Brightness optimization of ultra-fast Thomson scattering x-ray sources

We present simple scaling relations of the brightness a Thomson x-ray source on the electron and laser beam parameters in the case of a head (180 degree) interaction geometry. In particular, it is shown that a direct relation exists between the x-ray brightness and the electron beam brightness. These relations are discussed in the context of the PLEIADES Thomson x-ray source, where 10(7) photons per pulse, with photon energies as high as 140 keno have been produced by colliding a 0.25 nC, picosecond electron bunch with a 560 mJ, 50 fs, 800 nm laser pulse. The estimated peak brightness of the source is about 1016 photons/s/mm(2)/mrad(2)/0.1%b.w. A comparison of the current performance of the source and the predicted performance using optimized parameters is presented.