  Purpose: To measure dispersion of a clinical proton therapy beam.
  Methods and Materials: The proton center at our institution uses a Hitachi
PROBEAT V synchrotron that delivers beams with energies ranging from 70 to 230
MeV to five treatment rooms, four of which have gantries and one fixed beam.
For this study, the magnetic field strengths of all optics in the transport
line were varied to measure the dispersion of 230 MeV beams in each of the four
gantry rooms. Beam position was measured using the Spot Position Monitor (SPM),
a multi-wire proportional counter (MWPC) in the nozzle approximately 0.5 meters
upstream of the treatment isocenter. Measured beam positions as a function of
momentum offset were fitted to a linear function to extract dispersion. In one
gantry, dispersions for 70 and 140 MeV beams were also measured. Because spot
position is continuously monitored during treatments and a position deviation
will abort the beam delivery, the dispersion at the spot position monitor was
used to set an upper limit of range uncertainty originating from momentum
deviation. When dispersion was approximately zero, dose rate measurements were
used to set an upper limit of momentum deviation that could reach the patient.
  Results: Dispersion was 0.45 m, 0.48 m and 0.30 m for 70 MeV, 140 MeV, and
230 MeV beams in a gantry, respectively, corresponding to 0.3 mm, 1.0 mm and
3.5 mm maximum range uncertainty during treatments. For 230 MeV beams,
dispersion ranged from 0 to 0.73 m across the four gantries, corresponding to
the upper limits of range uncertainty due to momentum deviation of 1.4 to 6.2
mm (0.4 to 1.9% in fractional range uncertainty).
  Conclusions: The measured dispersion was both energy- and gantry-dependent
and ranged from 0 to 0.73 m.
