  The description of physical processes with many-particle systems is a key
approach to the modeling of countless physical systems. In storage rings, where
ultrarelativistic particles are agglomerated in dense bunches, the measurement
of their phase-space distribution (PSD) is of paramount importance: at any time
the PSD not only determines the complete space-time evolution but also provides
fundamental performance characteristics for storage ring operation. Here, we
demonstrate a non-destructive tomographic imaging technique for the 2D
longitudinal PSD of ultrarelativistic electron bunches. For this purpose, we
utilize a unique setup, which streams turn-by-turn near-field measurements of
bunch profiles at MHz repetition rates. To demonstrate the feasibility of our
method, we induce a non-equilibrium state and show, that the PSD
microstructuring as well as the PSD dynamics can be observed in great detail
with an unprecedented resolution. Our approach offers a pathway to control
ultrashort bunches and supports, as one example, the development of compact
accelerators with low energy footprints.
