Microbunch rotation in an x-ray free-electron laser using a first-order achromatic bend

Electrons in an x-ray free electron laser (XFEL) develop periodic density fluctuations, known as microbunches, which enable the exponential gain of x-ray power in an XFEL. When an electron beam microbunched at a hard x-ray wavelength is kicked, microbunches are often washed out due to the dispersion and <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:msub><a:mi>R</a:mi><a:mn>56</a:mn></a:msub></a:math> of the bend. An achromatic (dispersion-free) bend with a small <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"><c:msub><c:mi>R</c:mi><c:mn>56</c:mn></c:msub></c:math>, however, can preserve microbunches, which rotate to follow the new trajectory of the electron bunch. Rotated microbunches can subsequently interact in a repointed undulator to produce a new beam of off-axis x rays. In this work, we demonstrate hard x-ray multiplexing in the Linac Coherent Light Source hard x-ray undulator line using microbunch rotation through a <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"><e:mrow><e:mn>10</e:mn><e:mtext> </e:mtext><e:mtext> </e:mtext><e:mi mathvariant="normal">μ</e:mi><e:mi>rad</e:mi></e:mrow></e:math> first-order-achromatic bend created by transversely offsetting quadrupole magnets in the FODO lattice. Quadrupole offsets are determined analytically from beam-matrix theory. We also discuss the application of microbunch rotation to out-coupling a cavity-based XFEL.