have presented the dispersion characteristics of the space charge waves in a uniform and rigid rotation REB in ion channel without betatron oscillations .
After dispersion relations are derived, the influences of the beam bunch thickness and betatron oscillation parameter on the dispersion propagation property and interaction of different wave modes are discussed in detail by numerical calculations.
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.
Figure 13 shows the influences of the betatron oscillation characteristic parameter [[omega].sub.[beta]] on the TM dispersion properties for strong ion channel.
The influences of the inner and outer radii of the beam and betatron oscillation parameter on the dispersion characteristics of space charge modes, betatron modes, and TM modes are revealed by numerical calculations.