Quasi-transverse Research Articles

FOCUSING OF QUASI–TRANSVERSE MODES IN ZINC AT ULTRASONIC FREQUENCIES

The intense focusing of quasi-transverse (QT) modes along the symmetry axis of zinc is observed by various methods at ultrasonic frequencies. The focusing is associated with a conical point on the QT sheet of the ray surface, and thereby the phenomenon of external conical refraction. The observations have been made first, with pointlike longitudinal (L) and shear (S) piezoelectric transducers acting as acoustic source and detector; second, with a breaking capillary source with Heaviside time-dependence and a capacitive displacement detector at epicenter; and third, using a laser source and piezoelectric detector. The amplitudes of the signals observed by the piezoelectric sources and detectors in both time and frequency domains show intense focusing in the symmetry direction [0001], side-lobed by diffraction fringes caused by the interferences between collinear rays associated with different wave vectors k. A broadband capacitive displacement signal shows a very sharp deep minimum associated with the arrival of the conical rays, being consistent with the calculation of the dynamic Green's function and the theory of phonon focusing for the medium.

Imaging of group velocity surfaces in a cuspidal region of zinc by laser-generated ultrasonic waves

An image of group velocity surfaces within and outside a cuspidal region of a (0001) oriented zinc crystal is obtained with a pointlike scanning laser source and a fixed longitudinal (L) mode piezoelectric detector. Because of axisymmetric excitation and sensing, the group velocity surface of the pure transverse (PT) mode, being shear horizontally (SH) polarized, is absent in the obtained image. In the cuspidal region the quasi transverse (QT) mode has three group velocity branches in a given direction: the fast QT (FQT) branch, the intermediate speed QT (IQT) branch, and the slow QT (SQT) branch. The laser imaging clearly shows the wave fronts of the quasi longitudinal (QL), IQT, and SQT rays in the cuspidal region. Near the epicentral [0001] direction, the arrivals of the head wave (HW) and SQT rays are almost simultaneous and their wave fronts are not distinct. However, farther from the epicentral direction, they separate and outside the cuspidal region the imaging shows the group velocity surfaces of the QL, HW, and SQT rays.

Reversal of the Sense of Polarisation in Solar and Stellar Radio Flares

AbstractIt is shown that numerical integration of the equation of polarisation transfer for generalised Faraday rotation provides an alternative to mode-coupling theory for treating propagation through a quasi-transverse (QT) region. At a QT region, where the sign of the component of the magnetic field along the ray path reverses, the sense of circular polarisation reverses below a frequency ωt, and is unchanged above ωt. There is a long-standing difficulty in the interpretation of the polarisation of radio emission from bipolar regions on the Sun: observational and theoretical estimates of ωt appear inconsistent. The alternative approach may help resolve this difficulty.

Direct determination of group velocity surfaces in a cuspidal region in zinc

A direct determination of group velocity surfaces of zinc from the group velocities measured in various directions within and without a cuspidal region is described. A zinc crystal disk oriented in the symmetry direction [0001] is used as a specimen. Quasilongitudinal (QL) and quasitransverse (QT) elastic pulses propagating in a wide range of directions are generated by a broadband pointlike source activated by the fracture of a tiny glass capillary on the surface of the specimen and they are detected at epicentral and off-epicentral positions on the opposite face by a miniature capacitive transducer which senses a displacement normal to the surface. The group velocities associated with QL and QT modes are directly measured from the detected signals. The QL mode arrival is easily identified as the first point from which the signal jumps from the noise level. In the cuspidal region, there are three branches of QT group velocity: fast QT (FQT) ray branch, intermediate speed QT (IQT) ray branch, and slow QT (SQT) ray branch. It is observed that the arrivals of FQT, IQT, and SQT rays correspond to the first zero crossing, to the first negative minimum, and to the second local minimum, respectively, in the displacement signal. In the epicentral signal, both IQT and SQT rays coincide, whose arrivals correspond to single sharp negative minimum, and the FQT ray arrival is found at the first zero crossing after the arrival of a longitudinal wave. Outside the cuspidal region, both FQT and IQT branches disappear and so do their corresponding characteristics, i.e., the zero crossing and sharp negative minimum in the displacement curve. The SQT ray arrival outside the cuspidal region is observed at the first sharp minimum in the displacement signal. Finally, the group velocities of pure transverse waves with shear horizontal polarization propagating in various directions of a [0001] zonal section within and without the cuspidal region are measured with the miniature piezoelectric shear transducer (PZT) source and shear PZT detector.

Focusing of fast transverse modes in silicon and slow transverse modes in zinc

This paper presents focusing of fast transverse (FT) modes in silicon and slow transverse (ST) modes in zinc, both observed at utrasonic frequencies. Using a (001)-oriented silicon disk, the FT modes are generated and detected by two tiny shear PZT transducers, both polarized in the [100] direction. One transducer fixed on the bottom surface acts as a source and the other serves as a detector scanning the top surface along the [100] direction across various points on the [010] axis at some distances away from the epicenter. The observed focusing pattern indicates strong concentration of FT modes on the narrow band about the (100) plane containing the source. For a (001)-oriented zinc crystal, strong focusing of ST or quasi-transverse (QT) modes toward the symmetry direction is observed: first in theoretical and experimental, epicentral Green’s functions; second with very small PZT source and PZT detector; finally with focused pulsed laser excitation and small PZT detector. The focusing patterns observed both in silicon and in zinc are consistent with the results predicted by the theory of phonon focusing. [Work supported by ONR.]

Main-signal filamentation in free-electron lasers with deeply trapped particles

The filamentation of electromagnetic waves in a free-electron laser with deeply trapped electrons is analysed. This instability is the result of particle bunching along transverse directions (with respect to the fast wave vector), as opposed to the untrapped-electron case, where it is a result of longitudinal bunching. Two cases are considered: (i) the non-resonant or reactive one, with purely imaginary growth rates; and (ii) the resonant one, with large (small) values of the real (imaginary) part of the perturbing frequency. In particular, we find that the reactive instability occurs only when the wiggler amplitude is unusually large. On the other hand, we show that the resonant process (with frequencies close to the synchrotron frequency) may be relevant for conventional free-electron lasers and that the growth rate for quasi-trans verse perturbations may be larger than that corresponding to longitudinal perturbations. Owing to the inhomogeneity and anisotropy of our system, low-frequency magnetic fields are generated. These fields, as well as the transverse electric fields, are analysed, and their role in the low-frequency dynamics is clarified.

Approximations in magnetoionic theory

Approximate formulae exist for the two refractive indices and the two wave polarizations in a cold magnetoplasma, known as the QL (quasi-longtitidinal) and QT(quasi-transverse) approximations. Some of the commonly used forms of these formulae are wrong. The correct versions are given and the range of their validity is examined.

Group velocity of whistlers in a two‐ion plasma

Computations of the group velocity of whistlers in a two‐ion plasma show that a quasi‐longitudinal (QL) right‐handed polarized wave (electron wave) has a minimum group velocity at the so‐called crossover frequency; a QL left‐handed polarized wave has a maximum group velocity at the same frequency. A quasi‐transverse (QT) electron wave has a minimum group velocity at the ion hybrid frequency. In an oxygen/hydrogen plasma this minimum occurs only for almost perpendicular waves, whereas in a helium/hydrogen plasma it occurs also for waves propagating off perpendicular to the magnetic field. We also find that a small concentration of helium in a hydrogen plasma introduces a ‘stop band’ for quasi‐transverse waves with frequencies just above the helium gyrofrequency. The theoretical results are used to interpret satellite observations of quasi‐transverse low‐frequency whistlers.

On the determination of mean ionospheric height related to Faraday rotation experiment

Ionospheric refraction of HF signals from low orbit satellites is investigated and its significance in the determination of mean ionospheric height using the quasi-transverse (QT) point on Faraday fading records is discussed.

Characteristics of the electric field far from and close to a radiating antenna around the lower hybrid resonance in the ionospheric plasma

From a basic discussion of the behaviour of VLF waves propagated almost perpendicularly to the earth 's magnetic field, the lower hybrid resonance (LHR) frequency is seen as a boundary between compressional Alfv én waves and electrostatic sound waves. The disparity of the wavelengths involved leads to a fundamental difference between the characteristics of the AC electric field far from and close to the source.Some detailed observations of this field are presented, from an experiment that used both a mother-daughter technique for large distance measurements and a quadrupole probe technique for the local field, and that was performed in the equatorial ionosphere. The frequency dispersion of quasi-transverse (QT) waves received at a large distance and the amplitude-frequency response of the VLF quadrupole probe are compared with a theoretical analysis for the warm ionospheric plasma. From this analysis, the possibility is established of using the properties of fast and slow waves in active experiments, for measuring simultaneously the LHR, the electron density, a hybrid ion-electron thermal velocity and possibly the plasma drift velocity.

Wave propagation in a transversely isotropic heat‐conducting elastic material

A transversely isotropic elastic material can transmit three body waves in each direction, a quasi-longitudinal (QL) wave, a quasi-transverse (QT) wave, and a purely transverse wave. When the material is able to conduct heat the properties of small amplitude QL and QT waves are modified and we consider here the analysis of such thermo-elastic interactions in plane harmonic disturbances. The modified QL and QT waves are both found to exhibit frequency-dependent dispersion and damping of the kind known to affect dilatational waves in isotropic heat-conducting elastic materials, and in addition we show that the particle paths in the associated motions are ellipses with their axes inclined to the wave normal. This latter effect is peculiar to body waves travelling in anisotropic heat-conducting elastic materials and seems not to have been studied in detail hitherto. Numerical results referring to the propagation of plane harmonic body waves in a single crystal of zinc are presented and discussed.

Magnetoionic Mode Coupling at High Frequencies.

view Abstract Citations (179) References (6) Co-Reads Similar Papers Volume Content Graphics Metrics Export Citation NASA/ADS Magnetoionic Mode Coupling at High Frequencies. Cohen, M. H. Abstract The theory of magnetoionic mode coupling is extended to the case in which the superposed magnetic field varies in amplitude and direction. Calculations are limited to the case X, Y, Z « 1 and to the case of a medium stratified in planes parallel to the wave front. In the quasi-longitudinal (QL) case, there is a "transitional" frequency, ft, such that, when f «ft, the modes are weakly coupled and the ordinary magnetoionic theory prevails; when J «f , there is strong coupling, and the wave propagates as if the magnetic field were absent. The QL transitional frequency is given by ft = 3 X 10- NS, where N is electron density (cm i) and S is the scale of the magnetic field (cm). In the ionosphere and in interplanetary and interstellar regions, ft is estimated to be cps; thus the magnetoionic modes at radio frequencies are always weakly coupled in QL regions. In quasi-transverse (QT) regions the coupling may be much stronger because the characteristic polarizations change rapidly with 0. The QT transitional frequency is given by j4. = 1017 NSB3, and the modes are weakly or strongly coupled according to whether f4 «f4t or J4 »jt. Estimates of ft are on the order of tens of megacycles (ionosphere) and cps (interstellar and interplanetary regions). A circularly polarized wave has its sense of rotation reversed when propagating through a QT region, provided that the coupling is weak there. If the coupling is strong, the polarization is constant across the QT region. This mechanism might explain the commonly observed polarization reversal for the wide-band solar microwave bursts. This wide-band radiation propagates through a QT region above a sunspot, and at the earth the sense of rotation reverses at the QT transitional frequency. Tbe possibility that the ionosphere and the interplanetary gas can interfere with the sense of rotation of solar radio bursts is also examined, in terms of coupling in the QT regions. Some other special situations that might arise in QT regions are briefly considered. These include the production of linear polarization, effects on differential absorption of the two magnetoionic modes, and differences in polarization that might result when either the source or the observer is in the QT region. Publication: The Astrophysical Journal Pub Date: May 1960 DOI: 10.1086/146878 Bibcode: 1960ApJ...131..664C full text sources ADS |

The quasi-transverse (Q.T.) approximation to Appleton's magneto-ionic equation

It is shown that the usually accepted form of the quasi-transverse (Q.T.) approximation to Appleton's magneto-ionic equation is incorrect and the correct form is given.