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

A theoretical reevaluation of the Gabor lens and a comparison with an electrostatic quadrupole (ESQ) doublet are presented. It is 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 when the trapping efficiency is close to the theoretical Brillouin limit. However, 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. For the present analysis, an H⁺ beam and electrons for charge neutralization are assumed. Application to H^- beams is also discussed. The results presented are of interest in connection with the problem of focusing high-brightness, low-energy ion beams such as H⁺ and H^- in the range of 10 kV to 2 MV, 10 mA to 200 mA