Abstract
The spot size and focal length of a one-eighth betatron wavelength final focusing cell with a nonuniform current density distribution are predicted. The final focusing cell is modeled with an azimuthal magnetic field distribution that varies as rN. A Lie transform method is used to determine the behavior of the ion beam as it passes through the focusing cell. The analysis indicates that a final focusing cell with a current density distribution that is strongly concentrated at the channel edge focuses the beam much less efficiently than a channel with a uniform current density distribution, and provides a scaling relation for the focused beam radius: rfoc ∝rc (Ic/ If)1/2N, where rc is the unfocused beam radius, If is the discharge current in the focusing cell, and Ic is the discharge current in the transport channel.
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