Determination of the geometry factor for longitudinal perturbations in space-charge dominated beams

We present the results of an experimental investigation of the parametric dependence of the geometry factor g associated with line-charge perturbations in space-charge dominated beams. The experiment consists of a novel method of launching localized space-charge waves and measuring simultaneously the wave velocity and the radius a of an electron beam propagating through a periodic focusing channel with pipe radius b. We find that the g factor obeys the relation g=2 ln(b/a). This result is supported by theoretical analysis, and is also in agreement with previous theoretical work. The experimental technique can be used for any type of beam, whether space charge dominates over emittance or not.