NDLI: Linear Theory of Radially Inhomogeneous, Unneutralized, Relativistic Electron Beams

Content Provider	IEEE Xplore Digital Library
Author	Godfrey, Brendan B.
Copyright Year	1973
Description	A set of four, coupled, first-order differential equations describing the normal modes of a cylindrically symmetric, cold fluid, unneutralized, relativistic electron beam of arbitrary radial profile is derived. Effects of beam rotation and equilibrium fields are treated exactly. The differential equations are found to have singular points for a radially inhomogeneous beam wherever the eigenfrequency equals the cyclotron or Doppler resonance frequencies. The resulting branch cuts in the dispersion function give rise to secularly decaying contributions to the initial value problem. The rate of decay and the character of the eigenmode near the singularity are determined from the solution of the corresponding indicial equation. Discrete eigenmodes also exist and are obtained by numerical solution of the differential equations and boundary conditions. For realistic solid-beam equilibria, only one slow cyclotron-mode exists for any given pair of axial and azimuthal wavenumbers, and that mode is localized at the beam edge. Under identical conditions several slow space-charge modes exist and are not so distorted. However, even at the space-charge limit, the phase velocity of long-wavelength slow space-charge waves does not decrease to zero. These results are relevant to the Autoresonant and Converging Guide collective ion acceleration proposals.
Sponsorship	IEEE Nuclear and Plasma Sciences Society
Starting Page	53
Ending Page	61
Page Count	9
File Size	2186699
File Format	PDF
ISSN	00933813
Volume Number	7
Issue Number	1
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	1979-03-01
Publisher Place	U.S.A.
Access Restriction	One Nation One Subscription (ONOS)
Rights Holder	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subject Keyword	Electron beams Acceleration Differential equations Maxwell equations Cyclotrons Boundary conditions Differential algebraic equations Optical coupling Resonance Resonant frequency
Content Type	Text
Resource Type	Article
Subject	Nuclear and High Energy Physics Condensed Matter Physics

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