Second-Order Achromats with Arbitrary Linear Transfer Matrices

TL;DR

This paper develops conditions for designing second-order achromats with arbitrary linear transfer matrices, demonstrating that such systems can be achieved with minimal sextupole families, enhancing beam control in accelerator design.

Contribution

It formulates necessary and sufficient conditions for second-order achromats with arbitrary linear transfer matrices, enabling simpler designs with fewer sextupole families.

Findings

Achromats can be constructed with arbitrary linear transfer matrices.

Second-order achromats can be achieved using only two sextupole families.

Design flexibility is increased for beam optics in accelerators.

Abstract

In this article we consider a system where a bend magnet block arranged in an achromat-like fashion is followed by a straight drift-quadrupole cell which is not a pure drift space. We formulate the necessary and sufficient conditions for this system to be a second-order achromat and show that it can be achieved using six, four or even only two sextupole families.