Longitudinal Instabilities of Relativistic Beams in Axially Symmetric Magnetic Fields
Abstract
A canonical formalism has been developed for the description of the negative mass instability (N.M.I.) and longitudinal oscillations of relativistic beams. This formalism has been applied to ascertain the stabilizing effect of betatron oscillations, and to determine the dispersion relation governing counterstreaming ions and relativistic electrons. The results show that only the spread in p, the canonical angular momentum of the particles, contributes to stability. The N.M.I. equations for two streams is the same as though were separately present; and the dispersion relation for longitudinal oscillations of beams in a magnetic field is given by the N.M.I. dispersion relation, and not by the dispersion relation for longitudinal oscillations of collinear beams. Moreover, the dispersion relation for longitudinal oscillations of thin collinear beams differs from the usual equation by a non-trivial factor.
Document Details
- Document Type
- Technical Report
- Publication Date
- May 01, 1963
- Accession Number
- AD0413272
Entities
People
- R. W. Landau
Organizations
- New York State College of Ceramics