Particle orbit in a radial-sector scaling FFAG

The particle orbit in the bending magnet of a radial-sector FFAG accelerator is derived analytically in the approximation valid for a small bending angle. The orbit is described in terms of the distance from the machine center, r, and its variation is derived as a function of the bending angle. Also, the variation of the distance from the bending center, ρ , is derived as a function of the bending angle. The result shows how the ratio, r / ρ , can be made independent of the particle momentum, which is one of the conditions of the scaling property.