Fig. 7: Comparison between experimental and theoretical electron cyclotron dynamics.
From: Transient lensing from a photoemitted electron gas imaged by ultrafast electron microscopy
The ROI difference intensity trace for ILC = 1.1 A (blue circles, left axis) is fitted to the function \(1/{\it{f}}_{{\mathrm{EG}}}(t) = {\it{Ae}}^{ - {\it{t}}/{\it{\tau }}}/{\it{\sigma }}_{\mathrm{T}}^2\left( {\it{t}} \right)\) (dark blue line), where A and τ are phenomenological fitting parameters encompassing the time-dependent number of electrons in the cloud and TEM-specific lens settings. σT is the time-dependent transverse radius of the electron gas, which depends on the velocity spread σv, the minimum radius σr, and the cyclotron angular frequency ω (all fitted to the data). The fitting range is 100–900 ps, i.e. beyond the regime where Coulomb interactions are significant. The corresponding focal length of the electron gas, fEG, is plotted in red (right axis), which is only an order-of-magnitude estimate due to the approximations in the model (see text).
