We can produce very little antimatter and what we make is very difficult to store. These have been huge obstacles that have made antimatter propulsion many trillions of times beyond technological capabilities.
Positron Dynamics and Ryan Weed get around these issues by using isotopes of Krypton or sodium which naturally produce positrons (anti-electrons). They can use tiny amounts of Krypton isotopes to generation 100 billion to many trillions of positrons. They can also breed more of Krypton 79 isotopes by exposing Krypton 78 to neutrons.
Using a NASA NIAC study they have worked out more details and produced renderings of what the systems will look like.
They have worked out the reaction rate of the catalyzed fusion (R=0.1).
They have determined the mass, size and thickness of various materials.
They have worked out the moderation of the positrons (slowing down the positrons to use them).