Emittance growth in a modified betatron crossing the orbital-turning-point transition

Higher equilibrium current densities are possible in a modified betatron accelerator because the focusing provided by the added azimuthal magnetic field augments the vertical betatron focusing field. As a beam, initially in equilibrium, is accelerated, the vertical field focusing eventually becomes sufficient to overcome beam space charge. The net force consisting of the difference between the relativistically-corrected outward beam space charge force and the inward betatron focusing force then reverses direction. As this net force goes through zero the F × B direction of the poloidal drift also reverses direction going through zero, at which point the electrons can drift out of the beam. Depending on the parameters assumed, these outward drift motions can substantially increase the beam emittance.