Constant radius magnetic acceleration of a strong non-neutral proton ring

Abstract

The constrained or constant radius magnetic acceleration of a strong non‐neutral proton ring by a modified betatron field is considered. The modified betatron field consists of an azimuthal magnetic field B_ϑ superimposed on a betatron field B_z in which the 1 : 2 flux rule is satisfied. An important advantage of the constrained acceleration is that the energy of the nonrelativistic ions increases with the square of the magnetic field. It has been found that the orbits of the gyrating particles are stable when the self‐field index n_s{=ω²_p[2γ_0ϑ(t) Ω²₀(t)]⁻¹} is much greater than unity, provided that n_s< (B_ϑ/2B_z)² at the orbit. For B_ϑ=0, the orbits are stable only if n_s<1/2.