  With the planned turn-on of the PIP-II 800 MeV superconducting proton linac,
Fermilab will potentially become the world's best laboratory at which to carry
out fundamental muon measurements, sensitive searches for symmetry violation,
and precision tests of theory. In preparation, we propose to develop the
techniques that will be needed. An R&D and physics program is proposed at the
Fermilab MeV Test Area to use the existing 400 MeV Linac to demonstrate the
efficient production of a slow muonium beam using $\mu^+$ stopped in a
~100-$\mu$m-thick layer of superfluid helium, and to use that beam to measure
muonium gravity.
