  Increasing peak brightness is beneficial to various applications of Thomson
scattering x-ray source. Higher peak brightness of scattered x-ray pulse
demands shorter scattering electron beam realized by beam compression in
electron beam-line. In this article, we study the possibility to compress
electron beam in a typical S-band normal conducting photo-injector via
ballistic bunching, through just adding a short RF linac section right behind
the RF gun, so as to improve peak brightness of scattered x-ray pulse.
Numerical optimization by ASTRA demonstrations that peak current can increase
from ~50 A to >300 A for a 500 pC, 10 ps FWHM electron pulse, while normalized
transverse RMS emittance and RMS energy spread increases very little.
Correspondingly, the peak brightness of Thomson scattering x-ray source is
estimated to increase about 3 times.
