  A self-focusing of a coasting relativistic beam in a plasma channel that is
confined by an external magnetic field is studied as a means of reconditioning
the beam emerging from a beam injector [a radio frequency quadrupole (RFQ)] for
a linac. A detailed study of the beam stability in the self-focused beam has
been carried out. In order to explain beam filaments and the resistive hose
instability in a unified way, we treat all the azimuthal modes in the
derivation of the dispersion relation in a finite plasma channel that exhibit
many unstable modes, which are classified by Weinberg's scheme [Steven
Weinberg, J. Math. 8, 614 (1967)].
