Study of the hybrid mode in the helix with a partially filled plasma column

The dispersion equation of the axial symmetric hybrid mode inside the helix with a partially filled plasma column is derived, its dispersion curves are calculated, and the conditions to form that mode are illustrated. The effect of confining magnetic field on the radial profile of axial electric field is studied. In the situation that the strength of confining magnetic field has been entrusted with a practical low value, the calculated radial profile shows much stronger coupling of the field to the electron beam. In the situation without confining magnetic field, a Trivelpiece-Gould mode propagating along the surface of the plasma column is present.