During the recovery phase of the geomagnetic storm on 30-31 March 2013, Van Allen Probe A detected enhanced magnetosonic (MS) waves in a broad range of L =1.8-4.7 and MLT =17-22 h, with a frequency range ~10-100 Hz. In the meanwhile, distinct proton ring distributions with peaks at energies of ~10 keV, were also observed in L =3.2-4.6 and L =5.0-5.6. Using a subtracted bi-Maxwellian distribution to model the observed proton ring distribution, we perform three dimensional ray tracing to investigate the instability, propagation and spatial distribution of MS waves. Numerical results show that nightside MS waves are produced by proton ring distribution and grow rapidly from the source location L =5.6 to the location L =5.0, but remain nearly stable at locations L <5.0 Moreover, waves launched toward lower L-shells with different initial azimuthal angles propagate across different MLT regions with divergent paths at first, then gradually turn back toward higher L-shells and propagate across different MLT regions with convergent paths. The current results further reveal that MS waves are generated by a ring distribution of ~10 keV proton and proton ring in one region can contribute to the MS wave power in another region.