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DOE OSTI2021

A White Paper on Design and Fabrication of SRF Deflecting Cavities for Elletra-2

Synchrotron Trieste (ST) operates an X-ray light source Elettra and plans to upgrade it to a low-emittance high-brightness X-ray source Elettra-2.0 based on a multi-bend achromat lattice. There is also a significant interest among Elettra users to pursue time-resolved studies of matter choosing the appropriate X-ray pulse duration in the range from 20 picoseconds to a few picoseconds FWHM. Recently, X. Huang (SLAC) and A. Zholents (ANL) performed a study sponsored by ST and proposed modifications to the Elettra-2.0 design that will allow production of picosecond x-ray pulses on many beamlines. They showed that two radio frequency deflecting cavities with slightly different frequencies can be installed in the ring’s sector 8 and produce time-dependent orbit deflection to a few dedicated electron bunches without affecting other regular bunches. These special bunches produce X-ray pulses in which transverse position or angle, or both, are correlated with time. The short X-ray pulse is then obtained by using a narrow slit positioned downstream in the beamline. Many technical details of the proposed modification to Elettra-2.0 are discussed in the supplemental report. We present here the design of a multicell superconducting deflecting cavity for the purpose of the ST Short Pulse X-ray (SPX) project.

43 PARTICLE ACCELERATORS↗

NASA NTRS2013

Semi-Supervised Eigenbasis Novelty Detection

Recent discoveries in high-time-resolution radio astronomy data have focused attention on a new class of events. Fast transients are rare pulses of radio frequency energy lasting from microseconds to seconds that might be produced by a variety of exotic astrophysical phenomena. For example, X-ray bursts, neutron stars, and active galactic nuclei are all possible sources of short-duration, transient radio signals. It is difficult to anticipate where such signals might appear, and they are most commonly discovered through analysis of high-time- resolution data that had been collected for other purposes. Transients are often faint and difficult to detect, so improved detection algorithms can directly benefit the science yield of all such commensal monitoring. A new detection algorithm learns a low-dimensional linear manifold for describing the normal data. High reconstruction error indicates a novel signal that does not match the patterns of normal data. One unsupervised portion of the manifold model adapts its representation in response to recent data. A second supervised portion of the model is made of a basis trained in advance using labeled examples of RFI; this prevents false positives due to these events. For a linear model, an orthonormalization operation is used to combine these bases prior to the anomaly detection decision. Another novel aspect of the approach lies in combining basis vectors learned in an unsupervised, online fashion from the data stream with supervised basis vectors learned in advance from known examples of false alarms. Adaptive, data-driven detection is achieved that is also informed by existing domain knowledge about signals that may be statistically anomalous, but are not interesting and should therefore be ignored. The method was evaluated using data from the Parkes Multibeam Survey. This data set was originally collected to search for pulsars, which are astronomical sources that emit radio pulses at regular periods. However, several non-pulsar anomalies have recently been discovered in this dataset, making it a compelling test case. By explicitly filtering known false alarm patterns, the approach yields significantly better performance than current transient detection methods.

Wagstaff, Kiri L.↗

DOE OSTI2013

Laser wakefield generated X-ray probe for femtosecond time-resolved measurements of ionization states of warm dense aluminum

We have developed a laser wakefield generated X-ray probe to directly measure the temporal evolution of the ionization states in warm dense aluminum by means of absorption spectroscopy. As a promising alternative to the free electron excited X-ray sources, Betatron X-ray radiation, with femtosecond pulse duration, provides a new technique to diagnose femtosecond to picosecond transitions in the atomic structure. The X-ray probe system consists of an adjustable Kirkpatrick-Baez (KB) microscope for focusing the Betatron emission to a small probe spot on the sample being measured, and a flat Potassium Acid Phthalate Bragg crystal spectrometer to measure the transmitted X-ray spectrum in the region of the aluminum K-edge absorption lines. An X-ray focal spot size of around 50 μm was achieved after reflection from the platinum-coated 10-cm-long KB microscope mirrors. Shot to shot positioning stability of the Betatron radiation was measured resulting in an rms shot to shot variation in spatial pointing on the sample of 16 μm. The entire probe setup had a spectral resolution of ∼1.5 eV, a detection bandwidth of ∼24 eV, and an overall photon throughput efficiency of the order of 10{sup −5}. Approximately 10 photons were detected by the X-ray CCD per laser shot within the spectrally resolved detection band. Thus, it is expected that hundreds of shots will be required per absorption spectrum to clearly observe the K-shell absorption features expected from the ionization states of the warm dense aluminum.

36 MATERIALS SCIENCE↗

DOE OSTI2016

A high-current rail-type gas switch with preionization by an additional corona discharge

The characteristics of a high-current rail-type gas switch with preionization of the gas (air) in a spark gap by an additional corona discharge are investigated. The experiments were performed in a voltage range of 10–45 kV using a two-electrode switch consisting of two cylindrical electrodes with a diameter of 22 mm and a length of 100 mm and a set of laterally located corona-discharge needles. The requirements for the position and size of the needles are defined for which a corona discharge is ignited before a breakdown of the main gap and does not change to a sparking form, and the entire length of the rail electrodes is efficiently used. The fulfillment of these requirements ensures stable operation of the switch with a small variation of the pulse breakdown voltage, which is not more than 1% for a fixed voltage-pulse rise time in the range from 150 ns to 3.5 μs. A short delay time of the switch breakdown makes it possible to control the two-electrode switch by an overvoltage pulse of nanosecond duration.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

DOE OSTI2024

Focussing Protons from a Kilojoule Laser for Intense Beam Heating Using Proximal Target Structures

Proton beams driven by chirped pulse amplified lasers have multi-picosecond duration and can isochorically and volumetrically heat material samples, potentially providing an approach for creating samples of warm dense matter with conditions not present on Earth. Envisioned on a larger scale, they could heat fusion fuel to achieve ignition. We have shown in an experiment that a kilojoule-class, multi-picosecond short pulse laser is particularly effective for heating materials. The proton beam can be focussed via target design to achieve exceptionally high flux, important for the applications mentioned. The laser irradiated spherically curved diamond-like-carbon targets with intensity 4×10 18 W/cm 2 , producing proton beams with 3MeV slope temperature. A Cu witness foil was positioned behind the curved target, and the gap between was either empty or spanned with a structure. With a structured target, the total emission of Cu Kα fluorescence was increased 18 fold and the emission profile was consistent with a tightly focussed beam. Transverse proton radiography probed the target with ps order temporal and 10 μm spatial resolution, revealing the fast-acting focussing electric field. Complementary particle-in-cell simulations show how the structures funnel protons to the tight focus. The beam of protons and neutralizing electrons induce the bright Kα emission observed and heat the Cu to 100eV.

47 OTHER INSTRUMENTATION↗

DOE OSTI2020

Focussing Protons from a Kilojoule Laser for Intense Beam Heating using Proximal Target Structures

Proton beams driven by chirped pulse amplified lasers have multi-picosecond duration and can isochorically and volumetrically heat material samples, potentially providing an approach for creating samples of warm dense matter with conditions not present on Earth. Envisioned on a larger scale, they could heat fusion fuel to achieve ignition. We have shown in an experiment that a kilojoule-class, multi-picosecond short pulse laser is particularly effective for heating materials. The proton beam can be focussed via target design to achieve exceptionally high flux, important for the applications mentioned. The laser irradiated spherically curved diamond-like-carbon targets with intensity 4 × 10 18 W/cm 2 , producing proton beams with 3 MeV slope temperature. A Cu witness foil was positioned behind the curved target, and the gap between was either empty or spanned with a structure. With a structured target, the total emission of Cu Kα fluorescence was increased 18 fold and the emission profile was consistent with a tightly focussed beam. Transverse proton radiography probed the target with ps order temporal and 10 μm spatial resolution, revealing the fast-acting focussing electric field. Complementary particle-in-cell simulations show how the structures funnel protons to the tight focus. Here, the beam of protons and neutralizing electrons induce the bright Kα emission observed and heat the Cu to 100 eV.

47 OTHER INSTRUMENTATION↗

DOE OSTI2021

A dimensionality reduction algorithm for mapping tokamak operational regimes using a variational autoencoder (VAE) neural network

Abstract A variational autoencoder (VAE) is a type of unsupervised neural network which is able to learn meaningful data representations in a reduced dimensional space. We present an application of VAE in identifying the operational stability boundary of tokamak plasma discharges. This model was implemented using a dataset of over 3000 discharges from the high beta tokamak-extended pulse (HBT-EP) device. We found the VAE model to be capable of forming a continuous low-dimensional operational space map and identifying the operational boundaries using a specified warning time window. By projecting the operational parameters onto the same reduced space, this provides an intuitive way for the machine operator or an automated control system to perform disruption avoidance using a relevant control actuator as a discharge approaches a boundary. Pre-programmed GPU control experiments were conducted to demonstrate this control technique using HBT-EP’s saddle control coils as a horizontal position actuator, showing the ability to avoid the oncoming disruptive event and extend the duration of the discharge.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

NASA NTRS1991

Bandwidth requirements for direct detection optical communication receivers with PPM signaling

The performance of a direct detection optical communication receiver for pulse position modulation (PPM) signal formats which contains an avalanche photodiode photodetector is calculated as a function of the parameters which characterize a raised cosine filter used in the receiver. It is shown that the performance penalty of this receiver relative to that of an optimal receiver which contains an integrator and assumes a perfectly rectangular PPM pulse shape is less than 1 dB at a receiver bit error rate of 10 exp -6. The advantage of the raised cosine filter is that the electrical bandwidth required is no more than one-half that of the integrator, that is, 1/tau as opposed to 2/tau where tau is the PPM time slot duration.

Davidson, Frederic M.↗

NASA NTRS2000

VCL Laser Altimeter Surface Return Expected Geolocation Performance

The Vegetation Canopy Lidar (VCL) mission, expected to launch in the spring of 2002, will carry a unique Multi-Beam Laser Altimeter (MBLA) instrument designed to observe vegetative canopy structure for a nominal mission duration of 2 years. The VCL MBLA is a three-beam instrument where each laser is capable of producing returns with 30-m along-track spacing and 25-m-diameter footprints. Identifying the precise location of the point on the Earth's surface from which the laser energy reflects is a critical issue in the validation and application of the data. The resultant geolocation accuracy is dependent on the performance of many components of the VCL system including: laser pulse round trip travel time observation to surface, navigation tracking data, attitude determination system data, timing, laser pointing and body orientation stability, knowledge of instrument and navigation tracking point positions, media and geophysical corrections. Additionally, it is critical to calibrate on-orbit instrument parameters including pointing and range corrections. The geolocation and calibration methodology and algorithms will be summarized. A detailed geolocation error analysis identifying the contributions from each system component, along with the resultant expected geolocation accuracy, will be presented. A brief discussion of the operational geolocation process will also be presented. Science and data validation implications from geolocation performance will be summarized.

Luthcke, S. B.↗

DOE OSTI2021

Thermonuclear neutron emission from a sheared-flow stabilized Z-pinch

We report the fusion Z-pinch experiment (FuZE) is a sheared-flow stabilized Z-pinch designed to study the effects of flow stabilization on deuterium plasmas with densities and temperatures high enough to drive nuclear fusion reactions. Results from FuZE show high pinch currents and neutron emission durations thousands of times longer than instability growth times. While these results are consistent with thermonuclear neutron emission, energetically resolved neutron measurements are a stronger constraint on the origin of the fusion production. This stems from the strong anisotropy in energy created in beam-target fusion, compared to the relatively isotropic emission in thermonuclear fusion. In dense Z-pinch plasmas, a potential and undesirable cause of beam-target fusion reactions is the presence of fast-growing, “sausage” instabilities. This work introduces a new method for characterizing beam instabilities by recording individual neutron interactions in plastic scintillator detectors positioned at two different angles around the device chamber. Histograms of the pulse-integral spectra from the two locations are compared using detailed Monte Carlo simulations. These models infer the deuteron beam energy based on differences in the measured neutron spectra at the two angles, thereby discriminating beam-target from thermonuclear production. An analysis of neutron emission profiles from FuZE precludes the presence of deuteron beams with energies greater than 4.65 keV with a statistical uncertainty of 4.15 keV and a systematic uncertainty of 0.53 keV. This analysis demonstrates that axial, beam-target fusion reactions are not the dominant source of neutron emission from FuZE. These data are promising for scaling FuZE up to fusion reactor conditions.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2014

Ions Beams and Ferroelectric Plasma Sources

Near-perfect space-charge neutralization is required for the transverse compression of high perveance ion beams for ion-beam-driven warm dense matter experiments, such as the Neutralized Drift Compression eXperiment (NDCX). Neutralization can be accomplished by introducing a plasma in the beam path, which provides free electrons that compensate the positive space charge of the ion beam. In this thesis, charge neutralization of a 40~keV, perveance-dominated Ar$^+$ beam by a Ferroelectric Plasma Source (FEPS) is investigated. First, the parameters of the ion beam, such as divergence due to the extraction optics, charge neutralization fraction, and emittance were measured. The ion beam was propagated through the FEPS plasma, and the effects of charge neutralization were inferred from time-resolved measurements of the transverse beam profile. In addition, the dependence of FEPS plasma parameters on the configuration of the driving pulser circuit was studied to optimize pulser design. An ion accelerator was constructed that produced a 30-50~keV Ar$^+$ beam with pulse duration $<$300~$\mu$s and dimensionless perveance $Q$ up to 8$\times$10$^{-4}$. Transverse profile measurements 33~cm downstream of the ion source showed that the dependence of beam radius on $Q$ was consistent with space charge expansion. It was concluded that the beam was perveance-dominated with a charge neutralization fraction of approximately zero in the absence of neutralizing plasma. Since beam expansion occurred primarily due to space charge, the decrease in effective perveance due to neutralization by FEPS plasma can be inferred from the reduction in beam radius. Results on propagation of the ion beam through FEPS plasma demonstrate that after the FEPS is triggered, the beam radius decreases to its neutralized value in about 5~$\mu$s. The duration of neutralization was about 10~$\mu$s at a charging voltage $V_{FEPS}$~=~5.5~kV and 35~$\mu$s at $V_{FEPS}$~=~6.5~kV. With $V_{FEPS}$~=~6.5~kV, the transverse current density profile 33~cm downstream of the source had a Gaussian shape with $x_{rms}$=5~mm, which corresponds to a half-angle divergence of 0.87$^\circ$. The measurements show that near-perfect charge neutralization with FEPS can be attained. No loss of ion beam current was detected, indicating the absence of a neutral cloud in the region of beam propagation, which would cause beam loss to charge exchange collisions. This provides evidence in favor of using FEPS in a future Heavy Ion Fusion accelerator. The FEPS discharge was investigated based on current-voltage measurements in the pulser circuit. Different values of series resistance and storage capacitance in the pulser circuit were used. The charged particle current emitted by the FEPS into vacuum was measured from the difference in forward and return currents in the driving circuit. It was found that FEPS is an emitter of negative charge, and that electron current emission begins approximately 0.5~$\mu$s after the fast-rising high voltage pulse is applied and lasts for tens of $\mu$s. The value of the series resistance in the pulser circuit was varied to change the rise time of the voltage pulse; plasma density was expected to decrease with increasing values of resistance. However, the data showed that changing the resistance had no significant effect. The average charge emitted per shot depends strongly on the value of the storage capacitance. Lowering the capacitance from 141~nF to 47~nF resulted in a near-complete shut-off of charge emission, although the amplitude of the applied voltage pulse was as high, and rise time as short, as when high-density plasma was produced. Increasing the capacitance from 141~nF to 235~nF increased the average charge emitted per shot by a factor of$~$2.

ferroelectric plasma source↗

DOE OSTI2017

Measurements of Long-range Electronic Correlations During Femtosecond Diffraction Experiments Performed on Nanocrystals of Buckminsterfullerene

The precise details of the interaction of intense X-ray pulses with matter are a topic of intense interest to researchers attempting to interpret the results of femtosecond X-ray free electron laser (XFEL) experiments. An increasing number of experimental observations have shown that although nuclear motion can be negligible, given a short enough incident pulse duration, electronic motion cannot be ignored. The current and widely accepted models assume that although electrons undergo dynamics driven by interaction with the pulse, their motion could largely be considered 'random'. This would then allow the supposedly incoherent contribution from the electronic motion to be treated as a continuous background signal and thus ignored. The original aim of our experiment was to precisely measure the change in intensity of individual Bragg peaks, due to X-ray induced electronic damage in a model system, crystalline C 60 . Contrary to this expectation, we observed that at the highest X-ray intensities, the electron dynamics in C 60 were in fact highly correlated, and over sufficiently long distances that the positions of the Bragg reflections are significantly altered. Our paper describes in detail the methods and protocols used for these experiments, which were conducted both at the Linac Coherent Light Source (LCLS) and the Australian Synchrotron (AS) as well as the crystallographic approaches used to analyse the data.

43 PARTICLE ACCELERATORS↗

DOE OSTI2023

Time-domain Brillouin scattering theory for probe light and acoustic beams propagating at an angle and acousto-optic interaction at material interfaces

A theory has been developed to interpret time-domain Brillouin scattering (TDBS) experiments involving coherent acoustic pulse (CAP) and light pulse beams propagating at an angle to each other. It predicts the influence of the directivity pattern of their acousto-optic interaction on TDBS signals when heterodyne detection of acoustically scattered light is in backward direction to incident light. The theory reveals relationships between the carrier frequency, amplitude and duration of acoustically induced ”wave packets” in light transient reflectivity signals, and factors such as CAP duration, widths of light and sound beams, and their interaction angle. It describes the transient dynamics of these wave packets when the light and CAP encounter material interfaces, and how the light scattering by the incident CAP transforms into scattering by the reflected and transmitted CAPs. The theory suggests that single-point TDBS experiments can determine not only depth positions of buried interfaces but also their local inclinations/orientations.

42 ENGINEERING↗

DOE OSTI2023

Characteristics of upward-connecting-leader current leading to attachment in downward negative cloud-to-ground lightning strokes

For this work, we analyzed currents associated with upward connecting leaders (UCLs) initiated from the Kennedy Space Center Industrial Area Tower in two negative cloud-to-ground strokes that struck the tower. One stroke was also recorded using a high-speed video camera located 760 m from the KSC IAT. The NLDN-reported peak currents for the two strokes were – 31.7 and – 98.5 kA. During the UCL development phase the current waveforms exhibited a monotonically (quasi-exponentially) increasing “background” current overlaid with 10-μs scale pulses with a median amplitude of 51.1 A. The UCL current durations for the two strokes were 1039 and 449 μs, respectively. During the pre-attachment processes (UCL and slow front) the total negative charge effectively transferred to ground were 70.2 and 55 mC, respectively. For the stroke captured on high-speed video, the average line-charge-density for the 109-m long UCL was found to be 0.5 mC/m. The average UCL 2-D speed was 2.4 × 10 5 m/s, and it was observed to accelerate toward the downward leader prior to attachment. We observed that UCL-pulse amplitudes are larger, background currents are higher, and interpulse intervals are shorter at later times during UCLs, which can be attributed to the intensification of the local electric field due to the approaching downward negative leader. The median positive charge injected into the UCL by a pulse was 297 μC. The UCL associated with the higher peak-current stroke produced the highest injected pulse-charge values about three times sooner during its development, likely due to the 2–2.7 times faster average downward leader vertical speeds.

54 ENVIRONMENTAL SCIENCES↗

NASA NTRS2008

Mitigating Photon Jitter in Optical PPM Communication

A theoretical analysis of photon-arrival jitter in an optical pulse-position-modulation (PPM) communication channel has been performed, and now constitutes the basis of a methodology for designing receivers to compensate so that errors attributable to photon-arrival jitter would be minimized or nearly minimized. Photon-arrival jitter is an uncertainty in the estimated time of arrival of a photon relative to the boundaries of a PPM time slot. Photon-arrival jitter is attributable to two main causes: (1) receiver synchronization error [error in the receiver operation of partitioning time into PPM slots] and (2) random delay between the time of arrival of a photon at a detector and the generation, by the detector circuitry, of a pulse in response to the photon. For channels with sufficiently long time slots, photon-arrival jitter is negligible. However, as durations of PPM time slots are reduced in efforts to increase throughputs of optical PPM communication channels, photon-arrival jitter becomes a significant source of error, leading to significant degradation of performance if not taken into account in design. For the purpose of the analysis, a receiver was assumed to operate in a photon- starved regime, in which photon counts follow a Poisson distribution. The analysis included derivation of exact equations for symbol likelihoods in the presence of photon-arrival jitter. These equations describe what is well known in the art as a matched filter for a channel containing Gaussian noise. These equations would yield an optimum receiver if they could be implemented in practice. Because the exact equations may be too complex to implement in practice, approximations that would yield suboptimal receivers were also derived.

Moision, Bruce↗

NASA NTRS1993

The Compton Gamma Ray Observatory

The Arthur Holly Compton Gamma Ray Observatory (Compton) was launched by the Space Shuttle Atlantis on 5 April 1991. The spacecraft and instruments are in good health and returning exciting results. The mission provides nearly six orders of magnitude in spectral coverage, from 30 keV to 30 GeV, with sensitivity over the entire range an order of magnitude better than that of previous observations. The 16,000 kilogram observatory contains four instruments on a stabilized platform. The mission began normal operations on 16 May 1991 and is now over half-way through a full-sky survey. The mission duration is expected to be from six to ten years. A Science Support Center has been established at Goddard Space Flight Center for the purpose of supporting a vigorous Guest Investigator Program. New scientific results to date include: (1) the establishment of the isotropy, combined with spatial inhomogeneity, of the distribution of gamma-ray bursts in the sky; (2) the discovery of intense high energy (100 MeV) gamma-ray emission from 3C 279 and other quasars and BL Lac objects, making these the most distant and luminous gamma-ray sources ever detected; (3) one of the first images of a gamma-ray burst; (4) the observation of intense nuclear and position-annihilation gamma-ray lines and neutrons from several large solar flares; and (5) the detection of a third gamma-ray pulsar, plus several other transient and pulsing hard X-ray sources.

Gehrels, N.↗

NASA NTRS2004

Validation of Lithium-ion cell technology for JPL's 2003 Mars Exploration Rover Mission

n early 2004 JPL successfully landed two Rovers, named Spirit and Opportunity, on the surface of Mars after traveling >300 million miles over a 6-7 month period. In order to operate for extended duration on the surface of Mars, both Rovers are equipped with rechargeable Lithium-ion batteries, which were designed to aid in the launch, correct anomalies during cruise, and support surface operations in conjunction with a triple-junction deployable solar arrays. The requirements of the Lithium-ion battery include the ability to provide power at least 90 sols on the surface of Mars, operate over a wide temperature range (-20 C to +40 C), withstanding long storage periods (e.g., cruise period), operate in an inverted position, and support high currents (e.g., firing pyro events). In order to determine the viability of Lithium-ion technology to meet these stringent requirements, a comprehensive test program was implemented aimed at demonstrating the performance capability of prototype cells fabricated by Lithion, Inc. (Yardney Technical Products, Inc.). The testing performed includes, determining the (a) room temperature cycle life, (b) pulse capability as a function of temperature, (e) self-discharge and storage characteristics mission profile capability, (f) cycle life under mission simulation conditions, (g) impedance characteristics, (h) impact of cell orientation, and (i) performance in 8-cell engineering batteries. As will be discussed, the Lithium-ion prototype cells and batteries were demonstrated to meet, as well as, exceed the requirements defined by the mission.

2003 Mars Exploration Rover (MER)↗

NASA NTRS1994

Progress in modeling atmospheric propagation of sonic booms

The improved simulation of sonic boom propagation through the real atmosphere requires greater understanding of how the transient acoustic pulses popularly termed sonic booms are affected by humidity and turbulence. A realistic atmosphere is invariably somewhat turbulent, and may be characterized by an ambient fluid velocity v and sound speed c that vary from point to point. The absolute humidity will also vary from point to point, although possibly not as irregularly. What is ideally desired is a relatively simple scheme for predicting the probable spreads in key sonic boom signature parameters. Such parameters could be peak amplitudes, rise times, or gross quantities obtainable by signal processing that correlate well with annoyance or damage potential. The practical desire for the prediction scheme is that it require a relatively small amount of knowledge, possibly of a statistical nature, concerning the atmosphere along, the propagation path from the aircraft to the ground. The impact of such a scheme, if developed, implemented, and verified, would be that it would give the persons who make planning decisions a tool for assessing the magnitude of environmental problems that might result from any given overflight or sequence of overflights. The technical approach that has been followed by the author and some of his colleagues is to formulate a hierarchy of simple approximate models based on fundamental physical principles and then to test these models against existing data. For propagation of sonic booms and of other types of acoustic pulses in nonturbulent model atmospheres, there exists a basic overall theoretical model that has evolved as an outgrowth of geometrical acoustics. This theoretical model depicts the sound as propagating within ray tubes in a manner analogous to sound in a waveguide of slowly varying cross-section. Propagation along the ray tube is quasi-one-dimensional, and a wave equation for unidirectional wave propagation is used. A nonlinear term is added to this equation to account for nonlinear steepening, and the formulation has been carried through to allow for spatially varying sound speed, ambient density, and ambient wind velocities. The model intrinsically neglects diffraction, so it cannot take into account what has previously been mentioned in the literature as possibly important mechanisms for turbulence-related distortion. The model as originally developed could predict an idealized N-waveform which often agrees with data in terms of peak amplitude and overall positive phase duration. It is possible, moreover, to develop simple methods based on the physics of relaxation processes for incorporating molecular relaxation into the quasi-one-dimensional model of nonlinear propagation along ray tubes.

Pierce, Allan D.↗