Introduction: Since 1929 (O. D. Kellogg) it is known that uniformly filled ellipsoids of charge, waterbags in short, have linear self-fields in three coordinates.
A waterbag is the ideal shape for a charged particle bunch. The linear self-fields cause the bunch to expand and change aspect ratio, but they do not cause any degradation in rms brightness. It is no surprise that the accelerator community has used waterbag objects for decades as idealized beams in both analytical and numerical theory because of their mathematical elegance.
Astrophysicist (C.C. Lin et al.) proved in 1965 that an ellipsoid with
uniform mass density collapses into a flat disk. Jom Luiten from Eindhoven
University of Technology realized in 2004 that the time-reversed process
could lead to an experimental method to produce electron bunches with the
ideal waterbag shape. Applied to an rf-photogun, his analytical theory says
A 'half-sphere' transverse laser intensity profile must used.
The temporal profile of the photo-excitation laser is irrelevant, if sufficiently short.
Realistic fields: As outlined in the PRL, uniformly filled ellipsoids of charge can be created in practice. We could not resist to put the idea to the test in a standard 1.5 cell rf-photogun. Detailed GPT simulations including realistic fields, space-charge effects, image charges and path-length differences show: It works!
GPT Simulation of a 'waterbag' bunch produced in a 100 MV/m 1.5 cell rf-cavity.
Compression: The obvious next step in the waterbag endeavor is longitudinal compression. We gave an invited talk about this subject at the High Brightness Electron Beams workshop in Erice, Sicily, October 9 2005. The highlight is that detailed GPT simulations predict that a 1 kA peak current, 1 micron rms emittance bunch can be produced with standard 3 GHz technology with just 10 MW klystron power in a 1.5 m setup.