Four-Dimensional Emittance Measurements of Ultrafast Electron Diffraction Optics Corrected Up to Sextupole Order

Ultrafast electron diffraction (UED) is a technique in which short-pulse electron beams can probe the femtosecond-scale evolution of atomic structure in matter driven far from equilibrium. As an accelerator physics challenge, UED imposes stringent constraints on the brightness of the probe electron beam. The low normalized emittance employed in UED, often at the 10 nm scale and below, is particularly sensitive to both applied field aberrations and space charge effects. The role of aberrations is increasingly important in small probe systems that often feature multiple orders of magnitude variations in beam size during transport. In this work, we report the correction of normal quadrupole, skew quadrupole, and sextupole aberrations via dedicated corrector elements in an ultrafast electron micro-diffraction beamline. To do this, we generate precise 4-dimensional phase space maps of rf-compressed electron beams, and find excellent agreement with aberration-free space charge simulations. Finally, we discuss the role a probe-forming aperture can play in improving the brightness of bunches with appreciable space charge effects.