In (5), [r.sub.b0] is used to describe the betatron oscillation in the radial direction and [r.sub.b1] is used to describe the radial displacement induced by high frequency fields.
Equation (17) is the dispersion relation for space charge and betatron waves with ES approximation.
The asymptotic behaviors and the influences of the inner and outer radii on the space charge and betatron modes for strong ion channel are presented in Figures 2-5.
Stability of motion about the stationary reference orbit is described in terms of betatron oscillations with energy dependent Twiss parameters and betatron tunes.
The part [[??].sub.2] is responsible for linear betatron motion and chromaticity, while the remainder describes higher order contributions.
To extend the lifetime the vertical
betatron oscillation is excited (13,14), causing the vertical angular spread and beam size to increase.
(2005) Observation of vertical
betatron sideband due to elctron clouds in the KEKB low energy ring.
Newspapers, magazines, news services and radio broadcasters were soon ordered not to mention atomic power, cyclotrons,
betatrons, fission, uranium, deuterium, protoactinium and thorium.