emission, and flow of anodecurrent in violation of the Hull cut‐off condition is believed to be an electronic interaction which occurs almost entirely in the relatively dense region of space charge surrounding the cathode. The significant factors influencing the interaction appear to be applied electric and magnetic fields, space charge density, and thickness of the space charge sheath. The basic problem of electronic interaction in the static magnetron is partially defined. It is expected that when a realistic solution to this problem exists, including a correct account of cathode bombardment, the occurrence of enhanced emission would be automatically predicted.

Hollow Cathode for Positive Ion Studies in Cathode‐Ray Tubes
View Description Hide DescriptionApparatus has been designed and tested which makes possible the identification of the positive ions in the beam of a cathode‐ray tube. A hollow cathode construction allows the positive ions to pass through the conventional part of the electron gun and be studied as a positive ion beam by another set of focusing electrodes and deflection magnets. Curves of ion yield and bucking potential measurements indicate that most of the ions are formed in the early stages of electron acceleration.