A growing number of experiments require low emittance ultra-short electron bunches in the 100 fs range (rms value) for the production of coherent light or the injection into a plasma for laser-plasma acceleration. Especially in the last case it is highly desirable to have a compact accelerator; hence a strong experimental activity is carried out to get such a beam directly from a photo- injector. We have performed beam dynamic simulations using the PARMELA code to study the performances of the alphaX photo-injector installed in the University of Strathclyde in UK*. This RF gun is aimed to produce electron bunches which have 100 pC of bunch charge, 100 fs bunch length and 1 pi mmmrad transverse emittance. We will show the results of systematic parametric studies as a function of charge and laser pulse duration as well as the natural evolution of the beam phase space as a function of the distance from the photo- cathode.