On refined Reissner-type theories of plates
Reissner-type equations for linear stress distribution determination through plate thickness
PLATE THEORY↗
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A CONTRIBUTION TO THE SPECTRAL TYPE THEORY. IV. FORMATION OF LINES IN STELLAR SPECTRA
Stellar spectrum lines - formation and intensity
SPECTRAL LINE↗
Theory of Type 3 and Type 2 Solar Radio Emissions
The main features of some current theories of type III and type II bursts are outlined. Among the most common solar radio bursts, type III bursts are produced at frequencies of 10 kHz to a few GHz when electron beams are ejected from solar active regions, entering the corona and solar wind at typical speeds of 0.1c. These beams provide energy to generate Langmuir waves via a streaming instability. In the current stochastic-growth theory, Langmuir waves grow in clumps associated with random low-frequency density fluctuations, leading to the observed spiky waves. Nonlinear wave-wave interactions then lead to secondary emission of observable radio waves near the fundamental and harmonic of the plasma frequency. Subsequent scattering processes modify the dynamic radio spectra, while back-reaction of Langmuir waves on the beam causes it to fluctuate about a state of marginal stability. Theories based on these ideas can account for the observed properties of type III bursts, including the in situ waves and the dynamic spectra of the radiation. Type 11 bursts are associated with shock waves propagating through the corona and interplanetary space and radiating from roughly 30 kHz to 1 GHz. Their basic emission mechanisms are believed to be similar to those of type III events and radiation from Earth's foreshock. However, several sub-classes of type II bursts may exist with different source regions and detailed characteristics. Theoretical models for type II bursts are briefly reviewed, focusing on a model with emission from a foreshock region upstream of the shock for which observational evidence has just been reported.
Robinson, P. A.↗
Unified theory of type I and type II irregularities in the equatorial electrojet
A nonlinear unified theory of type I and II irregularities is presented that explains their principal observed characteristics. The power spectrum is predicted by using Kolmogoroff-type conservation law for the power flow in cascading eddies.
Sudan, R. N.↗
Stochastic Growth Theory of Type 3 Solar Radio Emission
The recently developed stochastic growth theory of type 3 radio sources is extended to predict their electromagnetic volume emissivities and brightness temperatures. Predicted emissivities are consistent with spacecraft observations and independent theoretical constraints.
Robinson, P. A.↗
Constraints on Nonlinear and Stochastic Growth Theories for Type 3 Solar Radio Bursts from the Corona to 1 AU
Existing, competing theories for coronal and interplanetary type III solar radio bursts appeal to one or more of modulational instability, electrostatic (ES) decay processes, or stochastic growth physics to preserve the electron beam, limit the levels of Langmuir-like waves driven by the beam, and produce wave spectra capable of coupling nonlinearly to generate the observed radio emission. Theoretical constraints exist on the wavenumbers and relative sizes of the wave bandwidth and nonlinear growth rate for which Langmuir waves are subject to modulational instability and the parametric and random phase versions of ES decay. A constraint also exists on whether stochastic growth theory (SGT) is appropriate. These constraints are evaluated here using the beam, plasma, and wave properties (1) observed in specific interplanetary type III sources, (2) predicted nominally for the corona, and (3) predicted at heliocentric distances greater than a few solar radii by power-law models based on interplanetary observations. It is found that the Langmuir waves driven directly by the beam have wavenumbers that are almost always too large for modulational instability but are appropriate to ES decay. Even for waves scattered to lower wavenumbers (by ES decay, for instance), the wave bandwidths are predicted to be too large and the nonlinear growth rates too small for modulational instability to occur for the specific interplanetary events studied or the great majority of Langmuir wave packets in type III sources at arbitrary heliocentric distances. Possible exceptions are for very rare, unusually intense, narrowband wave packets, predominantly close to the Sun, and for the front portion of very fast beams traveling through unusually dilute, cold solar wind plasmas. Similar arguments demonstrate that the ES decay should proceed almost always as a random phase process rather than a parametric process, with similar exceptions. These results imply that it is extremely rare for modulational instability or parametric decay to proceed in type III sources at any heliocentric distance: theories for type III bursts based on modulational instability or parametric decay are therefore not viable in general. In contrast, the constraint on SGT can be satisfied and random phase ES decay can proceed at all heliocentric distances under almost all circumstances. (The contrary circumstances involve unusually slow, broad beams moving through unusually hot regions of the Corona.) The analyses presented here strongly justify extending the existing SGT-based model for interplanetary type III bursts (which includes SGT physics, random phase ES decay, and specific electromagnetic emission mechanisms) into a general theory for type III bursts from the corona to beyond 1 AU. This extended theory enjoys strong theoretical support, explains the characteristics of specific interplanetary type III bursts very well, and can account for the detailed dynamic spectra of type III bursts from the lower corona and solar wind.
Cairns, Iver H.↗
Type 2 and type 3 burst theory
The present state of the theory of type 3 bursts is reviewed by dividing the problem into the exciting agency, radiation source, and propagation of radiation between the source and the observer. In-situ measurements indicate that the excitors are electron streams of energy about 40 keV which are continuously relaxing. An investigation of neutralization of an electron stream indicates that n sub s is much less than 100,000 n sub e, where n sub s is the stream density and n sub e the coronal electron density. In situ observations are consistent with this result. An analysis of propagation of electrons in the current sheets of coronal streamers shows that such propagation at heights greater than 1 solar radius is impossible. The mechanisms for radiation are reviewed; it is shown that fundamental radiation at high frequencies (approximately 100 MHz) is highly beamed in the radial direction and that near the earth second harmonic radiation must be dominant. Because of beaming of the fundamental at high frequencies, it can often be quite weak near the limb so that the second harmonic is dominant. In considering propagation to the observer, the results of scattering of radiation are discussed. The present state of the theory of type 2 bursts is reviewed in the same manner as type 3 bursts.
Smith, D. F.↗
The synchrotron-maser theory of type II solar radio emission processes - The physical model and generation mechanism
A theory is proposed to explain the generation mechanism of type II solar radio bursts. It is suggested that the shock wave formed at the leading edge of a coronal transient can accelerate electrons. Because of the nature of the acceleration process, the energized electrons can possess a 'hollow-beam' type distribution function. When the electron beam propagates along the ambient magnetic field to lower altitudes and attains larger pitch angles, a synchrotron-maser instability can set in. This instability leads to the amplification of unpolarized or weakly polarized radiation. The present discussion incorporates a model which describes the ambient magnetic field and background plasma by means of MHD simulation. The potential emission regions may be located approximately, according to the time-dependent MHD simulation. Since the average local plasma frequency in the source region can be evaluated from the MHD model, the frequent drift associated with the radiation may be estimated. The result seems to be in good agreement with that derived from observations.
Wu, C. S.↗
Theory of type 3b solar radio bursts
During the initial space-time evolution of an electron beam injected into the corona, the strong beam-plasma interaction occurs at the head of the beam, leading to the amplification of a quasi-monochromatic large-amplitude plasma wave that stabilizes by trapping the beam particles. Oscillation of the trapped particles in the wave troughs amplifies sideband electrostatic waves. The sidebands and the main wave subsequently decay to observable transverse electromagnetic waves through the parametric decay instability. This process gives rise to the elementary striation bursts. Owing to velocity dispersion in the beam and the density gradient of the corona, the entire process may repeat at a finite number of discrete plasma levels, producing chains of elementary bursts. All the properties of the type IIIb bursts are accounted for in the context of the theory.
Smith, R. A.↗
Theory of type IIIb solar radio bursts
During the initial space-time evolution of an electron beam injected into the corona, the strong beam-plasma interaction occurs at the head of the beam, leading to the amplification of a quasi-monochromatic large-amplitude plasma wave that stabilizes by trapping the beam particles. Oscillation of the trapped particles in the wave troughs amplifies sideband electrostatic waves. The sidebands and the main wave subsequently decay to observable transverse electromagnetic waves through the parametric decay instability. This process gives rise to the elementary striation bursts. Owing to velocity dispersion in the beam and the density gradient of the corona, the entire process may repeat at a finite number of discrete plasma levels, producing chains of elementary bursts. All the properties of the type IIIb bursts are accounted for in the context of the theory.
Smith, R. A.↗
Nonlinear theory of type I irregularities in the equatorial electrojet
By allowing for the effect of wave electric fields on electron orbits, a nonlinear dispersion relation for type I irregularities is obtained. This relation predicts (1) isotropy of the Doppler shift with elevation, (2) a limiting phase velocity equal to the ion acoustic speed, and (3) a saturation amplitude which is maximum for horizontally propagating waves and decreases with elevation. With the theory presented here, the in situ electric field measurements of Pfaff et al. (1980) in the electrojet environment could provide a quantitative check for the theory of orbit diffusion by stochastic electric fields.
Sudan, R. N.↗
New heavenly double copies
The double copy relates scattering amplitudes and classical solutions in Yang-Mills theory, gravity, and related field theories. Previous work has shown that this has an explicit realisation in self-dual YM theory, where the equation of motion can be written in a form that maps directly to Plebański’s heavenly equation for self-dual gravity. The self-dual YM equation involves an area-preserving diffeomorphism algebra, two copies of which appear in the heavenly equation. In this paper, we show that this construction is a special case of a wider family of heavenly-type examples, by (i) performing Moyal deformations, and (ii) replacing the area-preserving diffeomorphisms with a less restricted algebra. As a result, we obtain a double-copy interpretation for hyper-Hermitian manifolds, extending the previously known hyper-Kähler case. We also introduce a double-Moyal deformation of the heavenly equation. The examples where the construction of Lax pairs is possible are manifestly consistent with Ward’s conjecture, and suggest that the classical integrability of the gravity-type theory may be guaranteed in general by the integrability of at least one of two gauge-theory-type single copies.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
Concerning a new theory of Type I comet tails
Enhanced density plasma confinement hypothesis for formation of Type I comet tails following interaction with solar wind
COMET↗
Concerning a new theory of type I comet tails.
Type I comet trail relation to interaction of solar wind with geomagnetic field, noting tail ray formation mechanism, interplanetary plasma measurements, etc
INTERPLANETARY GAS↗
Progress and problems in the theory of type III solar radio emission
The experimental and theoretical status of type III solar radio emission is considered in detail. Very recent developments which are relevant to the underlying plasma physics are emphasized. In particular, the identity of the submegahertz emissions as fundamental, or second harmonic, the degree of correlation between emissivities, electron streams, and plasma (Langmuir) waves, paradoxes concerned with the time-ordering of these phenomena, and the role of background density irregularities and ion-acoustic turbulence in the solar wind, are discussed. From the theoretical point of view, the current picture of the underlying Langmuir turbulence, including such effects as the interaction between Langmuir waves and stream electrons, induced scatter off ions, and strong turbulence effects such as modulational instability and soliton collapse, is discussed.
Goldman, M. V.↗
On the Theory of Type 1 X-Ray Bursts: The Energetics of Bursts and the Nuclear Fuel Reservoir in the Envelope
The observed properties of type 1 X-ray bursts from 4U/MXB 1636-53 and those of models of thermonuclear flashes on accreting neutron stars are compared. Ways to explain variations in the burst recurrence properties without an apparent correlation with the accretion rate, including the rapid succession of bursts at intervals 10 min are discussed. The strongest X-ray bursts, which occur after a very long interval, are well described by thermonuclear flash models with simple accumulation of accreted fuel, and a spherically symmetric structure in the burning shell. The majority of observed bursts, however, occur after much shorter intervals, and radiate much smaller amounts of energy, by a factor of up to 10 times that predicted by the spherical models. An ignition mechanism of the bursts is proposed in terms of elemental mixing and dissipative heating associated with hydrodynamical instabilities in the neutron star envelope caused by angular momentum carried inward by accreted gas.
Fujimoto, Masayuki Y.↗
On the theory of type I X-ray bursts - The energetics of bursts and the nuclear fuel reservoir in the envelope
A comparison is made between the observed properties of type I X-ray bursts from 4U/MXB 1636-53 and those of models of thermonuclear flashes on accreting neutron stars. Possible explanations of variations in the burst recurrence properties without an apparent correlation with accretion rate are discussed. The strongest bursts with photospheric expansion are described well by current spherically symmetric models. The observed weak bursts suggest a mechanism that can promote the inward propagation and heating of accreted fuel so as to give rise to thermonuclear runaways much earlier than expected from spherical models. A sufficient amount of fuel to feed the weak bursts can be stored in the outer layers for neutron stars with radii greater than 8 km. The proposed mechanism and fuel storage can resolve the longstanding problem of bursts in rapid succession with intervals shorter than about 10 minutes. The proposed model explains the variation of burst peak fluxes observed from 4U/MSB 1636-53.
Fujimoto, Masayuki Y.↗
A theory of solar type III radio bursts
A theory of type III bursts is reviewed. Energetic electrons propagating through the interplanetary medium are shown to excite the one dimensional oscillating two stream instability (OTSI). The OTSI is in turn stabilized by anomalous resistivity which completes the transfer of long wavelength Langmuir waves to short wavelengths, out of resonance with the electrons. The theory explains the small energy losses suffered by the electrons in propagating to 1 AU, the predominance of second harmonic radiation, and the observed correlation between radio and electron fluxes.
Goldstein, M. L.↗