## HIF Analytic Work

Although numerical simulations are used for the detailed design and analysis of HIF experiments, analytic work provides a valuable complement. This work is used mainly to develop advanced numerical methods and to assess the importance of physical effects that are not yet in computer models.

Anaysis has been extensively used to improve the numerical methods used in WARP and other simulation codes, resulting both in reduced running times and in enhanced realism. Useful work has been done in the following areas:

The analytic work aimed at understanding physics that is missing from simulations includes several efforts:

- Devising algorithms that allow a longer time-step in WARP without sacrificing accuracy.
- Developing an improved outward-wave boundary condition for use in BPIC and other codes.
- Working out algorithms for reconstrucing a 6-D distribution function from slit-scan data.
- Adding adaptive mesh refinement to WARP to improve resolution where it is important
- Generating models for WARP with reduced dimensionality or physics content, such as a Darwin field solver and the fluid / envelope HERMES model.
- Developing algorithms for matching, steering, and shaping beams in accelerators.
A final area where analysis proves valuable is the distillation of simulation results into scaling laws that can be used in the systems code IBEAM.

- Understanding and modeling multiple-beam effects during acceleration and transport. This work includes the evaluation of transverse forces due to the beam electric and magnetic forces, the calculation of inductive effects on the electric fields of pulses, and the determination of whether plates with holes are needed in gaps to short out the transverse electric fields of beams.
- Estimating the generation of electrons by beam-gas or beam-wall collisions, and assessing the effects of these electrons on ion-beam transport and focusing.
- Analyzing collective instabilities driven by anisotropic pressure to determine the saturation levels and to identify operating regimes for stable propagation.
- Understanding the physics of beam-halo formation and predicting halo size and the production rate of halo particles.
- Using a Hamiltonian averaging technique to study the transport of intense beams in a periodic focusing system.
- Modeling self-pinched transport in a fusion chamber to ascertain whether a stable transport regime exists at background-gas pressures above a few milliTorr.
- Developing a phenomenological models for calculating emittance growth and collisional-ionization cross sections in a fusion chamber.

referencesR. C. Davidson, H. Qin, and P. J. Channell,

Special Top. Accel. Beams2,074401 (1999) and3,029901 (2000).J.-L. Vay, "A New Absorbing Layer Boundary Condition for the Wave Equation",

J. Comp. Phys.165, 511 (2000).

J.-L. Vay, "Asymmetric Perfectly Matched Layer for the Absorption of Waves.",

J. Comp. Phys.183, 367-399 (2002).

For comments or questions contact WMSharp@lbl.gov or DPGrote@lbl.gov. Work described here was supported by the Office of Fusion Energy at the US Department of Energy under contracts DE-AC03-76SF00098 and W-7405-ENG-48. This document was last revised June, 2002.