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Paper IPM / P / 8326  


Abstract:  
An analysis of the eigenmodes of a cylindrical metallic waveguide partially filled with a relativistic
electron beam, and guided with an ion channel, is presented. The analysis is performed in the rest
frame of the beam with selffields taken into account. Dispersion relations for five families of
electrostatic and EM modes are derived and solved numerically to study the characteristics of
azimuthally symmetric TM and TE waveguide modes, betatron modes, and spacecharge modes. A
strong dependence of the frequencies of these electromagneticelectrostatic waves on the ratio of the
radius of the waveguide to the beam radius is revealed. The physical insight given to the
electrostatic modes, at large and small wavelengths, equally applies to the TrivelpieceGould modes
in an electron beam with axial magnetic field guiding. Interactions between the dispersion curves of
different modes are used to find the infinitespace dispersion relation from the finiteradius
dispersion relation and to explain the transition from a weak to strong ion channel.
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