Final focusing of intense ion beams with radially nonuniform current density Z-discharges
The spotsize and focal length of a one-eighth betatron wavelength final focusing cell with 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/sub /theta//(r) /proportional to/ r/sup N/, 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/ /approximately/ r/sub c/(I/sub c//I/sub f/)/sup 1/2N/. 6 refs., 11 figs.
- Research Organization:
- Naval Research Lab., Washington, DC (USA)
- DOE Contract Number:
- AI03-79DP40092
- OSTI ID:
- 6688847
- Report Number(s):
- NRL-MR-6338; ON: DE89003512
- Resource Relation:
- Other Information: Portions of this document are illegible in microfiche products
- Country of Publication:
- United States
- Language:
- English
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Related Subjects
ION BEAMS
FOCUSING
BEAM TRANSPORT
BETATRON OSCILLATIONS
CURRENT DENSITY
EQUATIONS OF MOTION
INERTIAL CONFINEMENT
ION BEAM FUSION REACTORS
MAGNETIC FIELDS
NONLINEAR PROBLEMS
NUMERICAL SOLUTION
PHASE SPACE
TRAJECTORIES
BEAM DYNAMICS
BEAMS
CONFINEMENT
DIFFERENTIAL EQUATIONS
EQUATIONS
MATHEMATICAL SPACE
OSCILLATIONS
PARTIAL DIFFERENTIAL EQUATIONS
PLASMA CONFINEMENT
SPACE
THERMONUCLEAR REACTORS
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