Abstract
A method for stabilizing a relativistic coasting beam against the negative mass instability is described. It is shown that a beam above the transition energy can be stabilized, even in the absence of a frequency spread in the beam, by making the wave impedance at the beam inductive. Several possible structures that can result in such an inductive impedance are described, and the case of a thin dielectric material positioned against the tank wall is analysed in detail. The effect of the dielectric wall on the longitudinal and transverse resistive instabilities is considered. It is shown that the dielectric can also play an important role in the stability criteria for these resistive modes, and in some cases can make the requirements on the frequency spread for stability less stringent. Several numerical examples are given to illustrate the typical range of the parameters involved.
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