Optimum electron distributions for space charge dominated beams in photoinjectors

The optimum photo-electron distribution from the cathode of an RF photoinjector producing a space charge dominated beam is a uniform distribution contained in an ellipsoid. For such a bunch distribution, the space charge forces are linear and the emittance growth induced by those forces is totally reversible and consequently can be compensated. With the appropriate tuning of the emittance compensation optics, the emittance, at the end of photoinjector beamline, for an ellipsoidal laser pulse, would only have two contributions, the cathode emittance and the RF emittance. For the peak currents of 50 and 100 A required from the S-Band and L-Band RF gun photoinjectors discussed here, the RF emittance contribution is negligible. If such an ellipsoidal photo-electron distribution were available, the emittance at the end of the beamline could be reduced to the cathode emittance. Its value would be reduced by more than 40% from that obtained using cylindrical shape laser pulses. This potentially dramatic improvement warrants review of the challenges associated with the production of ellipsoidal photo-electrons. We assume the photo-electrons emission time to be short enough that the ellipsoidal electron pulse shape will come directly from the laser pulse. We shift the challenge to ellipsoidal laser pulse shaping. To expose limiting technical issues, we consider the generation of ellipsoidal laser pulse shape in terms of three different concepts.