  The neutral Higgs boson is expected to have a mass in the region 90-150 GeV
in various schemes within the Minimal Supersymmetric extension to the Standard
Model. A first generation Muon Collider is uniquely suited to investigate the
mass, width and decay modes of the Higgs boson, since the coupling of the Higgs
to muons is expected to be strong enough for it to be produced in the s channel
mode in the muon collider. Due to the narrow width of the Higgs, it is
necessary to measure and control the energy of the individual muon bunches to a
precision of a few parts in a million. We investigate the feasibility of
determining the energy scale of a muon collider ring with circulating muon
beams of 50 GeV energy by measuring the turn by turn variation of the energy
deposited by electrons produced by the decay of the muons. This variation is
caused by the existence of an average initial polarization of the muon beam and
a non-zero value of g-2 for the muon. We demonstrate that it is feasible to
determine the energy scale of the machine with this method to a few parts per
million using data collected during 1000 turns.
