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Articles 121 - 150 of 150

Full-Text Articles in Physics

Modelling Continuum Optical And Ultraviolet Polarization Of Active Galactic Nuclei, René W. Goosmann, C. Martin Gaskell Jun 2005

Modelling Continuum Optical And Ultraviolet Polarization Of Active Galactic Nuclei, René W. Goosmann, C. Martin Gaskell

Department of Physics and Astronomy: Faculty Publications

We present results from a new Monte Carlo radiative transfer computer code, STOKES, developed to model polarization induced by scattering off free electrons and dust grains. STOKES is freely available on the web and can be used to model scattering in a wide variety of astrophysical situations. For edge-on (type-2) viewing positions, the polarization produced by a dusty torus alone is largely wavelength-independent.

This is because the torus is optically thick and the change in albedo with wavelength is slight. Wavelength-independent polarization therefore does not necessarily imply electron scattering. We are able to fully explain wavelength independent type-2 polarization without …

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Nonlinear Absorption, Scattering And Optical Limiting Studies Of Cds Nanoparticles, N. Venkatra, D. Narayana Rao, Murty Akundi Feb 2005

Nonlinear Absorption, Scattering And Optical Limiting Studies Of Cds Nanoparticles, N. Venkatra, D. Narayana Rao, Murty Akundi

Faculty and Staff Publications

The nonlinear optical absorption, scattering and optical limiting properties of CdS nanoparticles dispersed in dimethylformamide (DMF) are investigated. The nanoparticles are synthesized using the standard chemical synthesis method with thioglycerol as the capping agent. The investigations are carried out at 532 nm in the ns regime. Strong two-photon absorption and nonlinear scattering are found to be responsible for good optical limiting characteristics in these nanoparticles.

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Manifestation Of The Color Glass Condensate In Particle Production At Rhic, Kirill Tuchin Jan 2005

Manifestation Of The Color Glass Condensate In Particle Production At Rhic, Kirill Tuchin

Kirill Tuchin

We discuss general properties of the Color Glass Condensate. We show that predictions for particle production in p(d)A and AA collisions derived from these properties are in agreement with data collected at RHIC.

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Monte Carlo Simulation Of Hole Transport And Terahertz Amplification In Multilayer Delta Doped Semiconductor Structures, Maxim Dolguikh Jan 2005

Monte Carlo Simulation Of Hole Transport And Terahertz Amplification In Multilayer Delta Doped Semiconductor Structures, Maxim Dolguikh

Electronic Theses and Dissertations

Monte Carlo method for the simulation of hole dynamics in degenerate valence subbands of cubic semiconductors is developed. All possible intra- and inter-subband scattering rates are theoretically calculated for Ge, Si, and GaAs. A far-infrared laser concept based on intersubband transitions of holes in p-type periodically delta-doped semiconductor films is studied using numerical Monte-Carlo simulation of hot hole dynamics. The considered device consists of monocrystalline pure Ge layers periodically interleaved with delta-doped layers and operates with vertical or in-plane hole transport in the presence of a perpendicular in-plane magnetic field. Inversion population on intersubband transitions arises due to light hole …

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High-Energy Effective Action From Scattering Of Qcd Shock Waves, Ian Balitsky Jan 2005

High-Energy Effective Action From Scattering Of Qcd Shock Waves, Ian Balitsky

Physics Faculty Publications

At high energies, the relevant degrees of freedom are Wilson lines—infinite gauge links ordered along straight lines collinear to the velocities of colliding particles. The effective action for these Wilson lines is determined by the scattering of QCD shock waves. I develop the symmetric expansion of the effective action in powers of strength of one of the shock waves and calculate the leading term of the series. The corresponding first-order effective action, symmetric with respect to projectile and target, includes both up and down fan diagrams and pomeron loops.

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Multiple Scattering Of Light In Inhomogeneous Media And Applications, Claudia Mujat Jan 2004

Multiple Scattering Of Light In Inhomogeneous Media And Applications, Claudia Mujat

Electronic Theses and Dissertations

Light scattering-based techniques are being developed for non-invasive diagnostics of inhomogeneous media in various fields, such as medicine, biology, and material characterization. However, as most media of interest are highly scattering and have a complex structure, it is difficult to obtain a full analytical solution of the scattering problem without introducing approximations and assumptions about the properties of the system under consideration. Moreover, most of the previous studies deal with idealized scattering situations, rarely encountered in practice. This dissertation provides new analytical, numerical, and experimental solutions to describe subtle effects introduced by the properties of the light sources, and by …

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Unique Electron Polarimeter Analyzing Power Comparison And Precision Spin-Based Energy Measurement, J. M. Grames, C. K. Sinclair, J. Mitchell, E. Chudakov, H. Fenker, A. Freyberger, D. W. Higinbotham, M. Poelker, M. Steigerwald, M. Tiefenback, Vipuli Dharmawardane Jan 2004

Unique Electron Polarimeter Analyzing Power Comparison And Precision Spin-Based Energy Measurement, J. M. Grames, C. K. Sinclair, J. Mitchell, E. Chudakov, H. Fenker, A. Freyberger, D. W. Higinbotham, M. Poelker, M. Steigerwald, M. Tiefenback, Vipuli Dharmawardane

Physics Faculty Publications

Precision measurements of the relative analyzing powers of five electron beam polarimeters, based on Compton, Moller, and Mott scattering, have been performed using the CEBAF accelerator at the Thomas Jefferson National Accelerator Facility ( Jefferson Laboratory). A Wien filter in the 100 keV beam line of the injector was used to vary the electron spin orientation exiting the injector. High statistical precision measurements of the scattering asymmetry as a function of the spin orientation were made with each polarimeter. Since each polarimeter receives beam with the same magnitude of polarization, these asymmetry measurements permit a high statistical precision comparison of …

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Measurement Of Beam-Spin Asymmetries For Π⁺ Electroproduction Above The Baryon Resonance Region, K. V. Dharmawardane, G. E. Dodge, C. E. Hyde-Wright, S. E. Kuhn, L. M. Qin, F. Sabatié, L. B. Weinstein, J. Yun, Et Al., Clas Collaboration Jan 2004

Measurement Of Beam-Spin Asymmetries For Π⁺ Electroproduction Above The Baryon Resonance Region, K. V. Dharmawardane, G. E. Dodge, C. E. Hyde-Wright, S. E. Kuhn, L. M. Qin, F. Sabatié, L. B. Weinstein, J. Yun, Et Al., Clas Collaboration

Physics Faculty Publications

We report the first evidence for a nonzero beam-spin azimuthal asymmetry in the electroproduction of positive pions in the deep-inelastic kinematic region. Data for the reaction e→pe'π+X have been obtained using a polarized electron beam of 4.3 GeV with the CEBAF Large Acceptance Spectrometer at the Thomas Jefferson National Accelerator Facility. The amplitude of the sin ᵠ modulation increases with the momentum of the pion relative to the virtual photon, z. In the range z = 0.5-0.8 the average amplitude is 0.038 ± 0.005 ± 0.003 for a missing mass Mx > 1.1 GeV and 0.037 …

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Measurement Of The Electric Form Factor Of The Neutron At Q² = 0.5 And 1.0 Gev²/C², Jefferson Lab E93-026 Collaboration, G. Warren, F. Wesselmann, H. Zhu, A. Klimenko, S. E. Kuhn, L. Yuan, J. Yun, B. Zihlmann, Et Al. Jan 2004

Measurement Of The Electric Form Factor Of The Neutron At Q² = 0.5 And 1.0 Gev²/C², Jefferson Lab E93-026 Collaboration, G. Warren, F. Wesselmann, H. Zhu, A. Klimenko, S. E. Kuhn, L. Yuan, J. Yun, B. Zihlmann, Et Al.

Physics Faculty Publications

The electric form factor of the neutron was determined from measurements of the →d( →e, e'n)p reaction for quasielastic kinematics. Polarized electrons were scattered off a polarized deuterated ammonia (15ND3) target in which the deuteron polarization was perpendicular to the momentum transfer. The scattered electrons were detected in a magnetic spectrometer in coincidence with neutrons in a large solid angle detector. We find GnE =0.0526 ± 0.0033(stat) ± 0.0026(sys) and 0.0454 ± 0.0054 ± 0.0037 at Q2=0.5 and 1.0 (GeV/c)2, respectively.

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Inclusive Photoproduction Of Lepton Pairs In The Parton Model, A. Psaker Jan 2004

Inclusive Photoproduction Of Lepton Pairs In The Parton Model, A. Psaker

Physics Faculty Publications

In the framework of the QCD parton model, we study unpolarized scattering of high energy real photons from a proton target into lepton pairs and a system of hadrons. For a given parametrization of parton distributions in the proton, we calculate the cross section of this process and show the cancellation of the interference terms.

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Ep → Ep Π⁰ Reaction Studied In The Δ(1232) Mass Region Using Polarization Asymmetries, M. Bektasoglu, L. Ciciani, K.V. Dharmawardane, G. E. Dodge, T.A. Forest, C.E. Hyde-Wright, A. Klein, A. V. Klimenko, S. E. Kuhn, S. Stepanyan, L. B. Weinstein, Et Al., Clas Collaboration Jan 2003

Ep → Ep Π⁰ Reaction Studied In The Δ(1232) Mass Region Using Polarization Asymmetries, M. Bektasoglu, L. Ciciani, K.V. Dharmawardane, G. E. Dodge, T.A. Forest, C.E. Hyde-Wright, A. Klein, A. V. Klimenko, S. E. Kuhn, S. Stepanyan, L. B. Weinstein, Et Al., Clas Collaboration

Physics Faculty Publications

Measurements of the angular distributions of target and double-spin asymmetries for the Δ+(1232) in the exclusive channel → p(→e,e'p)π0 obtained at the Jefferson Lab in the Q2 range from 0.5 to 1.5 GeV2/c2 are presented. Results of the asymmetries are compared with the unitary isobar model [D. Drechsel , Nucl. Phys. A645, 145 (1999)], dynamical models [T. Sato and T. S. Lee, Phys. Rev. C 54, 2660 (1996); S. S. Kamalov , Phys. Lett. B 27, 522 (2001)], and the effective Lagrangian theory [R. M. Davidson , Phys. Rev. …

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Kinematically Complete Measurement Of The Proton Structure Function F₂ In The Resonance Region And Evaluation Of Its Moments, M. Bektasoglu, L. Ciciani, K. V. Dharmawardane, G. E. Dodge, C. E. Hyde-Wright, A. Klein, A. V. Klimenko, S. E. Kuhn, F. Sabatié, S. Stepanyan, L. B. Weinstein, J. Yun, Et Al., Clas Collaboration Jan 2003

Kinematically Complete Measurement Of The Proton Structure Function F₂ In The Resonance Region And Evaluation Of Its Moments, M. Bektasoglu, L. Ciciani, K. V. Dharmawardane, G. E. Dodge, C. E. Hyde-Wright, A. Klein, A. V. Klimenko, S. E. Kuhn, F. Sabatié, S. Stepanyan, L. B. Weinstein, J. Yun, Et Al., Clas Collaboration

Physics Faculty Publications

We measured the inclusive electron-proton cross section in the nucleon resonance region (W <2.5 GeV) at momentum transfers Q2 below 4.5 (GeV/c)2 with the CLAS detector. The large acceptance of CLAS allowed the measurement of the cross section in a large, contiguous two-dimensional range of Q2 and x, making it possible to perform an integration of the data at fixed Q2 over the significant x interval. From these data we extracted the structure function F2 and, by including other world data, we studied the Q2 evolution of its moments, Mn(Q2), in order to estimate higher twist …

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Normal Mode Mixing And Ferromagnetic Resonance Linewidth, Andrew Kunz, R. D. Mcmichael Sep 2002

Normal Mode Mixing And Ferromagnetic Resonance Linewidth, Andrew Kunz, R. D. Mcmichael

Physics Faculty Research and Publications

The normal modes of an inhomogeneous thin film are obtained by diagonalization of the perturbed Hamiltonian. The resulting modes are mixtures of the spin-wave modes and the uniform mode. We find that the ferromagnetic resonance intensity spectrum of the diagonalized system has a Lorentzian profile, and that the results correspond to the two-magnon model for weak perturbations. For stronger perturbations, the density of states is smoothed, and the spectrum becomes asymmetric due to the low-frequency cutoff of the spin-wave manifold. The technique is expected to be valid for perturbation amplitudes that are large enough to invalidate the assumptions of the …

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Gamma Echo Interpreted As A Phase-Shift Induced Transparency, Gilbert R. Hoy, Jos Odeurs Jan 2001

Gamma Echo Interpreted As A Phase-Shift Induced Transparency, Gilbert R. Hoy, Jos Odeurs

Physics Faculty Publications

In the gamma-echo technique a radioactive source is moved, with respect to a nuclear-resonant absorber, during the lifetime of first-excited nuclear state. This introduces a phase shift between the source radiation and the radiation from the absorber. If the source is moved abruptly, introducing a pi phase shift, the time-dependent intensity shows a sharp increase in the intensity at that time, the "gamma echo." Using the recently developed one-dimensional quantum-mechanical model, based on the technique developed by Heitler and Harris, the gamma-echo effect is seen to be a phase-shift-induced transparency. A closed-form solution for the time-dependent transmitted intensity has been …

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Sans Polarization Analysis With Nuclear-Spin-Polarized He-3, T. R. Gentile, Gordon L. Jones, A. K. Thompson, J. Barker, C. J. Glinka, B. Hammouda, J. W. Lynn Jun 2000

Sans Polarization Analysis With Nuclear-Spin-Polarized He-3, T. R. Gentile, Gordon L. Jones, A. K. Thompson, J. Barker, C. J. Glinka, B. Hammouda, J. W. Lynn

Articles

A neutron spin filter based on transmission through nuclear-spin-polarized He-3 gas has been applied to polarization analysis of small angle neutron scattering (SANS). Such spin filters, which are based on the large spin dependence of the absorption of neutrons by He-3, make SANS polarization analysis possible because of their large angular acceptance. In the present experiment, a He-3-based analyzer was employed to separate nuclear scattering into its coherent and spin-incoherent components. Polarized He-3 analyzers were prepared by two different optical pumping methods and installed on the NG3 SANS instrument at the NIST Center for Neutron Research (NCNR). Measurements were taken …

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High Energy Effective Action From Scattering Of Shock Waves In Qcd, Ian Balitsky Jan 2000

High Energy Effective Action From Scattering Of Shock Waves In Qcd, Ian Balitsky

Physics Faculty Publications

The author demonstrates that the amplitude for high-energy scattering can be factorized as a convolution of the contributions due to fast and slow fields. The fast and slow fields interact by means of Wilson-line operators -- infinite gauge factors ordered along the straight line. The resulting factorization formula gives a starting point for a new approach to the effective action for high-energy scattering in QCD.

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Factorization And High-Energy Effective Action, Ian Balitsky Jan 1999

Factorization And High-Energy Effective Action, Ian Balitsky

Physics Faculty Publications

I demonstrate that the amplitude for high-energy scattering can be factorized as a convolution of the contributions due to fast and slow fields. The fast and slow fields interact by means of Wilson-line operators—infinite gauge factors ordered along the straight line. The resulting factorization formula gives a starting point for a new approach to the effective action for high-energy scattering in QCD.

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The Ultraviolet-Optical Albedo Of Broad Emission Line Clouds, Kirk Korista, Gary J. Ferland Mar 1998

The Ultraviolet-Optical Albedo Of Broad Emission Line Clouds, Kirk Korista, Gary J. Ferland

Physics and Astronomy Faculty Publications

We explore the effective UV-optical albedos of a variety of types of broad emission line clouds, as well as their possible effects on the observed spectra of active galactic nuclei (AGNs). An important albedo source in moderately ionized ionization-bounded clouds is that which is due to neutral hydrogen: Rayleigh scattering of continuum photons off the extreme damping wings of Lyα. The photons resulting from this scattering mechanism may contribute significantly to the Lyα emission line, especially in the very broad wings. In addition, line photons emitted near 1200 Å (e.g., N V λ1240) that stream toward the neutral portion of …

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Factorization For High-Energy Scattering, Ian Balitsky Jan 1998

Factorization For High-Energy Scattering, Ian Balitsky

Physics Faculty Publications

I demonstrate that the amplitude for the high-energy scattering can be factorized into a product of two independent functional integrals over “fast” and “slow” fields which interact by means of Wilson-line operators—gauge factors ordered along the straight lines.

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Enhanced Coupling To Microsphere Resonances With Optical Fibers, A. Serpengüzel, S. Arnold, G. Griffel, James A. Lock Apr 1997

Enhanced Coupling To Microsphere Resonances With Optical Fibers, A. Serpengüzel, S. Arnold, G. Griffel, James A. Lock

Physics Faculty Publications

Morphology-dependent resonances (MDR's) of polystyrene microspheres were excited by an optical fiber coupler. For optical elimination of the air-cladding interface at the optical fiber coupler surface, the microsphere was immersed in an index-matching oil. MDR's were observed, even though the relative refractive index between the microsphere and the oil was only 1.09. The observed MDR spectra are in good agreement with the generalized Lorenz-Mie theory and the localization principle. The scattering efficiency into each MDR is estimated as a function of the impact parameter by means of generalized Lorenz-Mie theory. (C) 1997 Optical Society of America.

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Intersubband Lasing Lifetimes Of Sige/Si And Gaas/Algaas Multiple Quantum Well Structures, Greg Sun, L. Friedman, Richard A. Soref Jun 1995

Intersubband Lasing Lifetimes Of Sige/Si And Gaas/Algaas Multiple Quantum Well Structures, Greg Sun, L. Friedman, Richard A. Soref

Physics Faculty Publications

The feasibility of population inversion is studied for the SiGe/Si system and compared with that of GaAs/AlGaAs. Because of the absence of strong polar optical phonon scattering in SiGe/Si, the lifetime difference of the upper and lower lasing levels, to which the population inversion and laser gain are proportional, is consistently an order of magnitude larger than that of GaAs/AlGaAs; nor does it show the sudden drop to zero or negative values when the lasing energy exceeds the optical phonon energy. Both systems studied are superlattices, each period of which consists of three coupled quantum wells and barriers.

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Alpha+28si Cluster Structure As Solitons On The Nuclear Surface, Andrei Ludu Jan 1995

Alpha+28si Cluster Structure As Solitons On The Nuclear Surface, Andrei Ludu

Andrei Ludu

No abstract provided.

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Multinucleon Effects In Muon Capture On ³He At High Energy Transfer, S. E. Kuhn, W. J. Cummings, G. E. Dodge, S. S. Hanna, B. H. King, Y. M. Shin, J. G. Congleton, R. Helmer, R. B. Schubank, N. R. Stevenson, U. Wienands, Y. K. Lee, G. R. Mason, B. E. King, K. S. Chung, J. M. Lee, D. P. Rosenzweig Jan 1994

Multinucleon Effects In Muon Capture On ³He At High Energy Transfer, S. E. Kuhn, W. J. Cummings, G. E. Dodge, S. S. Hanna, B. H. King, Y. M. Shin, J. G. Congleton, R. Helmer, R. B. Schubank, N. R. Stevenson, U. Wienands, Y. K. Lee, G. R. Mason, B. E. King, K. S. Chung, J. M. Lee, D. P. Rosenzweig

Physics Faculty Publications

Energy spectra of both protons and deuterons emitted following the capture of negative muons by 3He nuclei have been measured for energies above 15 MeV. A limited number of proton-neutron pairs emitted in coincidence were also observed. A simple plane wave impulse approximation (PWIA) model calculation yields fair agreement with the measured proton energy spectra, but underpredicts the measured rate of deuteron production above our energy threshold by a large factor. A more sophisticated PWIA calculation for the two-body breakup channel, based on a realistic three-body wave function for the initial state, is closer to the deuteron data at …

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Intervalley Scattering In Gaas And Inp Probed By Pulsed Far‐Infrared Transmission Spectroscopy, Peter N. Saeta, John F. Federici, Benjamin I. Greene, Douglas R. Dykaar Mar 1992

Intervalley Scattering In Gaas And Inp Probed By Pulsed Far‐Infrared Transmission Spectroscopy, Peter N. Saeta, John F. Federici, Benjamin I. Greene, Douglas R. Dykaar

All HMC Faculty Publications and Research

The dynamics of photoexcited electrons in GaAs and InP were studied using the transmission of 200‐fs pulses of far‐infrared radiation in the spectral range 15–100 cm−1. Kinetic traces of the infrared transmission as a function of delay between optical excitation and infrared probe show a probe‐limited decrease in transmission followed by a more gradual (0.7–2 ps) drop to a steady value, consistent with the slow return of electrons from high‐mass satellite valleys. Infrared transmission spectra, analyzed in the context of a Drude model, reveal density‐dependent electron mobilities 3–4 times below equilibrium n‐doped values. Electron‐hole collisions likely account …

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The Effect Of Diamagnetic Dilution On The Spin-Phonon Interaction And Scattering Cross Section In Fe1-Xznxf2, Christian Binek Jan 1992

The Effect Of Diamagnetic Dilution On The Spin-Phonon Interaction And Scattering Cross Section In Fe1-Xznxf2, Christian Binek

Christian Binek Publications

The temperature dependences of the first moments of phonon Raman scattering lines are studied for Fe1-xZnxF2. The diamagnetic dilution diminishes the spin-phonon coupling strength of phonons with both A1g and Eg symmetry in proportion to the decrease in the ordering temperature TN. Moreover, the Eg mode shows an asymmetrical lineshape for Zn concentrations x>0.3. It is explained by an unresolved superposition of two modes, one of which is ascribed to perturbed ZnF2 with broken translational symmetry.

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Effect Of Magnetic And Density Fluctuations On The Propagation Of Lower Hybrid Waves In Tokamaks, George Vahala, Linda L. Vahala, Paul T. Bonoli Jan 1992

Effect Of Magnetic And Density Fluctuations On The Propagation Of Lower Hybrid Waves In Tokamaks, George Vahala, Linda L. Vahala, Paul T. Bonoli

Electrical & Computer Engineering Faculty Publications

Lower hybrid waves have been used extensively for plasma heating, current drive, and ramp-up as well as sawteeth stabilization, The wave kinetic equation for lower hybrid wave propagation is extended to include the effects of both magnetic and density fluctuations. This integral equation is then solved by Monte Carlo procedures for a toroidal plasma. It is shown that even for magnetic/density fluctuation levels on the order of 10-4, there are significant magnetic fluctuation effects on the wave power deposition into the plasma. This effect is quite pronounced if the magnetic fluctuation spectrum is peaked within the plasma. For …

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Reply (To "Comment On 'The Absolute Scattering Cross Section At50 Mhz Of Equatorial Electrojet Irregularities' By Farley Et Al." By N. D'Angelo), D. T. Farley, Bela G. Fejer Dec 1981

Reply (To "Comment On 'The Absolute Scattering Cross Section At50 Mhz Of Equatorial Electrojet Irregularities' By Farley Et Al." By N. D'Angelo), D. T. Farley, Bela G. Fejer

Bela G. Fejer

No abstract provided.

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The Absolute Scattering Cross Section At 50 Mhz Ofequatorial Electrojet Irregularities, D. T. Farley, H. M. Ierkic, Bela G. Fejer Sep 1981

The Absolute Scattering Cross Section At 50 Mhz Ofequatorial Electrojet Irregularities, D. T. Farley, H. M. Ierkic, Bela G. Fejer

Bela G. Fejer

We have made carefully calibrated radar scattering measurements by using the large 50-MHz Jicamarca antenna. Typical results from the altitudes of maximum echo power for the vertically directed beam are σradar ∼1–2 × 10−10 m−1 for strong daytime electrojet conditions with type 1 irregularities present, with values a factor of 10 or so smaller during moderate conditions when only type 2 are observed. These cross sections, which are very large in comparison with those for incoherent scatter (σradar ≃5 × 10−18 m−1 for an electron density of 1011 m−3), are not nearly large enough, however, to cause pseudo-absorption events on …

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Optical Pulse Compression In A Cholesteric Liquid Crystal, D. N. Ghosh Roy, D.V.G.L.N. Rao, H. Bronk Sep 1981

Optical Pulse Compression In A Cholesteric Liquid Crystal, D. N. Ghosh Roy, D.V.G.L.N. Rao, H. Bronk

Physics Faculty Publications

A 20‐ns laser pulse is compressed to nearly 2.5 ns in a 10‐cm‐long sample of liquid‐crystal cholesteryl oleate in the isotropic phase. Pulse compression in a length as short as only 5 cm has been observed. A semiquantitative explanation is given in terms of stimulated Brillouin scattering.

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A Study Of The Elastic Scattering Of 25-Mev He3 Ions From Various Nuclei, Dale D. Armstrong May 1962

A Study Of The Elastic Scattering Of 25-Mev He3 Ions From Various Nuclei, Dale D. Armstrong

Physics & Astronomy ETDs

The validity of the assumption of strong absorption as the basis for the description of the interaction of He3 ions and nuclei was not definitely established and probably cannot be established without the application of more sophisticated theories.

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