Steep Wave Front Research Articles

Far-Wake Structure in Rarefield Plasma Flows past Charged Bodies

The asymptotic structure of the far-wake behind a charged body in a rarefied plasma flow is investigated under the assumption of small ion-to-electron temperature ratio and of flow speed hypersonic with respect to the ions but not with respect to the electrons. It is found that waves are excited even if the flow is subacoustic (flow velocity less than the ion-acoustic speed). For both superacoustic and subacoustic velocities a steep wave front develops separating the weakly perturbed, quasineutral plasma ahead, from the region behind where ion waves appear. Near the axis a trailing front develops; the region between this and the axis is quasineutral for superacoustic speeds. The decay laws in all of these regions, the self-similar structure of the fronts and the general character of the waves are determined. The damping of the waves and special flow detail for bodies large and small compared with the Debye length are discussed. A nonlinear analysis of the leading wave front in superacoustic flow is carried out. A hyperacoustic equivalence principle is presented.

Transient Interactions of Spherical Acoustic Waves and a Cylindrical Elastic Shell

The three-dimensional transient interaction between spherical acoustic waves with infinitely steep wavefronts and a circular cylindrical elastic shell of infinite length is investigated. The incident spherical wave is transformed into cylindrical partial waves by using the addition theorem for the modified Bessel function. The governing wave equation and equations of motion of the shell are solved by a series expansion-Laplace-Fourier transform technique. The transformed solution of the problem is obtained in closed form exact within the limit of series solution imposed by the Gibb's phenomenon. The physical solution is obtained by an accurate numerical scheme for the two-fold inverse Laplace-Fourier transforms. Detailed numerical results are obtained for the transient response of the shell and some quantitative effects of the sphericality of the incident waves on the response of the shell are also revealed.

The amplifying gate thyristor

High frequency, high current operation of thyristors requires simultaneous consideration of turn-off time, di/dt and dv/dt capability. The frequency of operation and the type of circuit dictate the turn-off time and dv/dt which are required of a device. These two parameters are established by suitable gold doping to control the minority carrier lifetime and by employing shorted emitter techniques to ccntrol the low current alpha's of the device. In addition, at high currents and voltages, a thyristor's capability of withstanding steep wavefront, high current pulses (i.e., di/dt capability) often also proves to be a major limiting factor in its application. This characteristic is primarily determined by the instantaneous junction temperature; thus, it is essential that localized heating be minimized. Unfortunately, this problem is aggravated by increased dissipation resulting from the lower lifetime that is required to achieve the short turn-off time. In order to minimize the instantaneous temperature rise, a substantial increase in effective conducting area during the turn-on interval is required.

The transmission of sound waves in liquid-filled catheter tubes used for intravascular blood-pressure recording.

The blood pressure wave-form recorded by a transducer of finite compliance at the end of a liquid-filled tube, is often distorted by acoustic resonance. In most recent publications, e.g.Leraand (1962),Yanov (1963), the theoretical treatment of this problem is based on the dubious asumption that the catheter compliance and the compressibility of the liquid are negligible, and that the system behaves as a simple resonant circuit with one degree of freedom, in which the mass of the fluid, or more correctly its inertance, resonates with the compliance (springiness) of the transducer. In a few cases the published theory does not rest on this assumption. In one article, the catheter has been considered as the π-section of a low-pass filter, in which half the compliance appears across the transducer,Vierhout (1965). This is shown to be quantitatively incorrect, as the effective fraction is one-third and not one-half. In any case the implication that there is a definite cut-off frequency is misleading.A. T. Hansen (1949) has made a more rigorous analysis in which the result is expressed in terms of complex hyperbolic functions, from which it seems difficult to draw conclusions except by numerical evaluation. It has, however, been found possible to simplify Hansen's results. It is shown that the catheter itself may be made incapable of causing resonance. This can be accomplished by a form of impedance matching at the input; this technique only differs from normal telecommunication practice in respect of the ability of the system to operate down to zero frequency and in the deliberate mismatching of the output. In principle the catheter input includes a constriction whose acoustic resistance is capable of absorbing half the pressure of a steepfronted pressure wave at the moment of its application. This loss of signal strength is exactly compensated by the response of the transducer both to the incident and reflected waves at the output, the latter being absorbed on its return to the constriction. This plan not only removes any sharply defined upper limit to the frequency which can be recorded, but also considerably simplifies the equalization problem. Except for minor adjustments, the equalization is independent of catheter length.

Analog inked-trace reader for automatic continuous high-speed multi-channel operation

A high-speed multi-channel transistorized analog system for continuous reconversion of inked traces of EEGs and other bio-electric data to their original form, for recording onto magnetic tape, onto another ink-writer, or for reading directly into a computer, is described. The system, which employs the principle of phase-modulated analog sampling, provides automatic compensation for the width of the inked trace of the original, thereby permitting remarkably faithful reproduction even of steep wave fronts. Use of the system permits computer analysis of EEGs and similar data available only in the form of inked traces, within the limitations of the frequency response of the ink-writers originally employed.

Behavior of thyristors under transient conditions

The capability of gate-triggered thyristors to withstand steep wavefront, high-current pulses (i.e., di/dt capability) is a function of both junction temperature and frequency of operation. Localized internal heating occurs during turn-on and may lead to thermal runaway. The conditions required for this to occur have been determined by destructively testing many devices. The initial conducting area of a thyristor largely determines di/dt capability, which is not necessarily related to the size of the device but is a function of the design of the gate region. Gate drive is very important for determining the di/dt capability of a thyristor having a conventional gate design. Two devices which have been designed to increase the initial conducting area are discussed. One of these devices, if improperly designed, can lose its effectiveness with high gate drive. This characteristic can be studied by observing the reverse recovery current immediately following short forward current pulses.

The measurement of short-duration impulse voltages

A description is given of a very-small-impulse voltage divider which is insulated by compressed gas. The divider was designed for the measurement of steep-front impulse waves, and its errors have been evaluated by the step-response method, using a pressurized sphere gap. It was then used for measuring the volt-time curve of a sphere gap, and the results have been compared with those obtained by others.

Measurements of steep-front impulse waves

THE MEASUREMENT of steep-front impulse waves presents problems seldom encountered in ordinary 1 1/2 × 40 microsecond impulse wave testing. The problem consists of obtaining linearly rising steep-front voltage oscillograms which faithfully reproduced, to a known scale, the voltage wave as seen by the test specimen. Stray or residual divider parameters, as well as the methods used in grounding, shielding, supplying power, and synchronizing the oscilloscope, may introduce spurious responses into the voltage oscillograms.

The response of resistance voltage dividers to steep-front impulse waves

At present there is no generally accepted technique for determining the response of high-voltage dividers to fractional microsecond impulse waves. This paper describes a method which uses a low-voltage cable-type pulse generator and a high-speed oscilloscope as the basic tools. A technique for calibrating the oscilloscope amplifier and the associated input attenuators is described. The effects of such parameters as total divider resistance, divider length, and connecting lead lengths have been investigated. The accuracy and limitations of vertical resistance dividers for measuring steep-front waves are evaluated.

The Analogy between Cochlear Fluid Motion and Formation of Surf on Sloping Beaches

Perilymphatic fluid motion in the cochlea on vibratory stimulation of the stapes creates an interface phenomenon along the cochlear duct, known as the Travelling Bulge (Békésy). Between this event and surf on sloping beaches, although the latter is a surface phenomenon, exist several similarities, which allow for an analogy in principle: wavelength is gradually lessened (“crowding”) and amplitude is built up toward a maximum (position is frequency dependent) beyond which it declines rather steeply; also eddies are formed. Analysis of surf as the more tangible of the two phenomena (especially that of the first crests of a steep wave front arriving at a slope) indicates that surf is caused by interaction of two events: (1) “shallow-water” opposition and (2) reflection. The first one causes a slowdown in wave velocity with subsequent crowding and amplitude buildup; these in turn are responsible for the onset of eddying. Thereafter, energy dissipation is critically increased, causing amplitude to decrease again.—The second (reflection) creates a shearing effect between the terminal phase of one wave (wave of translation) and its successor; thus, by accentuating the eddying and the dissipation of energy, surf is established as a confinement in space of eddying waves.

The Force Exerted by Surface Waves on Piles

The force exerted by unbroken surface waves on a cylindrical object, such asa pile, which extends from the bottom upward above the wave crest, is made upof two components, namely:A drag force proportional to the square of the velocity which may berepresented by a drag coefficient having substantially the same value as forsteady flow, andA virtual mass force proportional to the horizontal component of theaccelerative force exerted on the mass of water displaced by the pile. These relationships follow directly from wave theory and have been confirmedby measurements in the Fluid Mechanics Laboratory of the University ofCalifornia, Berkeley. The maximum force exerted by breakers or incipient breakers is impulsive innature, reaching a value much greater than that produced by unbroken waves butenduring for only a short time interval. This impulsive force represents theultimate development of the accelerative force and is produced by the steepwave front and large horizontal acceleration at the front of a breaker. Thisimpulsive force greatly exceeds the drag force computed from the particlevelocities of the breaker. The reader is cautioned that these preliminary results are applicable only tosingle piles without bracing and are likely to be modified somewhat wheremultiple piles are driven, one within the influence of the other or wheremultiple piles are connected by submerged bracing. This paper is essentially apreliminary report submitted at this time because of the current importance ofwave forces in the design of offshore structures. An extended series ofadditional experiments is planned for the near future. Theoretical Relationships For the sake of simplicity of treatment, the theory will be developed fromthe equations for waves of small amplitude. T.P.2846

Sound Pressure Measurement Equipment for the Range 50 Cycles to 250 kc

This paper describes a newly developed acoustic instrument that is now commerically available for making absolute sound pressure measurements over the frequency range 50 cycles to 250 kc. The microphone standard is only 18″ diameter, and is therefore completely free of diffraction errors throughout the entire audible spectrum to beyond 20 kc. In order to maintain constant phase shift between the generated voltage and the actuating pressure, the vibrating system is stiffness controlled to beyond 250 kc, thus insuring accurate reproduction of pressure wave transients having extremely steep wave fronts. The tiny size of the microphone and its very high acoustic impedance will permit free field measurements throughout the entire audible range without diffraction errors, as well as making easily possible many special acoustic measurements extending well into the ultrasonic region, heretofore very difficult to make. One such application now in progress is the analysis of the sound spectrum from jet engines up to frequencies of 250 kc. A preamplifier and power supply unit makes the equipment readily portable.

Sound Pressure Measurement Equipment for the Range 50 Cycles to 250 kc

This paper describes a newly developed acoustic instrument that is now commercially available for making absolute sound pressure measurements over the frequency range 50 cycles to 250 kc. The microphone standard is only 18″ diameter, and is therefore completely free of diffraction errors throughout the entire audible spectrum to beyond 20 kc. In order to maintain constant phase shift between the generated voltage and the actuating pressure, the vibrating system is stiffness-controlled to beyond 250 kc, thus insuring accurate reproduction of pressure wave transients having extremely steep wave fronts. The tiny size of the microphone and its very high acoustic impedance will permit free field measurements throughout the entire audible range without diffraction errors, as well as making easily possible many special acoustic measurements extending well into the ultrasonic region, heretofore very difficult to make. A preamplifier and power supply unit makes the equipment readily portable.

A Study of the Relative Severity of Steep Front Waves and Chopped Waves on Transformers

A Study of the Relative Severity of Steep Front Waves and Chopped Waves on Transformers

New Series Capacitor Protective Device

A series capacitor is best protected from overvoltage during fault by a gap having low arc drop with no tendency to cut off. In this manner the capacitor is not subjected to repetitive voltage peaks during fault, and high current oscillations in the circuit formed by the capacitor and gap are minimized. A special design of graphite gap with self-centering arc characteristics is described. A new type of by-pass switch is also described for automatically by-passing the gap and series capacitor and removing the by-pass after the fault has cleared. The switch shown provides an inherent time delay on closing thus allowing time for the capacitor to discharge through the gap and avoid damage to the switch contacts. The switch also provides time delay on reopening thus eliminating the necessity for a holding means which has been a problem always with magnetic contactors in this application. The motive power for closing the switch is derived from a sealed bellows using high resistance metal and containing a volatile liquid. The passage of current through the bellows changes the vapor pressure and furnishes the forces required to operate the switch. A device of this type is not subject to damage by steep wave front surges associated with the discharge of the capacitor through the protective gap, nor is it damaged by intermittent line faults.

A Radio-Frequency Device for Detecting the Passage of a Bullet

An unusual application of radio engineering is described in which the reaction of a radio-frequency oscillator to the presence of a metallic projectile in a link-coupled coil is utilized in connection with projectile velocity measurements. In order to obtain the accuracy of signal output required, the circuits are designed for good transient response. In addition, a unique method of differentiating, clipping, and amplifying is utilized in order to obtain a signal with steep wave front when the bullet is at the center of the coil regardless of the weight, shape, or velocity of the bullet. Pictures are included of the equipment and coils used. High-speed pictures of bullets in the tripping position in the coils and oscillograms of circuit voltages verify that circuit operation is as predicted.

High-Voltage D-C Point Discharges

D-c corona discharges from pointed and sharp-edged conductors have been found to give rise to severe radio interference on aircraft under certain precipitation conditions. Laboratory studies, employing a point-to-plane arrangement, have shown that these discharges are greatly influenced not only by voltage and polarity but also by the geometry of the points. Three distinct types of positive and two of negative corona have been found. One of these types, that occurring on sharp, slender points, is essentially common to both polarities and is free from radio interference at all frequencies up to at least several megacycles. Those discharges common to rather bluntly-backed points extend out some distance from the electrodes and are made up, in general, of a steady ion-migration component plus a series, orderly or otherwise, of ionic bursts. The latter phenomena, through an impulse excitation mechanism, give rise to the radio interference. A number of oscillograms were taken with the Duddell-type oscillograph showing the simultaneous current and radio-interference characteristics of the various types of point discharges. These oscillograms, taken with carefully constructed amplifiers, show the steady component of the discharge to be free from radio interference. Each impulsive burst, however, gives rise to a burst of radio output. Cathode-ray oscillograms show these current bursts to be typical double-exponential impulses of very steep wave front, and in general, of short duration. High resistance in the discharge circuit near the ionization point has a suppressing action on the impulses and greatly reduces the accompanying interference.

A cathode-ray oscillograph for the direct measurement of high-voltage transients

The paper describes a high-speed continuously-evacuated cathode-ray oscillograph for the recording of high-voltage transients; the distinctive feature of the instrument is that impulsive voltages of 100 kV to earth may be applied directly to either deflection plate singly, or +100 kV to one and − 100 kV simultaneously to the other, without the use of a potential divider. The reasons for. and advantages accruing from, the use of such an oscillograph are discussed, with particular reference to the distortion inherent in the use of potential dividers. Precautions to be observed in the operation of the high-voltage plates are described, reference being made to the means of producing the high vacuum required in the tube.A circuit producing a delayed high-voltage impulse is shown, and the possibilities of the instrument are demonstrated by a brief investigation of the characteristics of a sphere-gap when sparking over on the front of a steep-fronted wave.

Protection oi rotating A-C machines against traveling wave voltages

PROTECTION of rotating a-c machines against traveling wave voltages divides itself into 2 problems: protection of insulation to ground against impulse overvoltages and protection of the turn insulation against steep wave fronts. The impulse insulation strength of the machine to ground is assumed equal to approximately 2 times the terminal-to-terminal crest voltage (2.12E). The turn insulation strength is given in curve form and varies with machine kva and speed.

Interconnection of Primary Lightning Arrester Ground and the Grounded Neutral of the Secondary Main

This investigation of the relative merits of various possible transformer connections and protective devices was the result of statistical data secured, over a long period of years, by the Commonwealth Edison Company of Chicago regarding the number and types of distribution transformer failures during lightning storms.* It refers to standard, 60 cycle, overhead, power and lighting distribution systems having 4,000-volt, four-wire primaries and three-wire, 230-volt, three-phase power and 115-230-volt lighting secondary mains. Five spans of standard pole line construction were exposed to transient potentials of steep wave front, the latter being induced by the sudden charging of the well insulated artificial clould suspended over the line. The cloud was charged to potentials, up to 150 kv., by means of a surge generator. Measurements of potentials, ranging as high as 40 kv. in some instances which were induced upon various portions of the distribution system were made by means of ionized sphere gaps and the cathode-ray oscillograph. Some of the important conclusions reached as the result of this investigation are: 1. The value of an experimental wood pole distribution line with an insulated artificial cloud charged by means of a surge generator was definitely established for lightning protective investigations involving induced as well as direct stroke potentials. 2. The practicability and economy of studying, by means of such laboratory equipment, the operation of various transformer, lightning arrester and ground connections, when exposed to surges approximating those of lightning, were demonstrated. 3.