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Volume 22, Issue 3, 01 March 1951

Electron Optical Exploration of Space Charge in a Cut‐Off Magnetron
View Description Hide DescriptionThe main effort in the work described has been directed towards the measurement of the electric field distribution in a cut‐off magnetron, based on the electron optical shadow method. The space charge distribution can be determined qualitatively from the measuredelectric field distribution. The first objective is the development of a convenient method for such a study. In this work an elementary magnetron was investigated by sending an electron beam axially through the tube.
The conclusions of the study are that the space charge distribution does not conform to Hull's classical theory (which predicts that the space charge density is approximately constant out to a well‐defined radius and zero beyond this cloud radius). Three different space charge distributions have been observed. One distribution has a sharp maximum near the cloud radius. Another falls off gradually toward the cathode; a third is time‐variant. The shape of the space charge distribution is closely related to the symmetry of the magnetron.

A Note on Reflection and Transmission
View Description Hide DescriptionThe quantities characterizing wave propagation through the interface of two media or through a transmission line containing obstacles are the two reflection coefficientsr _{1} and r _{2} and the two transmission coefficientst _{1} and t _{2}. It is shown that for any lossless discontinuity r _{1} = r _{2}, argt _{1} = argt _{2}, and that argr _{1}+argr _{2} −2 argt _{1} = ±π. These relations are applied to the calculation of reflections from sheets of dielectric and metal‐plate media, the latter being distinguished by the fact that argt _{1}≠0.

Reflection and Transmission at the Surface of Metal‐Plate Media
View Description Hide DescriptionThe theory of Carlson and Heins has been extended; an expression is found for the reflection coefficient applicable in the presence of a diffracted beam. Tables and graphs are included for the coefficients associated with electromagnetic phenomena at the surface of metal‐plate media. The magnitude of the reflection coefficient was measured at normal incidence and the phase of the transmission coefficient for angles of incidence from 0 to 25°. A satisfactory agreement with theory is obtained.

Experimental Determination of the Reflection Coefficient of Metal‐Plate Media
View Description Hide DescriptionA method of measuring the reflection coefficient of metal‐plate media at 3 cm is described. The technique differs from that presented in the preceding paper in that the measurements are made in a closed system and back reflections are eliminated by an absorbing wedge. Angle of incidence and the plate thickness are varied. The agreement with the Carlson‐Heins theory is excellent for very thin plates. For plates of moderate thickness near normal incidence the measured reflection is higher than that predicted for an infinitely thin set of plates with identical index of refraction.

On Amplitude Bounds for Certain Relaxation Oscillations
View Description Hide DescriptionAmplitude bounds are obtained for the unique periodic solution of the generalized Lienard equation ẍ+f(x)ẋ+g(x)=0, when the functions f(x) and g(x) are restricted suitably. The restrictions are less severe for the lower than for the upper bounds. A class of equations is exhibited which includes the van der Pol equation and satisfies all the restrictions. Numerical results are given for the van der Pol equation.

A Theory of the Envelope Type of Thermal Conductivity Tests
View Description Hide DescriptionThe well‐known problem of the end effects in a cylinder of finite length has been circumvented by the use of spheroidal rather than cylindrical apparatus. After a general theory of heat flow is given, applications demonstrate the mathematical difficulties caused by discontinuities in the curvature of the surface of the heat conductor. The suitability of the spheroidal shape is demonstrated, and corresponding heat flow equations are derived demonstrating the effects of the variable distance between any two isotherms on the amount of heat crossing any unit area of an isotherm. It is proven that the amount of heat flowing through a slice of a spheroidal isotherm made perpendicular to the axis of the spheroid is proportional to the width of the slice, and independent of the position of the slice with respect to the spheroid. This theorem is applied to find the heat distribution necessary to keep the core of the apparatus at uniform temperature. Because all measurements are made at thermal equilibrium, a rough estimate is given for the time necessary to reach equilibrium.

Long‐Range Order in Beta‐Brass and Cu_{3}Au
View Description Hide DescriptionMeasurements have been made on single crystals of CuZn and Cu_{3}Au held at various temperatures below T_{c} to decide whether there is a single‐ordered phase whose order changes with temperature, or whether there is an ordered and a disordered phase the relative amounts changing with temperature. Precision measurements were made of the position and width of the (222) CuZn and (400) Cu_{3}Au reflections. The disordered phase has a larger cell dimension, so that reflections from the ordered and disordered phases are slightly displaced from one another. For both materials, a single peak was observed which was too narrow to correspond to the existence of two phases. At the stoichiometric compositions, it is concluded that below T_{c} there is only an ordered phase whose long‐range order varies with temperature. Measurements of the long‐range order in Cu_{3}Au have been made on briquets of filings, using quenched samples, and on a sample held at temperature.

Phase Equilibria in an Ordering Alloy System
View Description Hide DescriptionThe equilibria between phases in platinum alloys containing 42, 48, and 54 atomic percent cobalt were determined at temperatures below 1000°C. This system of alloys exhibits an order‐disorder transition analogous to that for CuAu. A temperature range in which ordered and disordered phases coexist in equilibrium was determined for each alloy. These data were incorporated in the phase diagram. The Co‐Pt system is the first ordering alloy system in which it has been shown that this reaction is a true phase transformation contrary to the prevalent concepts of the phenomena.

Boride Cathodes
View Description Hide DescriptionThe thermionic emissionproperties of the borides of the alkaline‐earth and rare‐earth metals and thorium have been investigated. These compounds all have the same formula MB_{6} and the same crystal structure consisting of a three‐dimensional boron framework in whose interlattice spaces the metal atoms are embedded. The valence electrons of the metal atoms are not accepted by the B_{6} complex, thus giving rise to the presence of free electrons which impart a metallic character to these compounds. This, together with the strong bonds between the boron atoms in the framework, produces a series of compounds which have high electrical conductivities and high thermal and chemical stabilities—ideal properties for a cathodematerial. When this structure is heated to a sufficiently high temperature, the metal atoms at the surface evaporate away. They are, however, immediately replaced by diffusion of metal atoms from the underlying cells. The boron frame work does not evaporate but remains intact. This process gives a mechanism for constantly maintaining an active cathode surface. Thermionic emission measurements made on these materials show the rare‐earth metalborides to be superior to the others. The highest emission was obtained from lanthanumboride. Its emission constants for the Dushman equation were φ=2.66 volts and A=29 amps/cm^{2}/degK^{2}. This is higher than the emission normally obtained from thoria. Lanthanumboride has a relatively low evaporation rate corresponding to a latent heat of evaporation of 169 kilocalories per mole. If the hexaborides are operated at high temperature in contact with the refractory metals,boron diffuses into their metal lattices forming interstitial boron alloys with them. When this occurs, the boron framework which holds the alkaline‐earth or rare‐earth metal atoms collapses, permitting the latter to evaporate. However, the hexaboride cathodes may be operated at high temperatures in contact with tantalum carbide or graphite. Lanthanumboridecathodes are especially useful in applications where high current densities are required. They are also suitable for high voltage applications because they stand up well under positive ion bombardment. Since they are atmospherically stable and activate easily, they have found wide use in experimental demountable systems.

Transmission‐Line Equivalent of Electronic Traveling‐Wave Systems
View Description Hide DescriptionIt is well known that the small‐signal behavior of long electron beams may be analyzed in terms of propagating space‐charge waves, suggesting an equivalence between such beams and longitudinally moving transmission lines. This in turn suggests the analysis of such electronic devices as the traveling‐wave amplifier, double‐stream or electron‐wave amplifier, and multicavity magnetron, in terms of coupled distributed‐parameter transmission lines moving relative to each other. It is shown that this approach is equivalent to a rigorous field‐theory analysis in certain cases of particular interest, and the procedure for calculating the significant distributed parameters is indicated. Final results for the idealized helix and thin cylindrical electron beam are presented.

Thickness‐Shear and Flexural Vibrations of Crystal Plates
View Description Hide DescriptionThe theory of flexural motions of elastic plates, including the effects of rotatory inertia and shear, is extended to crystal plates. The equations are solved approximately for the case of rectangular plates excited by thickness‐shear deformation parallel to one edge. Results of computations of resonant frequencies of rectangular, AT‐cut, quartz plates are shown and compared with experimental data. Simple algebraic formulas are obtained relating frequency, dimensions, and crystal properties for resonances of special interest in design.

A Correlating Modulus for Fluid Resistance in Accelerated Motion
View Description Hide DescriptionThe resistance to accelerating movement of objects in a fluid is normally evaluated with a mass term in the equation of motion that is greater than the actual mass of the object by an added mass described as a constant times the displaced mass of fluid. This added mass has been evaluated by numerous investigators for different body shapes from potential flow considerations. Published experimental results, mostly with oscillating systems with small amplitudes of motion, show an added mass constant that is higher than that derived from potential flow with values that are dependent upon the fluid and the object size. A few previous experiments on resistance in unidirectional acceleratedmotion indicate that the added mass is variable and depends upon the state of motion.
The present investigation includes a development from model law considerations that results in a resistance equation of the form . This is identical with the normal resistance equation for steady state except for the coefficient C which, in addition to being a function of Reynolds' modulus, Froude's modulus, and the geometry, is also a function of a modulus, AL/V ^{2}, where A is the acceleration,L is a characteristic length, and V is the velocity.
Experiments with circular disks moving perpendicular to the plane of the disk under the action of approximate constant driving forces show this resistance coefficient to be correlated by the modulus AL/V ^{2}.

Cut‐Off Frequency in Two‐Dielectric Layered Rectangular Wave Guides
View Description Hide DescriptionEquations for the modes and eigenvalues of two‐dielectric layered rectangular wave guides with cross sections as in Fig. 1(a), (b), and (c) are derived. From these equations are plotted graphs of cut‐off frequency over a range of geometric and dielectric parameters sufficiently wide to cover most requirements of design.

Maxwell's Demon Cannot Operate: Information and Entropy. I
View Description Hide DescriptionIn an enclosure at constant temperature, the radiation is that of a ``blackbody,'' and the demon cannot see the molecules. Hence, he cannot operate the trap door and is unable to violate the second principle. If we introduce a source of light, the demon can see the molecules, but the over‐all balance of entropy is positive. This leads to the consideration of a cyclefor Maxwell's demon as well as for the scientist in his laboratory. Boltzmann's constant k is shown to represent the smallest possible amount of negative entropy required in an observation.

Physical Entropy and Information. II
View Description Hide DescriptionThe laws of statistical thermodynamics are used for the definition of entropy, and it is shown that the definition of information can be reduced to a problem of Fermi‐Dirac statistics or to a generalized Fermi statistics. With these definitions, the entropy of a certain message can be defined, and the information contained in the message can be directly connected with the decrease of entropy in the system.
This definition leads directly to the formulas proposed by C. E. Shannon for the measure of information, and shows that Shannon's ``entropy of information'' corresponds to an equal amount of negative entropy in the physical system. The physical background of the whole method is discussed and found in agreement with previous discussions.

A Metallographic Study of Diffusion Interfaces
View Description Hide DescriptionBy sintering wires to flat metallic blocks, diffusion interfaces were obtained between the following pairs of metals: Cu‐Ni, Au‐Ag, Cu‐Ag, Cu‐Fe, Fe‐Ni, Cu‐Zn, Ni‐Zn, and 70/30 brass‐Cu. The interfaces were subsequently investigated metallographically. Grooves were observed in the lower melting point component in the vicinity of the sintered interfaces. This is attributed to the faster diffusion rate in the lower melting point metal.

Scattering and Absorption of Gamma‐Rays
View Description Hide DescriptionA formulation is presented of the scattering and absorption of gamma‐rays in different materials. The range of gamma‐ray energies considered is from 1 to 10 mc ^{2}. Results are given for the transmission of gamma‐rays through air and lead.

The Elastic Parameters of Beta‐Brass
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The Barium Oxide on Tungsten Cathode Interface
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