"In this paper we solve for the diffracted wave which results when a weak hydromegnetic shock impinges on a rigid perfectly conducting half plans."

"Adlam and Allen and Davis, Lust, and Schluter have studied nonlinear plane-waves, propagating normal to the magnetic field, in a cold plasma. One solution of particular interest is a solitary wave, or single pulse. We present a method for solving the analogous problem for a plasma with finite temperature, in the limiting case where the amplitude of the wave is small and where, consequently, the width of the waver is very large."

"A generalized discontinuous solution was found for the adiabatic two- fluid equations in the steady state: it covers the case of strong shocks and enables a complete account to be made of the steady state solutions of these equations. By considering a piston problem using numerical methods, time dependent solutions of the equations were also found; these rapidly steepened and converged to the discontinuous steady state solutions whenever these existed."

"Activities related to Project Sherwood are summarized under the following topics: propagation of waves, macroscopic magneto-fluid dynamics, stability, particle orbits, cusped geometries, collisionless shock theory, and other subjects."

"The canonical theory of motion of a charged particle in a slowly varying, static electromagnetic field is formulated. The Hamiltonian is written down explicitly in terms of the coordinates of the gyration and the drift. The method of approach is analogous to that of the canonical formalism with subsidiary condition as used in theories of collective motion in many-body systems, such as the motion of the center of gravity. In the lowest order of the perturbation, it is shown that the Hamiltonian for the drift motion averaged over the gyration phase is given by adding to the original Hamiltonian a potential term equal to the product of the magnetic moment and the magnetic field strength."

"A finite difference approximation to a non-linear set of parabolic differential equations arising in shallow water theory is given. These difference equations were used to determine the shape and rate of propagation of a hum of fluid down a channel of constant depth. The hump of fluid was found to spread instead of steepen, as is the case in the usual shallow water theory."

"The one-dimensional propagation of disturbances in an inviscid conducting fluid of finite magnetic Reynolds number is investigated. The basic equations are not hyperbolic but nevertheless the slow wave has a domain of dependence determined by the sound velocity."

"We compute the equilibrium configuration of a collision-free plasma contained in an axially symmetric magnetic field. The plasma is characterized by a non-scalar pressure tensor which is obtained from a microscopic distribution function in a form suggested b the guiding center approximation. The solution is calculated in the limit where the ratio of the width to the length of the plasma region and the ratio of the gas to the magnetic pressure are both small. Boundary values at the midplane as well as the shape of the plasma appear as arbitrary parameters in the solution. We give the solution to a corresponding scalar pressure problem for comparison."

"The long wavelength modes of excitation of a two component plasma in a steady magnetic field are examined. Two linearized Boltzmann equations are given with collision terms which are coupled through the difference in temperatures and difference in velocities of the two gases. A formal means of classification of phenomena is described in terms of the nature of the roots about k = 0. Two types of behavior are uncovered: MHD, magnetohydrodynamics, which include finite phase speed phenomena near k = 0; and PEM, plasma electromagnetics, which includes infinite phase speed phenomena near k = 0. The dissipative effects of collisions are included. In the limit of vanishing collision frequency, roots previously obtained are recaptured. The relevance of the pertinent domains are discussed and the complex interplay between the fast and Alfven modes of MHD and the plasma- magnetic modes of PEM is demonstrated. Equations macroscopic in appearance are derived which include the effects of the initial configuration. In the limit of large collision frequency the equations reduce to standard forms. The dispersion of the Nth order Larmor resonance is given which includes the effect of the mass ratio. A discussion of the transfer equations of a plasma is included."

An approximate Boltzmann equation, known as the single relaxation model is studied here. This equation is linearized and the fundamental solution is considered. Following N. Grad, the solution, asymptotic in small values of the ratio of mean-free-path to distance from the origin, is sought. It can be shown that the fundamental solution itself gives the asymptotic description of the flow field past an object. This solution gives the asymptotic description when the distance from the origin is much greater than either the mean-free-path or the body size. This is true independently of the Knudsen number.

"Sound propagation and the initial value problem in kinetic theory are investigated. Linearized forms of certain kinetic models suggested by Gross and Jackson employed. The most general model contains three relaxation times and is capable of producing Euler, Navier-Strokes, Burnett and thirteen moments equations for smooth phenomena. A study of dispersion relations is made and some novel features are uncovered. One finds that kinetic models are unable to describe phenomena of higher than a certain wave number, the latter depending on the model chosen. It compensates for this by introducing an interesting but unphysical dispersion picture for high wave numbers. It is further suggested by one of the models that the phase speed of sound waves achieves a maximum value. Existence, uniqueness, and boundedness of solutions of the initial value problem are shown for any model equations. It is further shown that asymptotically the solutions become hydrodynamical."