TWO-STREAM INSTABILITY IN A FINITE LENGTH,
Abstract
Two contra-streaming electron beams of equal densities and speeds interacting between two parallel planes are studied. The streams are cold and their average charge is compensated by a uniform positive background. For infinitely broad streams, an eigenfrequency equation is derived from the conditions that the entering beams be free of perturbations. The eigenfrequency equation is solved numerically and the results show there is no instability for omega sub b tau < pi/2(3/2), where omega sub b is the plasma frequency of either beam, and tau is half the transit time between the plates. For large values of omega sub b tau, the fastest-growing modes have a growth rate of omega sub b/2. The growth rate is also calculated from the dispersion relation assuming appropriate real values of wavenumber and is in good agreement with the exact results of the eigenfrequency equation. (Author)
Document Details
- Document Type
- Technical Report
- Publication Date
- Mar 01, 1964
- Accession Number
- AD0602321
Entities
People
- Donald J. Nelson
- Richard Gerwin
Organizations
- Boeing