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Several approximations to the Doppler broadening functions psi(x, theta) and chi(x, theta) are compared with respect to accuracy and speed of evaluation. A technique, due to A. M. Turning (1943), is shown to be at least as accurate as direct numerical quadrature and somewhat faster than Gaussian quadrature. FORTRAN 4 listings are included.
Several 3D finite element analyses of (0/theta/-theta)sub s graphite epoxy laminates, where theta=15, 20, 25, 30, and 45 deg, subjected to axial tension load were performed. The interlaminar stresses in the theta/-theta interface were calculated with and without a matrix crack in the central -theta plies. The interlaminar normal stress changes from a small compressive stress when no matrix crack is present to a high tensile stress at the intersection of the matrix crack and free edge. The analysis of local delamination from the -theta matrix crack indicates a high strain energy release rate and a localized mode I component near the free edge, within one ply distance from the matrix crack. In order to examine the stress state causing the matrix cracking the maximum principal normal stress in a plane perpendicular to the fiber direction in the -theta ply was calculated in an uncracked laminate. The corresponding shear stress parallel to the fiber was also calculated. The principal normal stress at the laminate edge increases through the ply thickness and reached a very high tensile value at the theta/-theta interface indicating that the crack in the -theta ply may initiate at the theta/-theta interface. Crack profiles on the laminate edge in the -theta ply were constructed from the principal stress directions. The cracks were found to be more curved for layups with smaller theta angles, which is consistent with experimental observations in the literature.
Several 3D finite element analyses of (O/theta/-theta)sub s graphite epoxy laminates, where theta = 15, 20, 25, 30, and 45 deg, subjected to axial tension load were performed. The interlaminar stresses in the theta/-theta interface were calculated with and without a matrix crack in the central -theta plies. The interlaminar normal stress changes from a small compressive stress when no matrix crack is present to a high tensile stress at the intersection of the matrix crack and free edge. The analysis of local delamination from the -theta matrix crack indicates a high strain energy release rate and a localized mode I component near the free edge, within one ply distance from the matrix crack. In order to examine the stress state causing the matrix cracking the maximum principal normal stress in a plane perpendicular to the fiber direction in the -theta ply was calculated in an uncracked laminate. The corresponding shear stress parallel to the fiber was also calculated. The principal normal stress at the laminate edge increases through the ply thickness and reached a very high tensile value at the theta/-theta interface indicating that the crack in the -theta ply may initiate at the theta/-theta interface. Crack profiles on the laminate edge in the -theta ply were constructed from the principal stress directions. The cracks were found to be more curved for layups with smaller theta angles, which is consistent with experimental observations in the literature.
Three-dimensional element analyses of (0/theta/-theta)s graphite epoxy laminates, where theta = 15, 20, 25, 30, and 45 deg, subjected to axial tensile load, were performed. The interlaminar stresses in the theta/-theta interface were calculated with and without a matrix crack in the central -theta plies. The interlaminar normal stress changes from a small compressive stress when no matrix crack is present to a high tensile stress at the intersection of the matrix crack and the free edge. The analysis of local delamination from the -theta matrix crack indicates a high strain energy release rate and a localized Mode I component near the free edge, within one-ply distance from the matrix crack. To examine the stress state causing the matrix cracking, the maximum principal normal stress in a plane perpendicular to the fiber direction in the -theta ply was calculated in an uncracked laminate. The corresponding shear stress parallel to the fiber was also calculated. The principal normal stress at the laminate edge increased through the ply thickness and reached a very high tensile value at the theta/-theta interface indicating that the crack in the -theta ply may initiate at the theta/-theta interface.
We report new high-resolution, wide-wavelength-coverage CCD observations of the visual and near-infrared spectra of the interferometric spectroscopic binaries theta(sup 2) Tau (primary spectral type A 7 III) and alpha And (primary spectral type B8 IVpMnHg), which allow the first direct spectroscopic detection of their secondaries. We have measured primary and secondary radial velocities and used them to redetermine the spectroscopic orbits of the primaries, make an improved determination of K(sub 2) for theta(sup 2) Tau, and measure K(sub 2) for alpha And for the first time. The spectroscopic orbits combined with the interferometrically measured visual orbits of theta(sup 2) Tau and alpha And provide masses and distances, M(sub 1) = 2.1 +/- 0.3 solar mass, M(sub 2) = 1.6 +/- 0.2 solar mass, and d = 44.1 +/- 2.2 pc for theta(sup 2) Tau and M(sub 1) = 5.5 +/- 0.5 solar mass, M(sub 2) = 2.3 +/- 0.2 solar mass, and d = 34.0 +/- 1.3 pc for alpha And. The distance to theta(sup 2) Tau and a foreground correction of 0.07 +/- 0.05 mag set the distance to the center of the Hyades cluster at 45.5 +/- 2.5 pc, or m - M = 3.29 +/- 0.12. Indirect estimates of the mass of theta(sup 2) Tau's primary, made via the mass-luminosity relation and via the Hyades cluster turnoff mass, are consistent with these dynamical masses for its primary and secondary. But in the case of alpha And, the mass-luminosity relation suggests that our dynamical masses for its primary and secondary may be too large. For alpha And somewhat smaller dynamical masses (4.0 and 1.9 solar mass) and the correspondingly smaller distance (31 pc), required by the corresponding larger orbital parallax, provide results consistent with the mass-luminosity relation for normal stars.
The Lawrence Berkeley National Laboratory (LBNL) and the National High Magnetic Field Laboratory (NHMFL) have published results on Bi-2212 superconductive magnets realized and tested in the canted cosine-theta and solenoid designs, respectively. Fermilab is now preparing for the assembly of the first Bi-2212 stress-managed cosine-theta insert magnet. The insert will be part of the first hybrid cosine-theta magnet made of Nb$_3$Sn outer layers within the US-MDP effort to reach a 20 T bore field. This paper presents the analytical analysis of the cosine-theta Nb$_3$Sn/Bi-2212 hybrid magnet. We report the parameters, logic, and implementation method of the 2D electromagnetic and mechanical FEM analysis of the LTS/HTS hybrid magnet. Results from a detailed heterogeneous model are compared to the homogeneous model implemented in the past. A Python code has been developed to simulate the current degradation due to stresses in the detail-modeled conductor areas. The current degradation has been introduced in the simulation dynamics for the HTS conductor as an iteration process, updating the input load of Lorentz forces of the energization at each step. The magnetic and mechanical analysis results of the 2D cosine-theta LTS/HTS dipole magnet have been described and analyzed.
After the recent results on Bi-2212 superconductive magnets realized and tested in canted cosine-theta and solenoid designs, respectively, at Lawrence Berkeley National Laboratory (LBNL) and NHMFL, the first Bi-2212 stress-managed cosine-theta insert magnet is in the assembly phase at Fermilab. This insert will be part of the first hybrid cosine-theta magnet made of Nb3Sn outer layers within the US-MDP effort to reach 20 T bore field. This paper reports the analytical analysis of the cosine-theta Nb3Sn/Bi-2212 hybrid magnet. As an introduction, it shows the validation of the finalized HTS coils' design optimized using the ROXIE code. Subsequently, it reports the parameters, logic, and implementation method of the 2D electromagnetic and mechanical FEM analysis of the LTS/HTS hybrid magnet. Results from the ANSYS detailed model made with sub-modeling geometry are compared with the homogeneous model implemented in the past. Moreover, a Python code was implemented to simulate the current degradation due to stresses in the detail-modeled conductor areas. The current degradation is introduced in the simulation dynamics for both conductors as an iteration process during the energization load step only after applying pre-stress and thermal loads. The numerical and graphic results of the 2D cosine-theta LTS/HTS magnet cross-section will be described and analyzed.
The Thermal Hydraulic Experimental Test Article (THETA) is a facility that is used to develop sodium components and instrumentation as well as to acquire experimental data for validation of reactor thermal hydraulic and safety analysis codes. The facility simulates nominal thermal hydraulic conditions as well as protected/unprotected loss of flow accidents in a sodium-cooled fast reactor (SFR). High fidelity distributed temperature profiles of the developed flow field may be acquired with Rayleigh backscatter based optical fiber temperature sensors. The facility was designed in partnership with systems code experts to tailor the experiment to ensure the most relevant and highest quality data for code validation. THETA is comprised of a traditional primary coolant and secondary coolant system. The primary system is submerged in the pool of sodium and consists of a pump, electrically heated core, intermediate heat exchanger, and connected piping and thermal barriers (redan). The secondary system, located outside of the sodium pool, consists of a pump, sodium to air heat exchanger, and connected piping and valves. In fiscal year 2023, thermal stratification tests were completed with the primary system online, while the secondary system was being constructed [1]. These tests had shown that the core barrel and intermediate heat exchanger (IHX) outlet required increased thermal insulation. The THETA primary system was removed from METL, cleaned, thermal insulators installed, and then inserted into METL Test Vessel 4. At the time of this writing the THETA primary and secondary system are operational. During this fiscal year 100+ hours of testing was completed to characterize thermal hydraulic phenomena associated with steady state and transient conditions in a pool type liquid metal cooled reactor. A majority of the testing campaign was completed to satisfy the experimental data acquisition requirements for the GAIN Voucher with Oklo, CRADA 2021-21121. THETA is still operational at the time of this publication and future testing is planned for fiscal year 2025. Work is underway to publish existing and future data to an online database to facilitate collaboration with SFR engineers looking to validate their systems code or computational fluid dynamics models.
A possible role for the hippocampus in alerting an animal to changes in cutaneous temperature was examined. Following local warming or cooling of the ears of unanesthetized, loosely restrained rabbits, theta waves (4-7 Hz EEG waves) were recorded from electrodes straddling the hippocampus. The onset of the hippocampal theta rhythm was correlated with changes in cutaneous temperature, an observation consistent with studies indicating that the theta rhythm is a nonspecific response evoked by stimulation of several sensory modalities. Additional data from cats and rabbits were correlated with specific neurons within the hippocampus, namely pyramidal cells. Post stimulus time histograms obtained by excitation of the dorsal fornix were interpreted in terms of excitatory and inhibitory inputs to pyramidal cells. Thus, the theta rhythm, which appears to be evoked by changes in cutaneous temperature, can be related to a specific type of hippocampal neuron which is in turn connected with other areas of the brain involved in temperature regulation.
Observations of a transpolar arc and simultaneous measurements of associated plasmas in the magnetotail lobe on March 25, 1982, are presented. The auroral imager on board Dynamics Explorer 1 observes a theta aurora in the northern polar cap for more than two hours, between 0502 and 0720 UT. ISEE 1 is located in the southern lobe of the geomagnetic tail at a distance of 22.2 R(E) during this time. The plasma and particle detectors measure intermittent bursts of particle fluxes between 0530 and 0705 UT. The observations suggest that these particle fluxes represent the high-altitude signature of a theta aurora in the southern polar cap. The relatively dense and energetic plasmas are organized into several filamentary structures. Magnetic mapping between the two polar regions indicates that the theta aurora in the Southern Hemisphere is a mirror reflection about the noon-midnight meridional plane of the theta aurora in the Northern Hemisphere.
We report the discovery of large-amplitude, periodic X-ray emission from the O7 V star Theta(sup 1) Orionis C, the central star of the Orion Nebula. Ten ROSAT HRI snapshots of the Trapezium cluster taken over the course of 21 days show that the count rate of Theta(sup 1) Ori C varies from 0.26 to 0.41 counts/ s with a clear 15 day period. The soft X-ray variations have the same phase and period as H(alpha) and He II (lambda)4686 variations reported by Stahl et al. and are in antiphase with the C(sub iv) and Si(sub iv) ultraviolet absorption features. We consider five mechanisms which might explain the amplitude, phase, and periodicity of the X-ray variations: (1) colliding-wind emission with an unseen binary companion, (2) coronal emission from an unseen late-type pre-main-sequence star, (3) periodic density fluctuations, (4) absorption of magnetospheric X-rays in a corotating wind, and (5) magnetosphere eclipses. The ROSAT data rule out the first three scenarios but cannot rule out either of the latter two which require the presence of an extended magnetosphere, consistent with the suggestion of Stahl et al. that Theta(sup 1) Ori C is an oblique magnetic rotator. As such, Theta(sup 1) Ori C may be the best example of a high-mass analog to the chemically peculiar, magnetic Bp stars.
Magnets in the accelerator interaction region (IR) present significant challenges because of high field requirements and limited available space. Conical-shaped magnets offer advantages in these environments by allowing closer placement to the interaction point while maintaining clearance from synchrotron radiation. Interestingly, numerical studies have shown that conical canted-cosine-theta (CCT) designs produce a constant field distribution along the axial direction in the IR quadrupoles for the Electron-Ion Collider (EIC) at Brookhaven National Laboratory. However, the field harmonics generated by conical CCT windings are not yet fully understood. This paper presents an analytical approach to describe the magnetic field produced by a conical surface current and proposes a method for designing conical CCT magnets for accelerator applications. First, we begin with a surface current sheet having a general cosine-theta distribution in spherical coordinates and solve the vector potential using the Green’s function. The magnetic fields generated by the conical current sheet are expressed using associated Legendre polynomials. These results are then related to circular field harmonics and integral field harmonics for designing a coil that produces a pure multipole field. Next, a single layer of the conical CCT winding path is produced based on the cosine-theta current distribution. Finally, the magnetic field quality of dipole and quadrupole conical CCT coils with multiple layers is verified using the Biot-Savart law.
Measurements of the interplanetary magnetic field taken with Imp 3, Pioneer 6, and Explorer 34 constitute a large portion of the data available at low and moderate solar activity and provide nearly continuous coverage from mid-1965 through 1966 without radial effects. Study of these observations provides further evidence for the following B sub theta effect initially discovered with Mariners 2, 4, and 5. At low or moderate solar activity, the mean value of B sub theta is negative (approximately northward in the observations) above the solar equatorial plane and positive below it for an interplanetary field directed outward from the sun, and vice versa for an inward field. Thus, for an outward field, the r-theta component of a line of magnetic force above or below the equatorial plane was skewed relative to the average value of r in the direction away from the equatorial plane. Comparisons between different spacecraft are discussed.
Warming and cooling the preoptic anterior hypothalamic area in awake, loosely restrained rabbits was found to evoke theta rhythm. This is consistent with previous studies indicating that theta rhythm is a nonspecific response evoked by stimulation of several sensory modalities. Several studies have correlated theta rhythm with alertness. A neural pathway involving the hypothalamus, the hippocampus, the septal area, and the reticular formation is proposed. Thus, a role of this pathway may be to alert the animal to changes in its body temperature.
Detailed analyses of the DE 1 high-altitude plasma instrument electron and ion data have been performed for four passes during which theta auroras were observed. The data indicate that the theta auroras occur on what appear to be closed field lines with particle signatures and plasma parameters that are quite similar to those of the magnetospheric boundary plasma sheet. The field-aligned currents computed from particle fluxes in the energy range 18-13 keV above the theta auroras are observed to be generally downward on the dawnside of the arcs with a narrower region of larger (higher density) upward currents on the duskside of the arcs. These currents are carried predominantly by field-aligned beams of accelerated cold electrons. Of particualr interest in regions of upward field-aligned current are downward electron beams at energies less than the inferred potential drop above the spacecraft.
During the 1990 December Astro-1 Space Shuttle mission, spectropolarimetry was conducted in the wavelength region from 1400 to 3200 A of the Wolf-Rayet stars EZ CMa (WN5) and Theta Mus (WC6 + O9.5I) with the Wisconsin Ultraviolet Photo-Polarimeter Experiment. The UV polarization of EZ CMa displays features which correspond to emission lines. This indicates a large, about 0.8 percent, intrinsic UV-continuum polarization, and provides further evidence that the wind of EZ CMa is highly distorted. The polarization of Theta Mus does not change across emission lines, or the strong interstellar 2200 A feature. The polarization decreases smoothly to shorter wavelengths, at constant position angle. The combined UV-optical polarization spectrum of Theta Mus can be described well with interstellar polarization following a Serkowski law.
A profile fitting technique is employed to identify the velocities and Doppler b values for H I and H II clouds along the line of sight to Theta Car. Total abundances and depletions for 12 elements, plus column densities for the J = 0 to J = 5 rotational levels of H2 are obtained. Electron densities for both clouds are calculated from the ratios of the fine-structure levels of C II and N II, obtaining 0.08/cu cm and 1.2/cu cm. The fine-structure levels of C I, which led to 120/cu cm, are used to calculate the neutral hydrogen density for the H I region. D I is also present in the data from the Theta Car line of sight, yielding a D/H ratio of 5 x 10 exp -6. Elemental depletions are calculated for the H I region as well. Comparison of the results for Theta Car and those for Zeta Oph and Alpha Vir shows that the absolute depletions are different; however, the relative depletions are remarkably stable for different physical conditions.
A new high-power propulsion concept that combines a rapidly pulsed theta-pinch discharge with upstream particle reflection by a magnetic mirror was evaluated under a Phase 1 grant awarded through the NASA Institute for Advanced Concepts. Analytic and numerical models were developed to predict the performance of a theta-pinch thruster operated over a wide range of initial gas pressures and discharge periods. The models indicate that a 1 m radius, 10 m long thruster operated with hydrogen propellant could provide impulse-bits ranging from 1 N-s to 330 N-s with specific impulse values of 7,500 s to 2,500 s, respectively. A pulsed magnetic field strength of 2 T is required to compress and heat the preionized hydrogen over a 10(exp -3) second discharge period, with about 60% of the heated plasma exiting the chamber each period to produce thrust. The unoptimized thruster efficiency is low, peaking at approximately 16% for an initial hydrogen chamber pressure of 100 Torr. The specific impulse and impulse-bit at this operating condition are 3,500 s and 90 N-s, respectively, and the required discharge energy is approximately 9x10(exp 6) J. For a pulse repetition rate of 10 Hz, the engine would produce an average thrust of 900 N at 3,500 s specific impulse. Combined with the electrodeless nature of the device, these performance parameters indicate that theta-pinch thrusters could provide unique, long-life propulsion systems for piloted deep space mission applications.