  The MuSEUM collaboration is planning measurements of the ground-state
hyperfine structure (HFS) of muonium at the Japan Proton Accelerator Research
Complex (J-PARC), Materials and Life Science Experimental Facility. The
high-intensity beam that will soon be available at H-line allows for more
precise measurements by one order of magnitude. We plan to conduct two staged
measurements. First, we will measure the Mu-HFS in a near-zero magnetic field,
and thereafter we will measure it in a strong magnetic field. We have developed
two microwave cavities for this purpose. Furthermore, we evaluated systematic
uncertainties from such a fluctuation of microwave fields and confirm the
requirement of the microwave system, we use a microwave field distribution
calculated from the finite element method.
