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Critical points in the theory of electron beam devices

Authors :
J R Pierce
Source :
Journal of Nuclear Energy. Part C, Plasma Physics, Accelerators, Thermonuclear Research. 2:73-80
Publication Year :
1961
Publisher :
IOP Publishing, 1961.

Abstract

In working on the theory of electron beam devices such as travelling-wave tubes and klystrons, it has been necessary to consider a number of knotty problems, some at least of which occur in mathematical formulation of other plasma problems. Among these is the matter of multi-velocity flow. Here there are two mathematically equivalent approaches. In one, the electron flow is divided into streams according to the initial unperturbed velocities of the electrons; the variables are the densities and velocities in the various streams. In the other, velocity is regarded as a co-ordinate of phase space and the variable is the density in phase space. These approaches give different appreciations of the phenomena involved and lead to different mathematical difficulties, but are the same in content. Each demonstrates the non-existence of wave-type solutions in many infinite velocity distributions. Only a few specialized solutions of multi-velocity problems exist. As different velocity co-ordinates can be used, so different spatial co-ordinates can be used. The Eulerian approach is common and leads to no difficulties if boundary conditions are met at fluctuating boundaries. In the case of thin beams, it is sometimes useful to use displacements from the mean position of the particles as variables. Some workers have made mistakes by mixing co-ordinate systems. In dealing with power flow in electron beams, one can either replace the actual physical system with a linear system and find an expression for power in this system, or try to deal with the power flow in the true non-linear system. The former alternative is much simpler. Kinetic power, as well as electromagnetic power, is important in considering the orthogonality of wave-type components. In solving an actual physical problem, one can either assemble various wave-type components so as to satisfy the boundary conditions, or solve the problem by transform or perhaps by other means. Components of the solution must be regarded as merely a part of the solution of an actual problem, but they can sometimes be given a reasonable physical interpretation. Thus, one finds waves with positive and negative powers. When two unattenuated waves having powers of the same sign are coupled together, one observes beats. When two unattenuated waves having powers of opposite signs are coupled together, one observes growing and decaying waves. Growing waves can also be produced when a moving discontinuity couples two unattenuated waves together (parametric amplification).

Details

ISSN :
03683281
Volume :
2
Database :
OpenAIRE
Journal :
Journal of Nuclear Energy. Part C, Plasma Physics, Accelerators, Thermonuclear Research
Accession number :
edsair.doi...........898d1cd907ce3a995d59c74b0ce2fbe8
Full Text :
https://doi.org/10.1088/0368-3281/2/1/310