| Objective: ||Develop algorithms for correctly (2nd order accuracy minimum) assigning current and charge for PIC particles passing near and intersecting conformal boundaries in an electromagnetic PIC simulation.
|| Description: ||Many of the numerical tools which are used in the design and testing of high power microwave (HPM) sources are built upon finite difference time domain (FDTD) techniques and rely on a tensor product grid with stair-stepped boundaries. This combination requires globally a very fine resolution grid to accurately predict the effects of small scale features. Furthermore, due to the stair-stepping boundary approximation, the global order reduces to first order for sufficiently high resolution. Even on today’s massively parallel computers, it is unfeasible to solve this problem with resolution alone. Traditionally these issues are overcome electromagnetically with one of the three techniques: body fitted coordinates , fractional cell or mixed boundary elements [2, 3] or fully unstructured mesh techniques . These techniques have various advantages and disadvantages which are very problem dependent. Properly accounting for the motion of PIC particles near these boundaries so that charge and current are properly considered and properly applying the local EM fields to the PIC particles are areas where more work is needed.
|| ||PHASE I: The goals of phase I are: 1) survey of techniques which are capable of correctly incorporating particle interaction near conformal boundaries; 2) identification of a solution technique; 3) prototype implementation into either testbed code or AFRL provided model and verified on relevant examples.
|| || ||PHASE II: The goal of phase II is implementation of the algorithms into fully functioning codes, complete with particle emission and propagation. Algorithm should be shown to be scalable, stable and globally second order accurate for problems defined in phase I. Issues such as self force, grid heating, non-physical radiation and self heating should also be mitigated.
|| ||DUAL USE COMMERCIALIZATION: Military application: As well as electromagnetic generation, improved PIC would help in the simulation of the following defense related technologies: plasma opening switches, ion propulsion, and hypersonic drag reduction. Commercial application: Improved PIC code would aid plasma processing and fluorescent lamps, basic plasma research such as dusty plasmas, accelerators, Penning traps, magnetic fusion plasmas, laser-plasma interaction.
|| References: ||1. Karmesin, S.R., P. C. Liewer, and J. Wang, "3D Electromagnetic Parallel PIC in Nonorthogonal Meshes," Plasma Science, IEEE International Conference on June 5, 1995. http://sciserv er.lanl.gov:80/cgi-bin/sciserv.pl?collection=confs&journal=ieee1912& issue=v1995i0506&article=138_3eppinm.
2. Railton, C. and J. Schneider, "An Analytical and Numerical Analysis of Several Locally Conformal FDTD Schemes," IEEE Trans. on Microwave Theory and Tech., Vol. 47, 1999, pp. 51-66.
3. Dridi, K., J. Hesthven, and A. Ditkowski, "Staircase-Free Finite-Difference Time-Domain Formulation for General Materials in Complex Geometries," IEEE Trans. on Ant. and Prop., Vol. 49, May 2001, pp. 749-756.
4. Hesthaven, J. and T. Warburton, "Nodal High-Order Methods on Unstructured Grids, I. Time-Domain Solution of Maxwell's Equations," J. Comp. Phys., Vol. 181, 2002, pp. 186-221.
|Keywords: ||particle-in-cell (PIC), electromagnetic (EM), simulation, conformal, boundary|