Comparison of Gabor lens, gas focusing, and electrostatic quadrupole focusing for low-energy ion beams

When a particle beam propagates through a background gas, a plasma is formed by collisional ionization resulting in (partial) neutralization of the beam's space charge and decrease of the beam radius. This gas focusing effect occurs naturally and is often utilized to improve high-current beam transport. Gabor, in 1947, proposed a nonneutral electron plasma confined in a magnetron-type trap as an effective space-charge lens for positive ion beams. This Gabor lens, which offers better control and focusing strength than both gas focusing and applied fields, has been investigated by several research groups since its invention. So far, however, the experimental results have been inconclusive. In this paper, the authors will present a theoretical reevaluation of the Gabor lens and a comparison with an electrostatic quadrupole (ESQ) doublet. It will be shown that the focusing strength of the Gabor lens depends on the electron trapping efficiency and is significantly higher than that of the ESQ doublet if the trapping efficiency is close to the theoretical Brillouin limit. On the other hand, an ESQ doublet with equivalent geometry and voltage parameters performs better than the Gabor lens if the trapping efficiency is below a certain threshold, as appears to be the case in experiments so far. 16 refs., 2 figs