Experimental test of an achromatic quadrupole lens doublet — Aberration coefficients of second degree in ion energy at the operating point

Abstract

Experimental tests of the focusing behaviour of an achromatic quadrupole lens doublet are made using protons of energy 350 < E < 800 keV. The procedure of experimental ray tracing is used, in which aberrations of a finely focused beam at the focal plane are measured as the location ( x 2, y 2) of the input ray within the lens aperture is varied. In general, the aberration is a linear function of the convergence angles a, b measured from the center of the image into the lens aperture. The magnitude of the linear slope, which indicates defocus, depends on the energy deviation e = dE E 0 , where E 0 is the achromatic operating energy. In both principal sections the slope decreases to a minimum at E 0, where the 1st-order, 1st-degree aberration coefficients are 〈 x, ae〉 = 0, and 〈 y, be〉 = 0. A quadratic dependence of the slope upon e 2 is fitted to the data, and experimental 1st-order, 2nd-degree coefficients 〈 x ae 2 〉 = 14 cm , 〈 y be 2 〉 = 2.7 cm are determined, in agreement with theory.