General Steady-state Theory of Linear Magnetrons. I†

The problem of electron velocity distribution

“…(12) gives the volume density of the electrons a t the surface of an emitter which is in a state of equilibrium with the adjacent electron cloud.…”

“….Although the definitions used in this paper are quite general, their physical meaning is made clear using a simple model of a plain, parallel diode. This does not limit the general validity of the argument which extends to other geometries, including crossed field devices [4], [12]- [14], or even plasma diodes [18]. I t might be added that ever since the rediscovery of thermionic power conversion, which intimately depends on the velocity distribution of the emitted electrons, the importance of the whole problem of electron velocity distribution greatly increased.…”

“…Second, the discussion of all problems associated with velocity distribution of the emitted electrons will be based on the concept of phase-space density, although, with few exceptions [1]-[4], i t was customary to use current density in the past [SI-[ l l 1. An exclusive use of the phase-space density, and of the related conditional probability density function, not only injects simple physical meaning into the concepts of mean value and mean flow, but also provides a method for solving the difficult problem of potential distribution, taking into account initial .velocity spread, when the electrons travel along curved paths [4], [12]- [14]. This is a valuable generalization and it was made possible only by treating the problem of velocity distribution in the manner suggested in this paper.…”

A Note on the General Steady-state Theory of Linear Magnetrons

“…Lindsay (1960) has presented a comprehensive general steady-state theory of linear magnetrons in which both space charge and the Maxwellian velocity distribution of the emitted electrons are taken into account. The purpose of this note is to show how the expression derived for the tangential component of current density may be simplified to a form more convenient for practical calculations and also to stress the difference between the cut-off curves predicted by Lindsay's formula and those expected from the simple Hull theory or from measurements on practical magnetrons.…”

Virtual Prototyping of Directed Energy Weapons

“…[7][8] These studies involved characterizing the steady-state behavior in magnetrons. [9][10][11][12] The evolution of particle methods [1,[13][14] allowed for the study of dynamical behavior.…”