  The production of anti-hydrogen ions in the GBAR experiment will occur via a
two step charge exchange process. In a first reaction, the anti-protons from
the ELENA ring at CERN will capture a positron from a positronium target
producing anti-hydrogen atoms. Those interacting in the same positronium target
will produce in a second step anti-hydrogen ions. This results in a dependence
for the anti-ions production rate which is roughly proportional to the
positronium density squared. We present a scheme to increase the anti-ions
production rate in the GBAR experiment by tailoring the anti-proton to the
positron pulse in order to maximise the temporal overlap of Ps and
anti-protons. Detailed simulations show that an order of magnitude could be
gained by bunching the anti-protons from ELENA. In order to avoid losses in
their capture in the Paul trap due to the energy spread introduced by the
bunching, debunching with a symmetrical inverted pulse can be applied to the
anti-hydrogen ions.
