A Theory of Resistive Hose Instability in Intense Charged Particle Beams Propagating Through Background Plasma With Low Electron Collision-Frequency

Stability properties of the resistive hose instability is investigated for a rounded current-density profile of a charged particle beam propagating through a background plasma where the electron collision time is comparable to or longer than the magnetic decay time . The eigenvalue equation is derived based on the energy group model, including the stabilizing influence of a finite magnetic decay time. The dispersion relation of the resistive hose instability in a charged particle beam with an arbitrary current density profile is derived, assuming that the eigenfunctions can be represented by the rigid displacement of the self magnetic field in the plasma. Stability analysis for perturbations propagating through the beam pulse from its head to tail is carried out for an arbitrary current profile of the beam. It is shown from the stability analysis that the width of the range corresponding to instability decreases drastically as the value of parameter decreases from infinity to zero, thereby being a very narrow bandwidth of instability. It is also shown for arbitrary current profile that any perturbation with frequency higher than the maximum betatron frequency is stable. Here, is the Doppler-shifted frequency seen by beam particles.