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In this article is discussed at some length positron formation in metallic surfaces. Positrons have work functions that describe how much energy they have to receive in order to be extracted from the surface (just like the photoelectric effects does with normal electrons)

If a ceramic insulator would be doped with some ions of high Z number on its surface, it would presumably be very good for containing a positron cloud. As long as there are surface protons insulating the positrons from the other electrons in the materials, and the material has strong insulation against giving up his electrons, the positrons should not have anything to bind or annihilate with.

Are there studies or experiments performed to find materials good for containing positrons without them annihilating with the electrons or neutrons in the material?

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I have only an amateurs understanding, but it seems to me that a strong vacuum and EM fields are needed to trap positrons (see Penning Trap on wikipedia). I have wondered if ionizing the remaining scant air within a vacuum tube would improve the preservation of positrons in a Penning Trap. My reasoning is that positively charged gas molecules would repel positrons, therefore reducing the rate of loss from annihilation. But as I said, I'm an amateur so I don't if this could really happen. I like your doped insulator idea.

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