Equilibrium and confinement of bunched annular beams

Abstract

The azimuthally invariant cold-fluid equilibrium is obtained for a periodic, strongly bunched charged annular beam with an arbitrary radial density profile inside of a perfectly conducting cylinder and an externally applied uniform magnetic field. The selfelectric and self-magnetic fields, which are utilized in the equilibrium solution, are computed self-consistently using an electrostatic Green's function technique and a Lorentz transformation to the longitudinal rest frame of the beam. An upper bound on the maximum value of an effective self-field parameter for the existence of a bunched annular beam equilibrium is obtained. As an application of the bunched annular beam equilibrium theory, it is shown that the Los Alamos National Laboratory relativistic klystron amplifier experiment is operating slightly above the effective s elf-field parameter limit, and a discussion of why this may be the cause for their observed beam loss and microwave pulse shortening is presented. The existence of bunched annular beam equilibria is also demonstrated for two other high-power microwave (HPM) experiments, the relativistic klystron oscillator experiment at Air Force Research Laboratory and the backward wave oscillator experiment at the University of New Mexico. In general, the results of the equilibrium analysis will be useful in the determination of the stability properties of strongly bunched annular beams in HPM devices.

On the relativistic cold fluid radial equilibrium of a nonneutral plasma

“…The equilibrium solution (20) shows that in the case of differential rotation the plasma density can exceed the Brillouin limit found for the case of rigid rotation, see inequality (11). The Brillouin limit is exceeded in the range 1 < ρ/a < [2 √ 1 + a 2 ] 1/(1+a 2 ) , which exists for every value of a. Eq.…”

“…In the theoretical analysis the axial motion is then allowed to be relativistic while the transverse motion is usually considered to be nonrelativistic (see, e.g., Refs. [10,11]). A short description of the case in which the azimuthal motion of the particles is allowed to be relativistic (while the axial motion is assumed to be nonrelativistic) is found in Ref.…”

Three-dimensional modeling of intense bunched beams in RF accelerators and sources

“…As an initial effort to generalize the previous model [4][5][6][7] to slow-wave structures, we pose the problem of determining the electrostatic Green function in an azimuthally symmetric slow-wave structure.…”

“…In this paper, we present updated comparisons between theory [4][5][6][7] and the PPM klystron experiments at SLAC [8,9,11] and KEK [10,12], and describe our initial efforts to generalize the previous model [4][5][6][7] to slow-wave structures. In particular, we derive an electrostatic Green's function for an azimuthally symmetric cylindrical conductor with small-amplitude axial variations of its radius.…”

“…Recent analytic and semi-analytic Green's function analyses to address these issues have resulted in confinement conditions for bunched pencil beams in round cylindrical pipes [4][5][6][7]. The model predicts beam losses, which have been measured in a number of periodic permanent magnet (PPM) focusing klystrons at SLAC and KEK [8][9][10][11][12].…”