Femtosecond electron pulse propagation for ultrafast electron diffraction

Ultrafast electron diffraction (UED) relies on short, intense pulses of electrons, which because of Coulombic repulsion will expand and change shape as they propagate. While such pulse expansion has been studied in other contexts, efforts to model this effect for typical UED parameters have only arisen fairly recently. These efforts have yielded accurate predictions with very simple models, but have left a number of unexplained results (such as the development of a linear self-similar profile with sharply defined end points). The present work develops a series of models that gradually incorporate more physical principles, allowing a clear determination of which processes control which aspects of the pulse propagation. This will include a complete analytical solution of the one-dimensional problem (including a fundamental limitation on temporal resolution), followed by the gradual inclusion of two-dimensional and inhomogeneous effects. Even very simple models tend to capture the relevant on-axis behavior to within 10% or better. This degree of success can be traced to the manner in which the pulse transitions from one dimensional to two dimensional. We also present methods for determining the most appropriate model for a given situation and suggest paths toward future modeling improvements as the field evolves. (c) 2006 American Institute of Physics.