Design of general apochromatic drift-quadrupole beam lines

Abstract

Chromatic errors are normally corrected using sextupoles in regions of large dispersion. In low emittance linear accelerators, use of sextupoles can be challenging. Apochromatic focusing is a lesser-known alternative approach, whereby chromatic errors of Twiss parameters are corrected without the use of sextupoles, and has consequently been subject to renewed interest in advanced linear accelerator research. Proof of principle designs were first established by Montague and Ruggiero and developed more recently by Balandin et al. We describe a general method for designing drift-quadrupole beam lines of arbitrary order in apochromatic correction, including analytic expressions for emittance growth and other merit functions. Worked examples are shown for plasma wakefield accelerator staging optics and for a simple final focus system.