Volume 35, Issue 5, 01 May 1964

Internal Resonances of a Discharge Column
View Description Hide DescriptionDipole resonance of a cold plasma column can be predicted quite simply and observed experimentally. It is normally accompanied, however, by a series of subsidiary resonances. These have recently been explained phenomenologically as depending on nonuniform electron density and nonzero electron temperature for their existence. Numerical results of an analysis of the resonances by Nickel, Parker, and Gould are compared to the recently published experimental work on which the phenomenological description was founded, and it is shown that there is very good agreement. These observations and the theory have considerable relevance to the pressure waves described by Bohm and Gross, and to the effectiveness of Landau damping under conditions of nonuniform electron density. It is also possible to use the computed data to estimate the error in dipole resonance measurements of electron density.

Model for the Electrical Behavior of a Microplasma
View Description Hide DescriptionThe complex current fluctuations observed in connection with microplasma breakdown can be explained by a simple model containing two constants: extrapolated breakdown voltage V_{b} and series resistanceR_{s} ; and two continuous probability functions: turnoff probability per unit time p _{10}(I) as a function of pulse currentI and turn‐on probability per unit time p _{01}. Experimental methods allowing an accurate measurement of these four quantities are described. The new concept of an extrapolated breakdown voltage V_{b} is discussed based on two independent measurements: one of secondary multiplication and the other of instantaneous current, both as a function of voltage. Within the experimental accuracy of 20 mV both methods extrapolated to one and the same breakdown voltage. The turnoff probability p _{10}(I) is determined by a new combination of experimental techniques to cover the current range from 5 to 70 μA with a variation of 11 decades for p _{10}(I). The observation of a narrow turnoff interval is explained quantitatively.

Multimode Oscillations in Solid‐State Masers
View Description Hide DescriptionPrevious work by the authors on the effects of slow spatial cross relaxation is extended in two directions. First, off‐axis modes are included in the calculations, and thus it becomes possible to calculate the number of oscillating off‐axis modes as a function of the various laser parameters. In this way the expected beam angle of a laser can be predicted. Second, a more detailed analysis of the spiking behavior is given; both regular and irregular spiking trains may be obtained depending upon the laser parameters and the pump power.

A Backward‐Wave Surface Mode in a Plasma Waveguide
View Description Hide DescriptionThe phase characteristics of a backward‐wave pass‐band mode have been measured in a plasma waveguide, consisting of a circular waveguide that is coaxial with the positive column of a mercury‐vapor discharge. The mode has been identified as an n = 1 surface mode similar to that described by Trivelpiece.
It is shown that zero‐temperature plasma‐waveguide theory predicts this mode accurately. This theory predicts that a simple relation exists between the lower cutoff frequency of the n = 1 mode and the electron plasma frequency. It is demonstrated that the calculated electron plasma frequency obtained from this relation, where the cutoff frequency is determined from a measurement of the phase characteristics, agrees well with an independent measurement of electron plasma frequency by the well‐known cavity‐perturbation method.
Both the n = 1 and symmetric n = 0 modes were excited by a novel coupler called the double‐ring coupler.
Noise measurements on the n = 1 and symmetric n = 0 modes indicate that the output signal‐to‐noise ratio is independent of input signal power and is about 7 dB for the n = 1 mode and varies from about 7 to greater than 30 dB for the n = 0 mode. A simple model of the plasma is proposed which explains all the noise observations reported here. Crawford and Lawson independently proposed a similar model.

Statistics of Time in Photomultiplication
View Description Hide DescriptionPhotomultiplication is considered as a branching process. The output current of the photomultiplier is studied as a function of the statistical distributions of photon emission, electron flight times, and secondary emission yields. Expressions are derived for the timing accuracy of photomultipliers and scintillation counters.

Multimoding in Lasers
View Description Hide DescriptionIt is well established that multimoding occurs in lasers within the homogeneous linewidth of the active medium. The oscillations at more than one frequency can be explained on the basis of the spatial or time dependence of the population difference. A threshold condition for multimoding is obtained in terms of the maximum power density from the laser with a single frequency output.

Determination of Particle Structure from Light Scattering
View Description Hide DescriptionLight scattering is well known as a useful tool in the investigation of the structure of particles. One of the disadvantages is that, whereas the scattering often may be calculated for a given structure, it has not been possible to carry out a Fourier inversion of the scattered intensity function to determine an unknown structure.
There are two major difficulties which are immediately recognizable. (1) The phase as well as the amplitude of the scattered radiation must be measured, and (2) the usual technique of Fourier inversion is not applicable because it requires knowledge of the scatteredwavefunction for experimentally unattainable values of parameters. Both of these problems are discussed, and it is noted that they may be overcome in certain cases of interest. A method of phase determination suited to optical wavelengths is suggested for scattering by a single particle. Further, for ``soft'' scatterers, a method of inverting the scattering data is developed that does not suffer from the difficulty associated with the Fourier method. Thus, the inversion may be carried through and the desired structure of a scatterer may be obtained.

Optical Constants in the X‐Ray Range
View Description Hide DescriptionIn conjunction with x‐ray transmission data, the integral relationship between the refraction index and the absorption coefficient can be employed to extend the range over which optical constants have been determined by Kramers‐Kronig analysis of reflectance data. The procedure is applied to measurements on aluminum and the optical constants are determined for the energy range 10^{−3} to 10^{5} eV. The results are useful in testing some general sum rules. They also permit a comparison of the behavior of the dielectric constant for energies above the K absorption edge with the expected asymptotic behavior.

Dielectric Breakdown of Single‐Crystal Strontium Titanate
View Description Hide DescriptionMeasurements of the intrinsic dielectric breakdown strength of single‐crystal strontiumtitanate over a temperature range from −195° to +100°C and under both pulse and dc conditions are described; dc breakdown at +100°C is thermal in origin. At room temperature and at −40°C the breakdown strength is independent of duration of applied field and of sample configuration and hence may properly be termed intrinsic. At −80° and −195°C, both the values of breakdown strength and the scatter of the data depend strongly on sample configuration. The breakdown strength unexpectedly decreases with increasing temperature. Current‐voltage curves show an anomalous saturation effect at low temperature. These effects may be qualitatively explained by postulating that the high electrostrictive stress causes the creation of electron trapping centers.

Luminous Front Thickness in Electric Shock Tubes
View Description Hide DescriptionFive electric shock tube arrangements have been studied by means of photomultiplier signals. The risetime of the luminous front as it passes the detector station is converted to a thickness by means of the measured front speed. These thicknesses are correlated with initial conditions of pressure from 0.15 to 5.0 Torr of argon, and input power from 0.8 to 262×10^{6} W, for tubes with luminous front speeds from 3 to 30 mm/μ sec. For each tube the front thickness increases with input energy and, in general, the thickness of the luminous transition zone is proportional to the peak current. Identification of the luminous front is with the ``hairpin'' driving current, rather than with a shock wave initiated by it. A maximum current density picture of this driving current is suggested by the data.

Measured Temperatures of Strong Shock Waves in Argon
View Description Hide DescriptionPlane shocks generated in atmospheric pressure argon by detonating Comp B‐3 have been viewed with a photomultiplier‐interference filter system. Visible radiation from these Mach 27 shocks was that from a blackbody at a color temperature of 29 000°±1000°K, about 20% higher than calculated. The risetime to peak intensity is interpreted in terms of increasing opacity, and consequently of emissivity, as the shocked zone increases in thickness. Photon absorption coefficients based on this interpretation are in reasonable accord with those calculated from a modified Kramers's formula.

Ferromagnetic Resonance in Multidomain Thin Films
View Description Hide DescriptionA thin Ni‐Fe film, having a uniaxial magnetic energy of the form E_{K} = K sin^{2}θ, usually exists as a single domain. If a magnetic field of sufficient magnitude is placed perpendicular to the easy axis of magnetization and then removed, the film splits into a large number of 180° domains. When this simple multidomain structure occurs, it is theoretically possible to excite two ferromagnetic resonance modes by applying a small magnetic field perpendicular to the easy axis. The first of these, a low‐frequency mode (0–10 Mc/sec) is excited by an rf field perpendicular to the domain walls; and the second, a high‐frequency mode (0–25 Gc/sec) is excited by an rf field parallel to the domain walls. The high‐frequency mode has been observed in a number of films having anisotropy fields from 3–5 Oe. The experimental results are compared with theoretical relations for frequency as a function of applied field. In addition, it is possible to estimate the domain wall separation from measurements of the high‐frequency mode. These measurements indicate that typical domain widths range from 30 to 50 μ. A difference is observed in the position of the absorption peak when measured in an increasing field than when measured in a decreasing field. This hysteresis is explained by the Bloch‐Néel wall transition theory which was used to explain the constricted M‐H loops. Attempts to observe the low‐frequency mode were not successful.

Square‐Loop Properties of Materials in the System NiFe_{2}O_{4}–Fe_{3}O_{4}–MnFe_{2}O_{4}
View Description Hide DescriptionToroids composed of polycrystallinematerials of a number of compositions in the system NiFe_{2}O_{4}–Fe_{3}O_{4}–MnFe_{2}O_{4} exhibit rectangular magnetic hysteresis loops. The squareness ratios, switching coefficients, and coercivities, and their temperature coefficients demonstrate the usefulness of these materials as the storage elements in coincident‐current computer memories. The square hysteresis loops in this system can be explained with the aid of existing knowledge of the magnetocrystalline and stress anisotropies.

Ultrasonic Relaxation Loss in SiO_{2}, GeO_{2}, B_{2}O_{3}, and As_{2}O_{3} Glass
View Description Hide DescriptionMeasurements of the temperature dependence of the longitudinal and shear ultrasonic attenuation from 5 to 50 Mc/sec were made in SiO_{2}, GeO_{2}, B_{2}O_{3}, and As_{2}O_{3} glass. In each case a relaxation loss with a distribution of relaxation times was found. The median activation energy of the relaxation process is about 500 cal/mole in SiO_{2}, 2500 cal/mole in GeO_{2}, 5400 cal/mole in As_{2}O_{3}, and 6300 cal/mole in B_{2}O_{3}. The results are interpreted in terms of a two‐bond‐length model of glass where the relaxation loss is associated with bridging oxygen atoms which have two stress‐sensitive equivalent equilibrium positions. A relationship between the relaxation loss mechanism and the viscosity of these glasses is assumed in this study. A calculation of the activation energies based upon this assumption agrees well with the values determined experimentally.

Application of Thermodynamics to Thermomechanical, Fracture, and Birefringent Phenomena in Viscoelastic Media
View Description Hide DescriptionA unified theory of the thermomechanical behavior of viscoelastic media is developed from studying the thermodynamics of irreversible processes, and includes discussions of the general equations of motion,crack propagation, and birefringence. The equations of motion in terms of generalized coordinates and forces are derived for systems in the neighborhood of a stable equilibrium state. They represent a modification of Biot's theory in that they contain explicit temperature dependence, and a thermodynamically consistent inclusion of the time‐temperature superposition principle for treating media with temperature‐dependent viscosity coefficients. The stress‐strain‐temperature and energy equations for small deformation behavior follow immediately from the general equations and, along with equilibrium and strain‐displacement relations, they form a complete set for the description of the thermomechanical behavior of media with temperature‐dependent viscosity. The role of thermodynamics in finite deformation and crack propagation problems is examined. Restrictions placed on the constitutive equations by thermodynamics is illustrated by considering a familiar stress‐strain equation for polymers, wherein the time and strain dependence of stress in a relaxation test appear as separate factors. In addition, an energy equation for crack propagation is derived and then applied to a specific problem. Thermodynamic implications concerning birefringence are also discussed and an operational stress‐optical coefficient is derived.

Analysis of High‐Power Effects in Ferrimagnetics from the Point of View of Energy Transfer. Part I. First‐Order Instabilities
View Description Hide DescriptionSpin‐wave instabilities in ferrimagnetics in the past have usually been analyzed by considering the perturbed equations of motion of the normal variables of the spin system. In this paper the spin‐wave behavior is analyzed without the use of the normal mode development. The properties of the kth spin wave—its energy and the phases and amplitudes of its transverse magnetization components—are derived using real variables exclusively. Then the criteria for all the first‐order instability thresholds are derived from the power balance of the spin system. The physical processes which lead to spin‐wave instabilities are discussed.

Piezoresistivity of Manganin
View Description Hide DescriptionThe change in resistance of a class of alloys called Manganin has been measured as a function of peak shock‐wave pressure up to 190 kbar. The pressures are obtained from explosively generated plane shock waves in a material of known Hugoniot equation of state. The Hugoniot of Manganin, which has been measured up to 359 kbar, is used with the resistance measurements to calculate the change in resistivity with volume. The results are compared with previous measurements.

Ultrasonic Attenuation and Velocity in Three Transformation Products in Steel
View Description Hide DescriptionUltrasonic attenuation measurements were made from 2 to 100 Mc/sec in the pearlitic‐plus‐ferritic, bainitic, and martensitic transformation products in SAE 4150 steel, a low‐alloy, 0.5% carbon variety. Measurements were also made in the martensitic specimen after tempering. Ultrasonic velocity measurements were made at 10 Mc/sec in each case. To eliminate the question of grain size and grain size distribution, three specimens were treated identically through the austenitizing operation. Then they were cooled differently to produce the three transformation products. The attenuation can be expressed as Af ^{4}+Cf ^{2}, where f is frequency. The first term is Rayleigh scattering and the second may be from dislocation damping, atomic relaxations, or magnetic domain boundary effects. Both A and C are strong functions of microstructure. Both coefficients decrease in the order pearlite‐plus‐ferrite, bainite, martensite, tempered martensite. On tempering, A decreased in the ratio 3:2 while C decreased 3:1. In pearlite‐plus‐ferrite, A is larger by a factor of 225 than it is in tempered martensite, and C is larger by a factor of 10. The ratio C_{T}/C_{L} (T = transverse waves, L=longitudinal waves) was a constant independent of microstructure and equal to 2.4. This suggests either dislocation damping, an atomic relaxation, or a magnetic effect. The large change in C on tempering (with C_{T}/C_{L} = constant) indicates that the interstitial carbon is involved. The ultrasonic velocity measurements showed an increase in velocity on tempering the martensite. Pearlite‐plus‐ferrite has the highest velocities and density, while raw martensite has the lowest. The differences in velocities arise primarily from differences in the elastic moduli of the transformation products, not from the density differences.

Ultrasonic Attenuation in Cadmium Sulphide above Room Temperature
View Description Hide DescriptionThe temperature dependence of the attenuation of 30‐Mc/sec longitudinal ultrasonic waves has been measured from room temperature to 380°C in CdS. The observed attenuation is in good agreement with the theory of Hutson and White and with the temperature dependence of the resistance measured on the same specimen.

A Study of Standing Spin Waves in Thin Permalloy Films at Radio and Ultrahigh Frequencies
View Description Hide DescriptionA study of standing spin waves in thin Permalloy films in the frequency range 50–4200 Mc/sec was conducted with a dc magnetic field applied perpendicular to the film surface. The purpose of the experiment was to study the behavior of the spin‐wave absorption lines at fields just above saturation and to investigate the possibility of exciting standing spin waves at fields below saturation. It proved possible to excite one spin‐wave line when the field was less than that required for saturation. Comparison of the field separating this line from the main absorption line with the separation of the spin‐wave lines when the dc field is above saturation indicates that this line is the N=1 line. Further study based on the concept of dynamic pinning demonstrates that the surface spins are not pinned in this unsaturated region and that this N=1 line is excited only by an inhomogeneous field. An expression for the rf susceptibility and the general boundary conditions are derived in the Appendix.