Finite Rise Time Research Articles

The response of a microwave multipolar bucket plasma to a high-voltage pulse with finite rise time

A collisional model that describes the response of a microwave multipolar bucket plasma to a high-voltage pulse with finite risetime has been developed for plasma immersion ion implantation (PIII). The agreement between this model and the measurements of the sheath position and target current in a 100 mtorr helium plasma is found to be much improved when the risetime of the pulse and the ion energy distribution during the PIII process is considered. >

Model of plasma immersion ion implantation for voltage pulses with finite rise and fall times

In plasma immersion ion implantation, a target is immersed in a plasma and a series of negative, high-voltage pulses are applied to implant ions into the target. An approximate analytical model in one-dimensional planar geometry is developed to determine the time-varying implantation current, the total dose, and the energy distribution of the implanted ions for a voltage pulse with finite rise and fall times. Scaling rules are presented for the implanted current and energy distribution with respect to plasma density, peak applied voltage, and ion mass. Comparisons with numerical simulations are used to demonstrate that the accuracy of the model is well characterized by a single parameter: the ratio of the ion flight time to the pulse rise time.

Phase transients in NMR probe circuits

NMR pulse transients for a tuned and matched probe circuit excited by a voltage source are calculated for the case of exact match and overcoupled or mismatched conditions. The consequences of finite rise and fall times on the pulse envelope are also explored. The quadrature transients calculated from the model are compared with experimental observations made on a breadboard probe circuit.

Molecular relaxation is insufficient to explain the shock structure and rise times of sonic booms; turbulence is apparently important

The authors have been recently examining some sonic‐boom waveforms that were recorded during overflights by the Air Force and that have become available to NASA and its contractors. The quality of the digitized data and the supporting meteorological data was such that one could test the applicability of molecular relaxation theories. In the late sixties it had been supposed that the finite rise times of sonic booms was attributable to atmospheric turbulence, but it was later pointed out that the first estimates of rise times in the absence of turbulence had neglected the vibrational relaxation of nitrogen molecules. Bass et al. [J. Acoust. Soc. Am. 74, 1514–1517 (1983)] have demonstrated that molecular relaxation definitely gives the correct order of magnitude of the observed rise times. However, the Air Force data in conjunction with the recent steady‐state shock profile model theory of Kang and Pierce give the first opportunity to make a detailed quantitative assessment of the molecular relaxation hypothesis. The agreement of theory with experiment in some cases is remarkably excellent, but in the preponderance of cases the rise of the shock is slower and the rise time is longer, typically by factors of the order of 2 to 3. [Work supported by NASA‐LRC and by the William E. Leonhard endowment to Penn State Univ.]

Fourier transforms and effective rise times of sonic booms propagating through a relaxing atmosphere

Sharp impulsive sounds, such as sonic booms, typically have sudden pressure jumps (shocks) that are principal contributors to their perceived annoyance. Rise time, the ostensible time over which the sudden pressure rise occurs, is somewhat of an inadequate descriptor because not all profiles are similar and because two profiles with the same over‐pressure and rise time may seem markedly different in perceived loudness. A previously developed numerical procedure determines the detailed pressure versus time profile during the interval that the leading shock nominally occurs, taking into account molecular relaxation effects, and the Fourier transform is determined using the known asymptotic behavior of the waveform profile immediately preceding and following the shock. The proposed definition of an effective rise time recognizes that the A‐weighted sound exposure of a waveform is a good descriptor of perceived loudness and that Fourier transforms of pressure waveforms with shocks with finite rise times tend to fall off as the inverse square of increasing frequency as one over the square of the frequency. Such considerations lead to a definition of rise time that is inversely proportional to the square root of the A‐weighted sound exposure of that portion of the waveform which includes the shock. The basis for this definition is explained, the constant is evaluated, and examples of atmospheric sonic booms are discussed. [Work supported by NASA‐LRC and by the William E. Leonhard endowment to Penn State Univ. The author acknowledges the advice of A. D. Pierce.]

Dispersion characteristics of square pulse with finite rise time in single, tapered, and coupled microstrip lines

The distortion of an electrical pulse, with finite risetime (quadratic-linear-quadratic transition) caused by dispersion as it propagates along a uniform microstrip, a tapered microstrip and a coupled pair of microstrips is investigated. Closed-form analysis equations for single and coupled microstrips are used to find the frequency-dependent phase velocities. Results are presented for two different taper profiles: exponential and triangular distributions. It is concluded that the optimization of the profile will provide the least pulse distortion.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Finite rise time step strain modeling of nearly monodisperse polymer melts and solutions

The step shear strain experiment is one of the fundamental transient tests used to characterize the rheology of viscoelastic polymer melts and solutions. Many melts and solutions exhibit homogeneous deformation and stress relaxation; in these cases the transient dynamics can be modeled by completely ignoring momentum effects and imposing singular kinematics. Recently, however, it has been observed that there are certain classes of nearly monodisperse melts and solutions that exhibit anomalous nonhomogeneous deformation and stress relaxation (Morrison and Larson (1990), Larson, Khan, and Raju (1988), Vrentas and Graessley (1982), and Osaki and Kurata (1980)). We demonstrate that, for these classes, a finite rise time must be incorporated, some source of inhomogeneity must be present, and a small amount of added Newtonian viscosity is necessary. We examine five nonlinear and quasilinear models; the Johnson-Segalman, Phan Thien Tanner, Giesekus, White-Metzner, and Larson models. We determine which mathematical features of the models are necessary and/or sufficient to describe the observed experimental behavior.

Flow to a heated borehole in porous, thermoelastic rock: Analysis

Exact solutions are obtained for fluid flow induced by the heating of a borehole. The rock is modeled as a fluid‐saturated, porous, thermoelastic medium. The temperature and pore pressure fields are governed by a pair of diffusion equations, which are coupled through a source term in the pressure equation proportional to the temperature rate. The pressure profile exhibits a maximum that grows in magnitude and propagates away from the borehole. For a constant heat flux applied as an instantaneous step, the fluid flux to the borehole takes a finite initial value, and decays monotonically. When the heat flux exhibits a finite rise time, the fluid flux is initially zero, rises to a maximum, and then decays. At late time, the inverse of the fluid flux is linear in ln t; this observation can be exploited to estimate the permeability and fluid diffusivity of low‐permeability rock. Sample calculations are shown for Westerly granite.

Nonlinear Luminescence Spectroscopy of Excitons in GaAs-AlAs Quantum Wells

We present the detailed experimental results of the time-resolved nonlinear luminescence of excitons in undoped GaAs-AlAs quantum wells. The observed nonlinearity results from the saturation in luminescence originated from the phase space filling and exchange effects of carriers. In some temporal profiles of nonlinear luminescence, anomalous anti-correlation profile has been observed. The origin of anti-correlation is ascribed to be the finite rise time of the exciton population at the luminescent tail state in the exciton band.

Simplified dynamic analysis of rigid-plastic beams

A new analytical procedure is developed to predict the dynamic response of axially restrained beams to intense pulse loads. The beams are assumed to have doubly symmetric cross-sections and to obey a rigid-plastic material law. The moment-axial force interaction relation for the beam section is approximated by a straight line. This uncouples the response into two distinct phases—an initial bending-only phase involving plastic hinge mechanisms, followed by a plastic string phase. Both these phases are governed by linear differential equations, and hence the response to arbitrary load pulses may be solved in closed form. The results for beams subjected to a rectangular load pulse compare very well with those from more exact solutions. Finally, results are presented for an arbitrary cross-section beam subjected to a triangular shaped pulse with a finite rise time. The effect of rise time is found to be very small for rise times less than 0.3 of the total pulse length.

Thermally induced degenerate four-wave mixing

Time-dependent aspects of thermally stimulated degenerate four-wave mixing (DFWM) in absorbing liquid solutions have been theoretically investigated through a coupled electromagnetic-hydrodynamic theory originally formulated to study stimulated scattering processes. The various time scales involved in the interaction (including those characteristic of acoustic modes and thermalization effects) are identified and relevant laser and media parametrical relations are sorted out. Suitable approximation regimes are then outlined, corresponding to specific experimental situations of interest and allowing for relatively simple and tractable analytic relations to be derived. In particular, the effects of finite rise time of thermalization were studied and found to lead to a possibly strong angular dependence in the conjugate reflectivity. Acoustic modes and their influence on the process efficiency were also investigated. The calculations culminate in a set of guidelines for optimizing conjugation efficiencies, through judicious choice of dye-solvent combinations, read pump time delays, experimental arrangements, and laser pulse parameters.

Evidence that the variable fluorescence in Chlorella is recombination luminescence

The fluorescence lifetime of oxygen-forming photosynthetic systems as a function of closed traps has been studied by several groups using light and poisons (usually 3-(3,4-dichlorophenyl)-1,1-dimethylurea (DCMU)) to fix the closed trap state during the experiment. These measurements have now been carried out using light alone, by means of pump and probe laser pulses and a very efficient fast photomultiplier-digitizing system. It is found that the absolute amplitude of fast fluorescence (mean ψ, approx. 0.3 ns) remains constant until over half the traps are filled. The amplitude of the slow fluorescence ( τ ≈ 1.2 ns) increases with pump energy, and its response is best fit with a lag or finite risetime of approx. 200 ps. This novel result is consistent with the hypothesis that the slow component of the fluorescence is actually recombination luminescence in the trap. Thus, the full trapping time, i.e., the time to form the P +I − state from an excitation in the O 2 photosystem, is relatively slow.

Effects of enhanced heating by surface oxides on arc cathodes

Heat conduction into and production within a metallic electrode can be affected drastically by the presence of thin surface oxides. Analytic expressions are derived for the temperature distribution in time and depth for a stratified oxide/metal cathode subjected to a pulsed DC arc with finite risetime. Results for cathode materials representing a wide spectrum of metallic and oxide properties indicate that oxides 50–250 Å thick can reduce premelt conditions at the electrode surface to nanosecond time scales for even modest current densities during the formative stage of arcs several millimetres long in atmospheric pressure air.

Relative contribution of carrier diffusion and spontaneous emission to the strength and damping of relaxation oscillations in InGaAsP/InP lasers

The damping and strength of relaxation oscillations in BH long-wavelength lasers have been investigated. In addition to previously published papers, the relative contribution of carrier diffusion effects and spontaneous emission is analysed. At moderate pumping rates, the calculated damping factor, using singlemode rate equations and a constant spontaneous carrier lifetime, is found to be in good agreement with experimental results if the finite rise time of the pulse generator is introduced. It is also shown that the overshoot depends mainly on the spontaneous emission factor. However, in general, for the calculated spontaneous emission factor, the predicted overshoot is greater than the measured one. Possible reasons for this disagreement are discussed.

Three-Dimensional Analysis of Axisymmetric Transient Waves in Hollow Elastic Cylinders

The axially symmetric problem of a semi-infinite, hollow, linear-elastic circular cylinder with traction-free lateral surfaces initially at rest and subjected to transient end loadings is solved using three-dimensional theory. Two cases are treated: an axial pressure applied to a radially clamped end and a prescribed axial velocity applied to an end that is free from shear stress. A double integral transform technique is used, and asymptotic solutions valid at large distances from the end are given for two types of time variation of the end loadings: step function and finite rise time function. A necessary condition for the validity of the asymptotic result is given.

On the study of the dynamical behaviour of dielectrics by thermal-noise correlation analysis

Relations are given for the complex permittivity ϵ(ω) and dielectric response function ϕ( t) of an arbitrary-type dispersion dielectric through the autocorrelation function (ACF) of the thermal-noise voltage existing across the terminals of a measuring cell with the sample under study. Experimentally observed ACFs and the resulting ϵ(ω) and ϕ( t) for liquid crystalline 4′- n-hexyl-4-cyanobiphenyl (6CB) are presented. A method for taking to account a finite risetime of the measuring amplifier's transient characteristic, and an algorithm for the numerical determination of ϕ( t) by solving a convolution-type integral equation are developed.

Techniques of flash radiometry

We analyze in detail flash radiometry techniques for the remote sensing of spectroscopic and physical properties of thin condensed matter samples. Such techniques rely on the transient infrared radiation from the sample heated by a short-duration pulsed radiation. Exact analytical solutions for the conventional transmission radiometry technique (in which the excitation source and the infrared detector are on opposite sides of the sample) as well as the new backscattering radiometry technique (in which the excitation source and the detector are on the same side of the sample) are presented with the effect of heat loss neglected. The analysis allows the determination of the thermal diffusivity or thickness, as well as the absorption coefficients at the excitation wavelength and at the detecting wavelength of the sample from the experimental radiometry profile. The effects of excitation pulse duration and finite rise time of the detection system are discussed. Experiments with pulsed radiometry measurements on thin-film samples are performed to verify some of these theoretical predictions. Radiation loss and lateral heat diffusion loss are shown to be negligible for thin-film samples.

Radiation From Expanding Circular Dislocation Loops and Elastic Precursor Decay

The solution is given for a circular dislocation loop that instantaneously begins to expand by gliding in its plane at constant velocity. The material is assumed to be elastic and isotropic. The solution, expressed as an integral over the loop and over previous times, is evaluated explicitly near the wavefront. This wavefront solution is used to derive an expression for the decay in amplitude of an elastic plane wave propagating in the direction perpendicular to the plane of the loop due to the radiation of elastic waves from the expanding loops. By superimposing the effects of many loops set in motion as the plane wavefront passes, a relation is derived for the decay of the front of the plane wave. This precursor decay relation is found to be the same as obtained previously for infinitely long, straight dislocations based on consideration of either elastic waves radiated from discrete dislocations or energy dissipated in an elastic/viscoplastic continuum model of the material. Thus, dislocation line curvature can apparently be regarded as unimportant in the attenuation of the amplitude of the wavefront. Because detectors have finite rise times, measured precursor amplitudes are indicative of wave amplitudes at small but finite times Δt after the wavefront arrives. Evaluation of the effects of dislocation line curvature on wave amplitudes behind the wavefront requires the consideration of higher order terms in Δt which are neglected in the present analysis.

Error Analysis of the Potential and Voltage Step Relaxation Techniques for the Measurement of Kinetics of Electrode Reactions

An error analysis of the potential and voltage step relaxation techniques is presented. For this error analysis, applicability of six data‐evaluation methods, ranging from simple graphical analysis to computer curve fitting, is investigated. The results are presented in applicability diagrams in terms of three characteristic times of the electrode reaction: , the time constant of the double layer capacitance—reaction resistance system; , the time constant of the diffusion impedance—reaction resistance system; and , the time constant of the double layer capacitance—solution resistance system. The error analysis takes into consideration (i) all random errors caused by the measurement of potential, solution resistance, and current density relaxation, and (ii) systematic errors caused by the mathematical approximations used in the data‐evaluation methods, the neglect of the finite rise time of the potentiostat, and the neglect of the effect of the uncompensated solution resistance. It is shown that a computer curve‐fitting data‐evaluation method, which eliminates the systematic errors, can extend the field of applicability to reactions at least five times faster than those measurable with the simplest graphical method, and, under the best conditions, the field can be extended to reactions faster by as much as two orders of magnitude. Under identical conditions, the limitations of the voltage step technique are the same as those of the potential step technique, but the practically achievable values will usually be larger for the voltage step technique and, consequently, the field of applicability will be decreased.

Performance of a Pseudorandom Binary Phase Code with Errors and Doppler-Shifted CW

The effects that various code imperfections have on the peak of the mainlobe and on the time sidelobes of the compressed coded signal are described. The imperfections considered are finite pulse rise time, timing errors, code integration mismatch, and Doppler shift of the coded signal.