W. B. Thompson

Covariant Poisson brackets for classical fields

Poisson brackets that are spacetime covariant are presented for a variety of relativistic field theories. These theories include electromagnetism, general relativity, and general relativistic fluids and plasmas in Eulerian representation. The examples presented suggest the development of a general theory; the beginnings of such a theory are presented. Our covariant bracket formalism provides a general setting for, amongst other things, clarifying the transition from the covariant formalism to the dynamical 3 + 1 Hamiltonian formalism of Dirac and Arnowitt, Deser, and Misner. We illustrate the relevant procedures with electromagnetism.

Elastic and inelastic scattering in orbital clustering

A Boltzmann-type equation is used to examine the effects of inelasticity on scattering between particles in Kepler orbits. A Fokker-Planck equation is found which predicts either radial clustering or diffusion. (auth)

In defense of anti-matter

There appears to be a prejudice in the astronomical world against an obvious high-energy source—the mutual annihilation of matter and anti-matter. In favor of this prejudice is the lack of any convincing evidence of the presence of naturally occurring anti-matter. Only recently have cosmic-ray antiprotons been detected (cf. Goldenet al., 1979), and then in numbers consistent with secondary production in flight, while annihilation X-rays have also been detected, but again in circumstances where they might well be attributed to secondary effects of some other high-energy process.

Neoclassical plasma transport in axisymmetric toroidal systems

The variational technique for calculating all the neoclassical transport processes in the banana regime, developed by Rosenbluth, Hazeltine, and Hinton for the case of tokamak with small rotational transform and large aspect ratio, is generalized to arbitrary axisymmetric toroidal systems with a small fraction of trapped particles. The use of the scalar magnetic potential as a coordinate, as in Rutherfords treatment of the Lorentz model, is eliminated by the use of a coordinate‐free solution procedure, allowing the treatment of nonvacuum fields. As an example, results are given for doublet II.

Fluctuations in guiding center plasma in two dimensions

Statistical mechanics is developed for a two‐dimensional guiding center plasma. Because there is no kinetic energy associated with guiding center motion, this development is unconventional. Thermal equilibrium is discussed, and an interesting limiting case is noted. Using the random phase assumption, a kinetic equation for the density fluctuations is obtained, which has thermal equilibrium and its limiting form as the only stationary states. However, despite the phase averaging this kinetic equation is reversible and when disturbed the system oscillates about equilibrium. Similar oscillatory behavior appears in the microscopic correlation function of the fluctuations, and the oscillation frequencies are obtained explicitly; however, these oscillations do not significantly change the macroscopic diffusion coefficient derived earlier by McNamara and Taylor.

Current Collection by a Long Wire in Near-Earth Orbit

Investigation of the current collected by a long wire in space has application to long antennas and the proposed space shuttle tethered subsatellite. Langmuirs result for current collection by a moving probe in a plasma is used to obtain expressions for the voltage and current as functions of position along a wire. Two cases are considered: firstly, one end of the wire is grounded to the plasma and secondly, the wire is allowed to assume a natural grounding point. Results are obtained as a function of the wire resistivity, length and diameter for various particle densities. Calculations for a 2mm diameter copper wire show that a current of 0.066 amperes of oxygen ions will be collected by a tether of 10 km in length.

On the propagation of energetic ion beams through a fusion target chamber

This article treats some aspects of the propagation of a highly energetic heavy ion beam through a fusion target chamber. The stability of this beam to various perturbations is especially emphasized, first for vacuum propagation, and then for propagation through a background plasma. The results are illustrated by detailed calculations for a beam carrying 3 kA of current and consisting of 70GeV, singly ionized uranium ions. We find that such a beam will propagate stably through the target chamber. As a second example we have applied some of our results to the recently proposed I 53+ concept in which up to a hundred beams of 40GeV iodine ions each carrying 4.2 kA of current are directed to the target. Our conclusions for this case are less optimistic, as such beams are likely to be subject to space-charge problems due to the increased value of v/γ and are prone to instabilities of the two-stream type.

The cosmogonical separation of matter and antimatter

Alfvén has shown that in the symmetric cosmology of O. Klein, matter and antimatter can be separated as clouds of solar masses. By considering the dynamics of these clouds it is shown that a further separation process driven by the release of rest energy can separate matter on a galactic scale.

Scattering from magnetic fluctuationst

Scattering of optical and radio frequency radiation from electron density fluctuations in a plasma has been extensively studied and bids fair to become a useful diagnostic tool (see, for example, Davies & Ramsden, 1964, 1966). The scattered spectrum, although difficult to observe, contains a great deal of information. The electron density, ion and electron temperatures, the shape of the tail of the electron distribution function, spectral fluctuations in unstable systems, the magnitude and direction of the magnetic field and the charge to mass ratio of the ions present all seem to be contained in it.

PASSIVE CURRENT COLLECTION

Electromagnetic applicatons of tethers usually depend on the collection of fairly large currents from the plasma environment. A number of approaches have been considered-particle beams, plasma sources and simple conducting probes. Here we discuss the last of these, and investigate the problem of collecting substantial currents to a conducting plate at a potential significantly different from that of the plasma through which it passes, with the object of understanding the fundamental processes, determining the voltage current characteristics, and estimating the size of the conductor needed to collect a given current. Superficially, this seems like the classic Langmuir probe problem; however, there are major noveltieethe collected current is large, the magnetic field is strong, the probe moves supersonically with respect to the plasma, and is moreover so large that, with respect to the plasma, it is not at constant potential. In addition the electron mean free path is so large that collisions are negligible. What we have discovered is that useful currents can be collected from large, but possible, probes and that the current-voltage characteristics depend on the probe geometry, and do not show the exponential character of the Langmuir probe. The details of the collection process are extremely complex, and depend essentially on fluctuations developed in the plasma by instabilities produced by the current collection itself; a purely laminar collection process does not seem possible under these conditions. Since reliable, predictive theories of plasma turbulent effects are not really available, detailed calculations seem unpromising, and model experiments important.