Magnetic damping of ℓ=1 diocotron mode

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Abstract
Previous work has treated the diocotron mode for a low‐energy beam and has found that any dissipative effect will cause this mode to grow. However, a treatment that considers the axial velocity of the beam shows that this mode will damp if the beam is relatively thin and the axial velocity of the beam is comparable with c. This damping is attributed to the perturbed magnetic field and is similar to the stabilization of sausage and kink modes in neutral plasmas. The damping rate for this case is compared with the damping observed in the University of California, Irvine (UCI) modified Betatron. Additionally, beam temperature effects are considered and these results are compared with the diocotron mode damping in the collective focusing ion accelerator.