Noise in Multi-Dimensional Electron Streams
Abstract
The purpose of this investigation is to study the noise transport and reduction phenomena in multi velocity electron beams with significant potential variations in the transverse direction. Correlations between the noise reduction mechanism and the multi-dimensional nature of the electron beams are sought. The investigation was carried out by means of a high-speed digital computer employing two different numerical methods. The mathematical model assumes an infinite confining magnetic field so that transverse motions are not allowed. In addition a one-dimensional half Maxwellian velocity distribution function is considered for the electrons at the potential minimum. Details of the derivation of a small signal linearized Boltzmann equation in terms of a statistical electron density function and the electric field in a two- dimensional space-charge limited diode are presented, together with some discussion on the singularities in the boundary conditions and the formulation of the a-c electric fields. To facilitate a solution of the transport equation, velocity classes are introduced as an approximation so that digital techniques become applicable. Haus's noise theory for small-signal longitudinal beam devices is employed to evaluate the noise transport characteristics of the two-dimensional electron beam.
Document Details
- Document Type
- Technical Report
- Publication Date
- Mar 01, 1963
- Accession Number
- AD0406863
Entities
People
- Cheng P. Wen
Organizations
- University of Michigan