  In the next decade the Fermilab Muon Campus will host two world class
experiments dedicated to the search for signals of new physics. The Muon g-2
experiment will determine with unprecedented precision the anomalous magnetic
moment of the muon. The Mu2e experiment will improve by four orders of
magnitude the sensitivity on the search for the as-yet unobserved Charged
Lepton Flavor Violation process of a neutrinoless conversion of a muon to an
electron. Maintaining and preserving a high density of particles in phase-space
is an important requirement for both experiments. This paper presents a new
experimental method for mapping the transverse phase space of a particle beam
based on tomographic principles. We simulate our technique using a GEANT4 based
tracking code, to ascertain accuracy of the reconstruction. Then we apply the
technique to a series of proof-of-principle simulation tests to study injection
and transport of muon beams for the Fermilab Muon Campus.
