We cannot store useful amounts of antimatter.
We can only generate tiny amounts of antimatter.
Antimatter particles that are created need to be slowed down for use.
It would be very difficult to develop the designs for antimatter propulsion into actual working systems.
Positron Dynamics will use Krypton isotopes to generate positrons. They would breed more Krypton isotopes. They sidestep the issue of antimatter storage. The designs that they have seem to have more manageable problems and they are able to get to actual lab experiments.
It would take 10 school buses of volume at the Brillouin limit to trap 1 microgram.
They are slowing the positrons that are generated.
Krypton 79 isotope to generate hot positrons.
Use their system to moderate the positrons so they can be used.
They then use the Positrons to catalyze nuclear fusion. Neutrons from nuclear fusion can then breed more Krypton 79.
They have done momentum transfer and deuterium loading experiments.
There would be 1-10% momentum transfer from catalyzed fusion propulsion.
They need one trillion positrons to generate nuclear fusion events according to the Lawson Criteria.
Energy balance and 2-D pic models indicate maybe 100 billion positrons would be needed.