• J.J. Barnard
  LLNL, Livermore, California
• J.E. Coleman, D. Ogata, P.A. Seidl
  LBNL, Berkeley, California
• D.R. Welch
  Voss Scientific, Albuquerque, New Mexico

Funding: Work performed under the auspices of the U.S. Department of Energy under contract DE-AC52-07NA27344 at LLNL, and University of California contract DE-AC03-76SF00098 at LBNL.
We estimate the energy fluence (energy per unit area) at the focal plane of a beam undergoing neutralized drift compression and neutralized solenoidal final focus, as is being carried out in the Neutralized Drift Compression Experiment (NDCX) at LBNL. In these experiments, in order to reach high beam intensity, the beam is compressed longitudinally by ramping the beam velocity (i.e. introducing a velocity tilt) over the course of the pulse, and the beam is transversely focused in a high field solenoid just before the target. To remove the effects of space charge, the beam drifts in a plasma. The tilt introduces chromatic aberrations, with different slices of the original beam having different radii at the focal plane. The fluence can be calculated by summing the contribution from the various slices. We develop analytic formulae for the energy fluence for beams that have current profiles that are initially either constant or parabolic in time. We compare with envelope and particle-in-cell calculations. The expressions derived are useful for predicting how the fluence scales with accelerator and beam parameters.