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NASA NTRS1996

Non-Linear Cosmological Power Spectra in Real and Redshift Space

We present an expression for the non-linear evolution of the cosmological power spectrum based on Lagrangian trajectories. This is simplified using the Zel'dovich approximation to trace particle displacements, assuming Gaussian initial conditions. The model is found to exhibit the transfer of power from large to small scales expected in self-gravitating fields. Some exact solutions are found for power-law initial spectra. We have extended this analysis into red-shift space and found a solution for the non-linear, anisotropic redshift-space power spectrum in the limit of plane-parallel redshift distortions. The quadrupole-to-monopole ratio is calculated for the case of power-law initial spectra. We find that the shape of this ratio depends on the shape of the initial spectrum, but when scaled to linear theory depends only weakly on the redshift-space distortion parameter, beta. The point of zero-crossing of the quadrupole, kappa(sub o), is found to obey a simple scaling relation and we calculate this scale in the Zel'dovich approximation. This model is found to be in good agreement with a series of N-body simulations on scales down to the zero-crossing of the quadrupole, although the wavenumber at zero-crossing is underestimated. These results are applied to the quadrupole-to-monopole ratio found in the merged QDOT plus 1.2-Jy-IRAS redshift survey. Using a likelihood technique we have estimated that the distortion parameter is constrained to be beta greater than 0.5 at the 95 percent level. Our results are fairly insensitive to the local primordial spectral slope, but the likelihood analysis suggests n = -2 un the translinear regime. The zero-crossing scale of the quadrupole is k(sub 0) = 0.5 +/- 0.1 h Mpc(exp -1) and from this we infer that the amplitude of clustering is sigma(sub 8) = 0.7 +/- 0.05. We suggest that the success of this model is due to non-linear redshift-space effects arising from infall on to caustic and is not dominated by virialized cluster cores. The latter should start to dominate on scales below the zero-crossing of the quadrupole, where our model breaks down.

Taylor, A. N.↗

NASA NTRS1971

Thermal conductivity and resonant multipole interactions

The influence of multipole interactions on exchanges of rotational energy in molecular collisions was investigated by means of a simple two-state impact parameter approximation. The calculations are restricted to linear molecules and to dipole and quadrupole fields. The effects of such exchanges on the thermal conductivity of gases and of gaseous mixtures was investigated, after correcting the kinetic theory of mixtures to include exchanges between unlike molecules. It was found that dipole-quadrupole and quadrupole-quadrupole interactions may have a significant effect for molecules with low moments of inertia. In particular, quadrupole interactions are important in the hydrogen isotopes, and the calculated corrections for H2 are consistent with recent experimental work by Harris. The theory seems capable of accounting for the anomalies observed in HF + DF and HCl + DCl mixtures in terms of multipolar accidental resonances.

Nyeland, C.↗

NASA NTRS1996

An efficient and robust method for predicting helicopter rotor high-speed impulsive noise

A new formulation for the Ffowcs Williams-Hawkings quadrupole source, which is valid for a far-field in-plane observer, is presented. The far-field approximation is new and unique in that no further approximation of the quadrupole source strength is made and integrands with r(exp -2) and r(exp -3) dependence are retained. This paper focuses on the development of a retarded-time formulation in which time derivatives are analytically taken inside the integrals to avoid unnecessary computational work when the observer moves with the rotor. The new quadrupole formulation is similar to Farassat's thickness and loading formulation 1A. Quadrupole noise prediction is carried out in two parts: a preprocessing stage in which the previously computed flow field is integrated in the direction normal to the rotor disk, and a noise computation stage in which quadrupole surface integrals are evaluated for a particular observer position. Preliminary predictions for hover and forward flight agree well with experimental data. The method is robust and requires computer resources comparable to thickness and loading noise prediction.

Brentner, Kenneth S.↗

NASA NTRS1996

BATSE Observations of the Large-Scale Isotropy of Gamma-Ray Bursts

We use dipole and quadrupole statistics to test the large-scale isotropy of the first 1005 gamma-ray bursts observed by the Burst and Transient Source Experiment (BATSE). In addition to the entire sample of 1005 gamma-ray bursts, many subsets are examined. We use a variety of dipole and quadrupole statistics to search for Galactic and other predicted anisotropies and for anisotropies in a coordinate-system independent manner. We find the gamma-ray burst locations to be consistent with isotropy, e.g., for the total sample the observed Galactic dipole moment (cos theta) differs from the value predicted for isotropy by 0.9 sigma and the observed Galactic quadrupole moment (sin(exp 2) b - 1/3) by 0.3 sigma. We estimate for various models the anisotropies that could have been detected. If one-half of the locations were within 86 deg of the Galactic center, or within 28 deg of the Galactic plane, the ensuing dipole or quadrupole moment would have typically been detected at the 99% confidence level. We compare the observations with the dipole and quadrupole moments of various Galactic models. Several Galactic gamma-ray bursts models have moments within 2 sigma of the observations; most of the Galactic models proposed to date are no longer in acceptable agreement with the data. Although a spherical dark matter halo distribution could be consistent with the data, the required core radius is larger than the core radius of the dark matter halo used to explain the Galaxy's rotation curve. Gamma-ray bursts are much more isotropic than any observed Galactic population, strongly favoring but not requiring an origin at cosmological distances.

Briggs, Michael S.↗

NASA NTRS2001

Evaluating Mass Analyzers as Candidates for Small, Portable, Rugged Single Point Mass Spectrometers for Analysis of Permanent Gases

For Space Shuttle launch safety, there is a need to monitor the concentration Of H2, He, O2, and Ar around the launch vehicle. Currently a large mass spectrometry system performs this task, using long transport lines to draw in samples. There is great interest in replacing this stationary system with several miniature, portable, rugged mass spectrometers which act as point sensors which can be placed at the sampling point. Five commercial and two non-commercial analyzers are evaluated. The five commercial systems include the Leybold Inficon XPR-2 linear quadrupole, the Stanford Research (SRS-100) linear quadrupole, the Ferran linear quadrupole array, the ThermoQuest Polaris-Q quadrupole ion trap, and the IonWerks Time-of-Flight (TOF). The non-commercial systems include a compact double focusing sector (CDFMS) developed at the University of Minnesota, and a quadrupole ion trap (UF-IT) developed at the University of Florida.

Arkin, C. Richard↗

NASA NTRS2001

Evaluating Mass Analyzers as Candidates for Small, Portable, Rugged Single Point Mass Spectrometers for Analysis of Permanent Gases

For Space Shuttle launch safety, there is a need to monitor the concentration of H2, He, O2 and Ar around the launch vehicle. Currently a large mass spectrometry system performs this task, using long transport lines to draw in samples. There is great interest in replacing this stationary system with several miniature, portable, rugged mass spectrometers which act as point sensors which can be placed at the sampling point. Five commercial and two non-commercial analyzers are evaluated. The five commercial systems include the Leybold Inficon XPR-2 linear quadrupole, the Stanford Research (SRS-100) linear quadrupole, the Ferran linear quadrupole array, the ThermoQuest Polaris-Q quadrupole ion trap, and the IonWerks Time-of-Flight (TOF). The non-commercial systems include a compact double focusing sector (CDFMS) developed at the University of Minnesota, and a quadrupole ion trap (UF-IT) developed at the University of Florida. The System Volume is determined by measuring the entire system volume including the mass analyzer, its associated electronics, the associated vacuum system, the high vacuum pump and rough pump. Also measured are any ion gauge controllers or other required equipment. Computers are not included. Scan Time is the time required for one scan to be acquired and the data to be transferred. It is determined by measuring the time required acquiring a known number of scans and dividing by said number of scans. Limit of Detection is determined first by performing a zero-span calibration (using a 10-point data set). Then the limit of detection (LOD) is defined as 3 times the standard deviation of the zero data set. (An LOD of 10 ppm or less is considered acceptable.)

Arkin, C. Richard↗

NASA NTRS2010

Suppressing Loss of Ions in an Atomic Clock

An improvement has been made in the design of a compact, highly stable mercury- ion clock to suppress a loss of ions as they are transferred between the quadrupole and higher multipole ion traps. Such clocks are being developed for use aboard spacecraft for navigation and planetary radio science. The modification is also applicable to ion clocks operating on Earth: indeed, the success of the modification has been demonstrated in construction and operation of a terrestrial breadboard prototype of the compact, highly stable mercury-ion clock. Selected aspects of the breadboard prototype at different stages of development were described in previous NASA Tech Briefs articles. The following background information is reviewed from previous articles: In this clock as in some prior ion clocks, mercury ions are shuttled between two ion traps, one a 16- pole linear radio-frequency trap, while the other is a quadrupole radio-frequency trap. In the quadrupole trap, ions are tightly confined and optical state selection from a 202Hg lamp is carried out. In the 16-pole trap, the ions are more loosely confined and atomic transitions are interrogated by use of a microwave beam at approximately 40.507 GHz. The trapping of ions effectively eliminates the frequency pulling that would otherwise be caused by collisions between clock atoms and the wall of a gas cell. The shuttling of the ions between the two traps enables separation of the state-selection process from the clock microwave-resonance process, so that each of these processes can be optimized independently of the other. This is similar to the operation of an atomic beam clock, except that with ions the beam can be halted and reversed as ions are shuttled back and forth between the two traps. When the two traps are driven at the same radio frequency, the strength of confinement can be reduced near the junction between the two traps, depending upon the relative phase of the RF voltage used to operate each of the two traps, and can cause loss of ions during each transit between the traps and thereby cause loss of the 40.507-GHz ion-clock resonance signal. The essence of the modification is to drive the two traps at different frequencies typically between 1.5 and 2 MHz for the quadrupole trap and a frequency a few hundred kHz higher for the 16- pole trap. A frequency difference of a few hundred kHz ensures that the ion motion caused by the trapping electric fields is small relative to the diameter of the traps. Unlike in the case in which both traps are driven at the same frequency, the trapping electric fields near the junction are not zero at all times; instead, the regions of low electric field near the junction open and close at the difference frequency. An additional benefit of making the 16-pole trap operate at higher frequency is that the strength or depth of the multipole trap can be increased independent of the quadrupole ion trap.

Prestage, John↗

NASA NTRS1990

Determining gravitational radiation from Newtonian self-gravitating systems

Quadrupole gravitational radiation formulas are tested and compared in a calculation of rotating stellar core collapse. While the standard quadrupole formula (SQF) allows an economical calculation of the waveform in postlinear gravity, it has several shortcomings that become apparent in a finite difference (FD) calculation. These shortcomings are related to the large-moment arm of the quadrupole moment and the two (numerical) time derivatives that separate it from the waveform. These shortcomings lead to high-frequency noise in the SQF waveform. Several alternatives to the SQF are developed. Each is mathematically equivalent to the SQF and applicable to self-gravitating sources. For FD calculations, the new quadrupole formulas are all superior to the SQF and capable of producing waveforms free of the high-frequency noise characteristics of its use.

Finn, Lee Samuel↗

NASA NTRS1994

On the rms anisotropy at 7 deg and 10 deg observed in the COBE-DMR two year sky maps

The frequency-independent rms temperature fluctuations determined from the Cosmic Background Explorer-Differential Microwave Radiometer (COBE-DMR) two-year sky maps are used to infer the parameter Q(sub rms-PS), which characterizes the normalization of power-law models of primordial cosmological temperature anisotropy, for a forced fit to a scale-invariant Harrison-Zel'dovich (n = 1) spectral model. Using a joint analysis of the 7 deg and 10 deg 'cross'-rms derived from both the 53 and 90 GHz sky maps, we find Q(sub rms-PS) = 17.0(sub -2.1 sup +2.5) micro Kelvin when the low quadrupole is included, and Q(sub rms-PS) = 19.4(sub -2.1 sup +2.3) micro Kelvin excluding the quadrupole. These results are consistent with the n = 1 fits from more sensitive methods. The effect of the low quadrupole derived from the COBE-DMR data on the inferred Q(sub rms-PS) normalization is investigated. A bias to lower Q(sub rms-PS) is found when the quadrupole is included. The higher normalization for a forced n = 1 fit is then favored by the cross-rms technique.

Banday, A. J.↗

NASA NTRS1997

Design of An Improved Miniature Ion Neutral Mass Spectrometer for NASA Applications

The ion optics of NASA's Ion Neutral Mass Spectrometer (INMS) sensor was simulated with three dimensional models of the open source, the quadrupole deflector, the exit lens system and the quadrupole mass analyzer to design more compact models with lower weight. Comparison of calculated transmission with experimental results shows good agreement. Transmission analyses with varying geometrical parameters and voltages throw light on possible ways of reducing the size of the sensor. Trajectories of ions of mass 1-99 amu were simulated to analyze and optimize transmission. Analysis of open source transmission with varying angle of attack shows that the angular acceptance can be considerably increased by programming the voltages on the ion trap/ collimator. Analysis of transmission sensitivity to voltages and misalignments of the quadrupole deflector rods indicate that increased transmission is possible with a geometrically asymmetrical deflector and a deflector can be designed with much lower sensitivities of transmission. Bringing the disks closer together can decrease the size of the quadrupole deflector and also increase transmission. The exit lens system can be redesigned to be smaller by eliminating at least one electrode entirely without loss of transmission. Ceramic materials were investigated to find suitable candidates for use in the construction of lighter weight mass spectrometer. A high-sensitivity, high-resolution portable gas chromatograph mass spectrometer with a mass range of 2-700 amu has been built and will be commercialized in Phase 3.

Swaminathan, Viji K.↗

NASA NTRS2001

Toward a Micro Gas Chromatograph/Mass Spectrometer (GC/MS) System

Miniature mass filters (e.g., quadrupoles, ion traps) have been the subject of several miniaturization efforts. A project is currently in progress at JPL to develop a miniaturized Gas Chromatograph/Mass Spectrometer (GC/MS) system, incorporating and/or developing miniature system components including turbomolecular pumps, scroll type roughing pump, quadrupole mass filter, gas chromatograph, precision power supply and other electronic components. The preponderance of the system elements will be fabricated using microelectromechanical systems (MEMS) techniques. The quadrupole mass filter will be fabricated using an X-ray lithography technique producing high precision, 5x5 arrays of quadrupoles with pole lengths of about 3 mm and a total volume of 27 cubic mm. The miniature scroll pump will also be fabricated using X-ray lithography producing arrays of scroll stages about 3 mm in diameter. The target detection range for the mass spectrometer is 1 to 300 atomic mass units (AMU) with are solution of 0.5 AMU. This resolution will allow isotopic characterization for geochronology, atmospheric studies and other science efforts dependant on the understanding of isotope ratios of chemical species. This paper will discuss the design approach, the current state-of-the art regarding the system components and the progress toward development of key elements. The full system is anticipated to be small enough in mass, volume and power consumption to allow in situ chemical analysis on highly miniaturized science craft for geochronology, atmospheric characterization and detection of life experiments applicable to outer planet roadmap missions.

Wiberg, D. V.↗

NASA NTRS2011

Dipole Field Effects on Ion Ejections from a Paul Ion Trap

Attempts at improving the quality of mass spectra obtained from a Paul trap mass spectrometer prompted an investigation of the effects of additional fields to supplement the primary rf quadrupole trapping field. Reported here are the results of the first in a series of tests that focuses on the application of a single dipole field to augment the trapping and subsequent ejections of ions stored within a Paul trap. Measurements are presented for a fixed quadrupole frequency with varying dipole frequencies. The presence of the dipole field during the quadrupole trapping phase causes ion ejections of single m/z species at discrete dipole frequencies. During the mass analysis phase, the varying dipole frequency produces a complex set of resonant structures that impact ejection time (mass range), as well as mass spectral peak intensity and width

dipole↗

NASA NTRS1972

Geomagnetic field distortions and their effects on radiation belt particles.

One of the quadrupole terms in the main geomagnetic field is found to contribute to a north-south 'shear distortion' of the particle-drift shells, whereas one of the octupole components causes a longitude-dependent radial deformation and associated 'drift-shell splitting.' The collective action of all higher multipoles on trapped-particle motion is then used to analyze the 'true' anomalies or distortions of the internal geomagnetic field that are independent of the quadrupole-related eccentricity of the main dipole. These 'true' anomalies must originate in upper-mantle or crustal perturbations that lie relatively near the earth's surface on both sides of the mid-Atlantic ridge; they influence trapped-particle drift shells only where the latter have their closest approach to the earth (South Atlantic and South African areas). The quadrupole and octupole perturbations, on the other hand, obviously originate deep in the earth's core. In the final part of this review, we discuss the effects of external magnetospheric currents. A time-dependent symmetric ring current causes drift shells to be displaced radially, with associated particle acceleration; magnetopause currents introduce a day-night asymmetry, causing shell splitting.

Roederer, J. G.↗

NASA NTRS1972

Thermal conductivity and resonant multipole interactions.

Investigation of the influence of resonant multipole interactions on exchanges of rotational energy in molecular collisions, by means of a simple two-state impact-parameter approximation. It is found that dipole-quadrupole and quadrupole-quadrupole interactions can have a significant effect for molecules with low moments of inertia.

Nyeland, C.↗

NASA NTRS1977

Design and fabrication of a basic mass analyzer and vacuum system

A two-inch hyperbolic rod quadrupole mass analyzer with a mass range of 400 to 200 amu and a sensitivity exceeding 100 packs per billion has been developed and tested. This analyzer is the basic hardware portion of a microprocessor-controlled quadrupole mass spectrometer for a Gas Analysis and Detection System (GADS). The development and testing of the hyperbolic-rod quadrupole mass spectrometer and associated hardware are described in detail.

Judson, C. M.↗

NASA NTRS1977

Approximations for proton excitation of coronal ion fine structure

Explicit approximations that yield proton excitation cross sections and rate coefficients for fine-structure transitions in a wide variety of ions over the low and intermediate energy ranges are obtained in terms of the electric quadrupole transition probability and quadrupole radial integral of a given ion. The range of applicability of these approximations is discussed, and comparisons are made with available cross sections and rate coefficients. Values of quadrupole radial integrals are given for ground configurations of even-Z elements in higher stages of ionization. Proton excitation rate coefficients are computed for coronal transitions involving fine-structure levels in the ions Fe XIII, Fe XV, Fe XVIII, Fe XXI, and Ca XIII.

Kastner, S. O.↗

NASA NTRS1981

A High Resolution Spectroscopic Study of the Nu2 Band of Hydrogen Sulfide and the 1-0 Band of Hydrogen Iodide

A tunable diode laser spectrometer was constructed and used to study: (1) the effects of centrifugal distortion on the transition frequencies and strengths of the nu sub 2 band of H2S, and (2) nuclear quadrupole hyperfine structure in the 1-0 band of HI. A total of 126 line frequencies and 94 line strengths in the nu sub 2 band of H2S were measured. The average accuracy of the line frequency measurements was + or - 0.0016 cm. The line strengths were measured to an average accuracy of about 3 percent. The effect of the finite spectral width of the diode laser on the measurement of line strengths is discussed. The observed H2S line frequencies were fit to Watson's AS and NS reduced Hamiltonian in both the Ir and IIIr coordinate representations in order to determine the best set of rotation distortion constants for the upper state of the nu sub 2 band. Comparisons of the observed line strengths in this band to rigid rotor line strengths are also presented. Nuclear quadrupole hyperfine structure in the low J lines of the 1-0 band of HI was observed. The upper vibrational state nuclear quadrupole coupling constant, determined from the observed splittings, was -1850 MHz + or - 12 MHz or 1.2 percent + or - 0.7 percent larger than the ground state coupling constant.

Strow, L. L.↗

NASA NTRS1985

Theoretical transition probabilities between the lowest 2S, 2P and 2D states of Na, K, Rb and Cs

Theoretical transition probabilities between the lowest 2S, 2P and 2D states of the alkali atoms Na through Cs have been computed using near Hartree-Fock quality Slater basis sets. The important core-valence correlation effects are incorporated explicitly by a configuration-interaction procedure. For Cs, the calculations were repeated using a Gaussian basis set so that relativistic effects could be incorporated through an effective core potential procedure. The best calculated electric quadrupole Einstein coefficients are Na(196.3/s), K(103.6/s), Rb(72.4/s) and Cs(19.7/s). Core-valence effects become increasingly important down the column, and reduce the quadrupole transition strengths to about the same degree as for the 2P-2S and 2D-2P dipole-allowed transitions. Relativistic effects increase the quadrupole moment of Cs, but less so than in Ba, presumably because the alkali 2D states are more diffuse.

Langhoff, S. R.↗