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The Lagrange characteristics method and the constants of motion method are applied to various collisional kinetic equations. The relationship between the characteristics and the particle equations of motion is discussed. A special solution of Chandrasekhar equation is given.
Based upon a boundary-value formulation, a new approximate expression is derived for the total axial current on an infinite antenna immersed in an unbounded, cold, collisional magnetoplasma with a dc magnetic field oriented parallel to the antenna. Numerical results are presented for the current distributions over plasma parameters corresponding to each of the eight regions of the Clemmow-Mullaly-Allis diagram and for different values of the collision frequency.
Using semiclassical Coulomb excitation theory, proton collisional excitation and deexcitation cross sections are calculated for all transitions between the Fe(+12) ground configuration levels. Rate constants pertaining to these processes are then derived for coronal temperatures. These rates are shown to be comparable in all cases to the corresponding electron rate constants.
A collisional electromagnetic dispersion relation is derived from two-fluid theory for the interchange mode coupled to the Alfven, acoustic, drift and entropy modes in a partially ionized plasma. The fundamental electromagnetic nature of the interchange model is noted; coupling to the intermediate Alfven mode is strongly stabilizing for finite k sub z. Both ion viscous and ion-neutral stabilization are included, and it was found that collisions destroy the ion finite Larmor radius cutoff at short perpendicular wavelengths.
A collisional electromagnetic dispersion relation is derived from two-fluid theory for the interchange mode coupled to the Alfven, acoustic, drift, and entropy modes in a partially ionized plasma. The fundamental electromagnetic nature of the interchange mode is noted: coupling to the intermediate Alfven mode is strongly stabilizing for finite perturbations of the magnetic field. Both ion-viscous and ion-neutral stabilization are included; and it is found that collisions destroy the FLR (finite Larmor radius) cutoff at short perpendicular wavelengths.
Values of proton collisional cross-sections at coronal energies have been computer for all transitions between magnetic sublevels of the Fe(+12) and Fe(+13) ground configurations. Semiclassical Coulomb excitation theory was used with the resulting truncated Schroedinger equations being directly integrated. The corresponding rate constants for coronal temperatures are presented and comparison is made with previous results.
The paper examines the basic principles underlying the molecular transitions responsible for interstellar molecular spectra. The energy levels of molecules are discussed in detail with special attention given to the Born-Oppenheimer approximation, the electronic Hamiltonian, and the parameters of vibrational and rotational energy. The probabilities for radiative and collisional transitions are calculated. A brief review of techniques for molecular spectroscopy is presented along with methods used to determine collision cross sections on both an experimental and a theoretical basis.
For the purpose of deriving appropriate Lagrangians for plasma equations that include effects of energy loss, the paper examines the inverse problem of the calculus of variations for systems of first- and second-order quasi-linear partial differential equations. This results in convenient forms of the sufficient conditions under which the given differential equations are Euler-Lagrange equations of a Lagrangian. These conditions are then applied to determine the necessary transformation that converts equations, apparently not already in it, into Euler-Lagrange form. The appropriate Lagrangian for a warm collisional plasma is obtained, and the Lagrangian is derived for a resistive transmission line.
The problem of thermal escape is considered in which both the effects of thermospheric winds at the exobase and collisions below the exobase are included in a Monte Carlo calculation. The collisions are included by means of a collisional relaxation layer of a background gas which models the transition region between the exosphere and the thermosphere. The wind effects are considered in the limiting cases of vertical and horizontal flows. Two species are considered: terrestrial hydrogen and terrestrial helium. In the cases of terrestrial hydrogen the escape fluxes were found to be strongly filtered or throttled by collisions at high exospheric temperatures. The model is applied to molecular hydrogen diffusing through a methane relaxation layer under conditions possible on Titan. The results are similar to the case of terrestrial hydrogen with wind enhanced escape being strongly suppressed by collisions. It is concluded that wind enhanced escape is not an important process on Titan.
Ar-40/Ar-39 age dating of a number of shocked ordinary chondrites is interpreted in terms of collisional degassing events of meteorite parent bodies, probably in the asteroid belt. Examples of L, H, and at least one LL chondrite show episodic degassing. Degassing ages suggest several distinct events ranging from about 0.03 aeon to 0.7 aeon and probably higher. All specimens of either the H or L chondrites are not consistent with a single age event. A direct correlation exists between the degree of shock heating and the fraction of argon lost during degassing. However, no chondrite yet analyzed shows complete degassing of its high-temperature phase. Consequently, whole rock K-Ar ages are not accurate monitors of the time of the shock event.
Effects of collisions and finite winds characteristic of a highly perturbed atmosphere on the thermal escape of terrestrial hydrogen and helium are investigated using a Monte Carlo approach. The limiting cases of vertical and horizontal winds are considered, and the relaxation layer between the collisionless exosphere and the collision-dominated thermosphere is modeled as a plane-parallel slab of given column density, depth, and atmospheric density. For both gases, the upwardly injected flux at the base of the relaxation layer is compared with the returning downward flux distribution at the same location; the technique is also applied to the atmosphere of Titan. The results show that inclusion of collisions in the escape model for terrestrial hydrogen with winds effectively throttles the escape process, that collisional throttling is negligible for helium when the exobase temperature is at least 5000 K, and that the escape of a planetary-atmosphere constituent depends on the ratio of its gravitational and kinetic energies as well as on the ratio of its mass to that of the background gas.
The plasma instrument on Mariner 10 carried out measurements of electron density and temperature in the interplanetary medium between heliocentric distances of 0.85 and 0.45 AU. Due to the stable coronal configuration and low solar activity during the period of observation, the radial variations of these quantities could be obtained. The power-law exponent of the core temperature was measured to be -0.3 + or - 0.04, and the halo temperature was found to be almost independent of heliocentric distance. The exponent of the power law for the density variation was 2.5 + or - 0.2 and the extrapolated value at 1 AU was consistent with measured values during the same period. Calculations of the core electron self-collision time, and the core-halo equipartition time were made as a function of radial distance. These measurements indicate a macroscale picture of a Coulomb-collisional core and a collisionless isothermal halo. Extrapolating back to the sun, core and halo temperatures become equal at a radial distance of approx. 2-15 radii.
The paper presents a quantum mechanical formalism for treating ionizing collisions occurring in the presence of an intense laser field. Both the intense laser radiation and the internal electronic continuum states associated with the emitted electrons are rigorously taken into account by combining discretization techniques with expansions in terms of electronic-field representations for the quasi-molecule-plus-photon system. The procedure leads to a coupled-channel description of the heavy-particle dynamics which involves effective electronic-field potential surfaces and continua. It is suggested that laser-influenced ionizing collisions can be studied to verify the effects of intense laser radiation on inelastic collisional processes. Calculation procedures for electronic transition dipole matrix elements between discrete and continuum electronic states are outlined.
Proton collisional excitation cross sections at solar coronal energies for the Fe(11+) /3S(2)3p(3)/ ground-configuration transitions are presented. Semiclassical Coulomb excitation theory is used with direct integration of the resulting Schroedinger equation. The rate constants at coronal temperatures are compared with the corresponding ones for electron impact excitation.
In a simulation of collisional and gravitational interaction in the early solar system, planets of approximately 500 km diameter are generated from an initial swarm of kilometer-sized planetesimals. Collisions are treated in accordance with experimental and theoretical impact results (such as rebound, cratering, and catastrophic fragmentation) for a variety of materials whose parameters span plausible values for early solid objects. In this model, the small planets form in approximately 10,000 yr; during this time, most of the mass of the system continues to reside in particles near the original size. It is thought that the few 500-km planets may act as 'seeds' for the subsequent gradual accretional growth into full-sized planets.
A semiclassical approach based on the propagation of classical trajectories on potential surfaces analytically continued into the complex plane, together with a discretization procedure, has been developed for the problem of collisional ionization. Based on Franck-Condon considerations the formalism is reduced to that of the two-state approximation. Preionization loss and tunnelling beyond turning points have not been considered. Calculated partial ionization cross sections for the Ar-He system show good agreement with a fully quantum mechanical treatment.
Proton collisional excitation cross sections and rate constants are presented for transitions between the 3P(J) fine-structure levels of the lowest-lying sp configurations in a number of astrophysically important ions belonging to the Be and Mg isoelectronic sequences. The calculations were made by direct integration of the Schroedinger equation resulting from semiclassical Coulomb excitation theory. The cross sections and rate constants for the 3P(J) transitions in the lowest-lying P(2) configurations are expected to be similar to those for the corresponding sp configuration transitions, and this is illustrated for C III. For the high-temperature ion Ca XVII alpha particle excitation is shown to be unimportant for situations involving ordinary values of the He/H abundance ratio. A simple, but apparently accurate method for determining certain radial integrals for low-lying excited configurations is proposed.
The collisional and dynamical processes in moon and planet formation are discussed. A hydrodynamic code of collision calculations, the orbital element changes due to gravitational scattering, a validation of the mass shifting algorithm, a theory of rotations, and the origin of asteroids are studied. A numerical model of planet growth is discussed and a methodology to evaluate the rate at which megaregolith increases its depth as a function of total accumulate number of impacts on an initially smooth, coherent surface is described.