Electrical and Computer Engineering ETDs

Publication Date

5-5-1972

Abstract

The purpose of this report is to investigate the nature of propagation processes for intense, relativistic charged particle beams in vacuum. Three areas of the problem are studied. The first subject, envelope optics, includes a formal development of the envelope equations and consideration of this approach as a device of approximation. Secondly, assuming laminar behavior, the entire beam is modeled in a closed set of partial differential equations in configuration space. A general study of this condition emphasizes invariants of laminar flow and geometric scaling. Finally, the coupled beam-field equations are solved exactly for several special cases. The optical properties of the beam envelope are found to be extremely sensitive to the magnitude and distribution of the axial electric field. For this reason, it is not possible to state a law with broad applicability, such as that enjoyed by the universal spreading curve for low density, nonrelativistic beams. Instead, the equations must be used in conjunction with an experimental procedure, designed to test validity of the assumed electric field in the direction of propagation. After deriving the equations of steady, laminar particle flow, a relativistic form of vorticity is deduced. From this definition, it is demonstrated that Lagrange's vorticity conservation law holds relativistically and that extended validity of Poincare's invariant and Busch's theorem can be achieved with only minor modification. Geometric scaling is found to be impossible for the general relativistic case, but scale factors are presented for ultrarelativistic beams. The first exact solution is an investigation of one­dimensional particle flow in planar drift space. Propagation is classified as injection limited if all injected charges propagate across the drift region and as space charge limited when the beam is partially reflected. The optimum transport condition is an injection limted flow, but exists in a region of charge injection rates for which the solution of the governing equations is not unique. A generalized Child's law, describing the transmitted current density in terms of the injection rate, results from study of space charge dominated streams. When the transport variables of an axially symmetric beam depend only upon the radial co-ordinate, the results describe an equilibrium flow condition. It is shown that such an equilibrium can exist and is energetically feasible in a vacuum drift chamber, when one or more additional conductors are introduced to establish favorable boundary conditions. Furthermore, this z-invariant propagation mode is not physically restricted to currents less than the Alfven critical limit. The last exact solution is two-dimensional and is obtained by similarity analysis. This result is shown to be the most general solution for an axially symmetric beam, in which the components of particle momentum can be expressed as a function of one similarity variable. Physically, the similarity equations correspond to particle flow under force equilibrium in a converging or diverging drift cone.

Sponsors

A National Science Foundation Graduate Traineeship Grant

Document Type

Dissertation

Language

English

Degree Name

Electrical Engineering

Level of Degree

Doctoral

Department Name

Electrical and Computer Engineering

First Committee Member (Chair)

Ahmed Erteza

Second Committee Member

James Daniel Finley III

Third Committee Member

William Jackson Byatt

Fourth Committee Member

Martin D. Bradshaw

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