A confinement criterion for a finite sired'azimuthally symmemc relativistic bunched electron beam propagating through a perfectly conducting cylindrical pipe with a slight off-axis displacement while in the presence of either a uniform or periodic solenoidal field is studied. We compute the center-of-mass force on each off-axis beam bunch due to the induced surface charges on the pipe using a Green's function technique. By analyzing the center-of-mass dynamics of each bunch due to magnetic focusing and its in…
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