Final Focusing of Intense Ion Beams with Radially Nonuniform Current Density Z-Discharges
Abstract
The spotsize and focal length of a one-eighth betatron wavelength final focusing cell with a nonuniform current density distribution are predicted. The predictions are based on a Lie Transform solution to the equations of motion of an ion in an azimuthal magnetic field that models various distributions of the discharge current density. The solution to the nonlinear equations of motion is coupled to a simple phase space concept that yields both the minimum spotsize and focal length of the final 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. Quantitatively, by employing a simple model azimuthal magnetic field distribution of the form B(r) sub theta proportional to r to the Nth power, the analysis provides an approximate relation between the focused beam radius (r sub foc), the unfocused beam radius (r sub c), and the ratio of discharge current in the focusing cell (I sub f) to that in the transport channel (I sub c): r sub foc approx. = r sub c (I sub c/I sub f) 1/2 to the Nth power. Keywords: Ion beams; Focusing; Z discharges.
Document Details
- Document Type
- Technical Report
- Publication Date
- Oct 26, 1988
- Accession Number
- ADA200347
Entities
People
- J. J. Watrous
- Paul F. Ottinger
Organizations
- United States Naval Research Laboratory