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.
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