Abstract
The analytical Gaussian electron pulse propagation model of Michalik and Sipe [J. Appl. Phys. 99, 054908 (2006)] is extended to include the action of external forces on the pulse. The resultant ability to simulate efficiently the effect of electron optical elements (e.g., magnetic lenses and radio-frequency cavities) allows for the rapid assessment of electron pulse delivery systems in time-resolved ultrafast electron diffraction and microscopy experiments.
Highlights
The development of laboratory-scale instrumentation for the direct visualization of fundamental ultrafasti.e., subnanosecondevents with nanoscaleeven atomicspatial resolution is a current active area of research.2 In many areas of physics, chemistry and materials science a space-time resolution in the sub-1 nm ps range is ideally required to allow for the observation of the fastest structural events
We have presented an extension to the mean-field selfsimilar analytic GaussianAGelectron pulse propagation model of Michalik and Sipe1 that provides for the inclusion of linear external forces acting on the pulse
This extended formalism enables the model to simulate the action of electron optical elements on the electron pulse; in particular, magnetic lenses in the transverse direction and rf cavities in the longitudinalpropagationdirection
Summary
The development of laboratory-scale instrumentation for the direct visualization of fundamental ultrafasti.e., subnanosecondevents with nanoscaleeven atomicspatial resolution is a current active area of research. In many areas of physics, chemistry and materials science a space-time resolution in the sub-1 nm ps range is ideally required to allow for the observation of the fastest structural events. 9 and 10͒ have been developed for both single-shot imaging with ϳ105 nm ps spacetime resolutione.g., 30 ns electron pulses and 5–10 nm spatial resolution11,12͒ and ϳ1 nm ps space-time resolutionϳ100 fs with a few nanometer resolution13͒ in the multishot data acquisition mode of operation Both of these instruments employ retrofitted standard electron microscope columns and are limited in performance mainly by space-charge effects. For free-space propagation, the AG model of charge bunch dynamics has already been shown to be very consistent with full Monte Carloi.e., particle trackingsimulations for a wide variety of electron pulse shapes, including the uniform ellipsoid.19 This successful benchmarking is due primarily to the versatility of the AG model which results from its use of transverse and longitudinal pulse position and momentum variances. Extension to include relativistic effects is straightforward using standard transformations between the laboratory and electron pulse reference frames
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