Recent progress in the simulation of heavy ion beams

Production of electric power by using a beam of heavy ions to ignite an inertially-confined fusion target requires the focusing of high-power beams onto a small spot several meters distant from the final lens system. Beams with the necessary intensity generally behave like warm nonneutral bounded plasmas where beam kinetic temperatures are sufficiently high that a cold-plasma description can be inadequate for describing the collective space-charge modes. In view of the complexity of the self-consistent nonlinear dynamics, analytic study has largely been limited to the singular Kapchinskij–Vladimirskij (K–V) distribution. Numerical simulations, primarily using the WARP [D. P. Grote, A. Friedman, I. Haber, W. Fawley, and J. L. Vay, Nucl. Instrum. Methods Phys. Res. A 415, 428 (1998)] particle-in-cell (PIC)/accelerator code, have been employed to identify the degree to which the analytic results, especially the predictions of unstable modes, are applicable to realistic beam distributions. During extensive benchmarking of the code against experiments at Lawrence Berkeley National Laboratory, Lawrence Livermore National Laboratory, and the University of Maryland, a particular feature of the beam which has been seen in both experiment and simulation is the launching, in the source region, of collective warm-plasma oscillations similar to those predicted on the basis of the K–V analysis.