  Positron beams, both polarized and non-polarized, low and high energy have a
wide range of applications and many methods can be used to produce them. In
this paper we analyse the two main methods used to produce positrons for
accelerator applications, the "traditional" electro-production and the more
recent "photo-production". After having determined the best target material,
the positron production yield is determined for various target thickness and
primary beam energy. Production efficiency up to about 7.6% and 200% are
achievable for photo-production and electro-production respectively. Then the
quality, i.e. the emittance and the normalized emittance of the produced beam
is evaluated; the proposed "Gruber" correction for calculating the normalized
emittance is considered too. The brightness of the obtained beams is
calculated, relating it to the intrinsic temporal lengthening of the positron
beam. The time structure of the primary beam is preserved for long bunches down
to the ps scale. A very preliminary evaluation of the energy deposition in the
target and its effect is done. The polarization is not take, so far, into
account.
