Experimental verification of the smooth-approximation theory for a space-charge dominated beam in an axisymmetric periodic focusing channel

The predictions of the smooth-approximation theory for the effective radius of a space-charge dominated beam in a periodic solenoid focusing channel were checked experimentally over a wide range of focusing conditions. Electron beams with an energy of 5 keV and currents of 50 to 70 mA were transported through a 5-m-long periodic channel and beam radii were measured by an axially moveable phosphor screen and a charge-coupled device camera. The phase advance of betatron oscillation per period without space-charge, σ0, was varied from σ0=45° to σ0=90°. The tune depression due to space-charge, σ/σ0, was in the range of 0.2–0.3. The theoretical results for average beam radius R̄ over one period and the ratio R̄/Rmax were found to agree with the experimental data to better than 5% when a correction due to spherical aberration was taken into account.