have a time average azimuthal speed of u03c9 rmf r o the spatial separation reduces the frequency of impacts of the fast betatron segments with the slower cyclotron segments the cause of the radial distillation is the u03b5 u03c6 u00d7 b z radial drift executed by cyclotron orbits where b z is the frc 39 s axial field the value of a pbo particle 39 s peak azimuthal energy w u03c6 max is approximately proportional to u03b6 u03c9 rmf b rmf r o u03c6 pbo where u03b6 is the charge on the particle accordingly 3 he 2 will have twice the energy as d but because of 3 he 39 s greater mass its peak azimuthal velocity will only be 15 faster than d 39 s about 1 3of the particles will have velocity within 80 of the maximum the ratio of a betatron orbit particle 39 s radial to azimuthal energy w r w u03c6 will depend on the initial position and velocity of an ion relative to the rmfo 39 s phase in a scenario w r w u03c6 max u02dc 1 2for one pbo in other scenarios w r w u03c6 u02dc 1 3is common though values as small as 1 200and as large as 1 1have been seen in simulations the value of w r w u03c6 at a collision depends on the azimuthal extent of the pbo crescent u03c6 pbo in the rmf frame its radial.