Isochronous lattice design with time-of-flight fluctuation reaching subattoseconds based on high-order achromat

The fluctuation in electron time of flight during lattice transport is crucial for various applications, such as ultrafast electron diffraction, optical stochastic cooling in storage rings, and sustaining steady-state microbunching in storage rings. A major issue impacting the time-of-flight fluctuation of the electron beam during transport is the lattice’s nonlinear effects. In this study, we introduce a design concept aimed at reducing the electron beam’s time-of-flight fluctuation in an isochronous lattice up to the subattosecond level. This approach employs a high-order achromat lattice that effectively eliminates time-of-flight contributions arising from low-order nonlinearities. We also present an optimized design example based on this concept, achieving approximately 0.3 attoseconds root-mean-square time-of-flight fluctuation (equivalent to 0.1 nm) with specific beam emittance values of <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"> <a:msub> <a:mi>ε</a:mi> <a:mi>x</a:mi> </a:msub> <a:mo>∼</a:mo> <a:mn>1</a:mn> <a:mrow> <a:mtext> </a:mtext> <a:mtext> </a:mtext> </a:mrow> <a:mi>nm</a:mi> <a:mo>,</a:mo> <a:msub> <a:mi>ε</a:mi> <a:mi>y</a:mi> </a:msub> <a:mo>∼</a:mo> <a:mn>1</a:mn> <a:mrow> <a:mtext> </a:mtext> <a:mtext> </a:mtext> <a:mi>nm</a:mi> </a:mrow> <a:mo>,</a:mo> </a:math> and <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"> <c:mrow> <c:msub> <c:mrow> <c:mi>σ</c:mi> </c:mrow> <c:mrow> <c:mi>δ</c:mi> </c:mrow> </c:msub> <c:mo>∼</c:mo> <c:mn>1</c:mn> <c:mo>×</c:mo> <c:msup> <c:mrow> <c:mn>10</c:mn> </c:mrow> <c:mrow> <c:mo>−</c:mo> <c:mn>3</c:mn> </c:mrow> </c:msup> </c:mrow> </c:math> .