1. The Heavy Ion Fusion Virtual National Laboratory Towards An Analytic Model for Beam Spot Size in Ballistic Neutralized Transport Simon Yu, J. Barnard, W.M. Sharp, D. Welch, D. Rose, C. Olson ARIES Meeting, San Diego 1/10/2002

2. The Heavy Ion Fusion Virtual National Laboratory Beam Envelope Model The propagation of a beam from beam port to target can be described by an envelope equation: WhereR-beam radius  -beam emittance U-Net perveance z-distance

3. The Heavy Ion Fusion Virtual National Laboratory Existing Model in System Code Assume total neutralization (i.e. beam is force-free) Then U =0  =constant Solution: WhereR t = beam radius at target R o = beam radius at beam port L = chamber radius

4. The Heavy Ion Fusion Virtual National Laboratory Generalization to incomplete neutralization Emittance growth  (z) Nonzero net perveance U(z)  0 Approximate solution for R t Observations: R t depends on final emittance  t and net perveance near the target U t When space charge dominates U t < O, R t  When pinch forces dominate U t > O, R t 

5. The Heavy Ion Fusion Virtual National Laboratory Neck radius depends primarily on final emittance, not on the evolution of the emittance

6. The Heavy Ion Fusion Virtual National Laboratory To Calculate Emittance Growth (exact) - dimensionless radial shape factor = 0 for flat charge distribution 0.5 for nearly charge neutralized beams U~ Z m e /m i Final emittance given by (for U constant)