Laser ray tracing and power deposition on an unstructured three-dimensional grid

Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics

Volumn 61, Issue 1, 2000, Pages 895-905

  Kaiser, Thomas B ^a  

^a LAWRENCE LIVERMORE NATIONAL LABORATORY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

ELECTROMAGNETIC WAVES; GAUSSIAN BEAMS; LASER BEAMS; RAY TRACING;

ELECTRON-DENSITY GRADIENTS; GAUSSIAN QUADRATURES; POWER DEPOSITION; RAY TRAJECTORY EQUATION; SPATIAL VARIATIONS; THREE DIMENSIONS; THREE-DIMENSIONAL GRIDS; UNSTRUCTURED GRID;

DEPOSITION;

EID: 0005320454     PISSN: 1063651X     EISSN: None     Source Type: Journal    
DOI: 10.1103/PhysRevE.61.895     Document Type: Article

References (31)

1. D. S. Kershaw, M. K. Prasad, M. J. Shaw, and J. L. Milovich, Comput. Methods Appl. Mech. Eng. 158, 81 (1997).
2. A. I. Shestakov, M. K. Prasad, J. L. Milovich, N. A. Gentile, J. F. Painter, and G. Furnish, ICF Quarterly Report, Lawrence Livermore National Laboratory, Livermore, CA, UCRL-LR-105821-96-6, Vol. 6, No. 4, July-Sep. 1996, pp. 165–180.
3. A. I. Shestakov, J. Milovich, and D. Kershaw, SIAM News, 32(4), 6 (1999). This paper presents results of a parallelized simulation of a laser-driven 3D implosion that uses the scheme developed in the present paper.
4. D. S. Miller (private communication)on KULL, an LLNL ASCI code being developed to perform ICF simulations.
5. E. Mazzucato, Phys. Fluids B 1, 1855 (1989).
6. G. V. Pereverzev, Nucl. Fusion 20, 109 (1992).
7. A. Friedman, Bull. Am. Phys. Soc. 28, 1124 (1983).
8. In general, more than one way exists to compute (Formula presented) from the available data. Care must always be taken that the method chosen satisfies crucial constraints, e.g., that (Formula presented) computed by Eq. (1) be non-negative.
9. L. D. Landau and E. M. Lifshitz, Electrodynamics of Continuous Media (Addison-Wesley, Reading, MA, 1966).
10. G. Zimmerman (private communication).
11. L. Lapidus and G. F. Pinder, Numerical Solution of Partial Differential Equations in Science and Engineering (Wiley, New York, 1982), Chap. 3.
12. The order of the nodes is important: each unique ordering determines a different surface.
13. That coplanarity implies (Formula presented) is clear. To prove the converse, define (Formula presented) Then (Formula presented) from which it is obvious that (Formula presented) implies that (Formula presented) can have no component parallel to (Formula presented) i.e., either (Formula presented) (Formula presented) and (Formula presented) (the displacements of nodes 1, 2, and 3 from node 0) are coplanar, or one of them vanishes, in which case two nodes coincide.
14. Nothing in the derivation of Eqs. (20),(21) depends on (Formula presented) so that those equations are also applicable to the nonplanar case. Equations (16),(17) are simpler to compute, however, and therefore preferable.
15. Jose Milovich (private communication).
16. In practice, the smallest root larger than (Formula presented) where (Formula presented) is a few times the machine roundoff error, (Formula presented) is the zone volume, and c is the speed of light, would be used.
17. Gary Kerbel (private communication).
18. Nicholas Wilt, Object-Oriented Ray Tracing in C++ (Wiley, New York, 1994).
19. W. L. Kruer, The Physics of Laser Plasma Interactions (Addison-Wesley, Redwood City, CA, 1988).
20. D. L. Book, NRL Plasma Formulary, NRL Publication 0084-4040, 1986.
21. T. W. Johnston and J. M. Dawson, Phys. Fluids 16, 722 (1973).
22. S. I. Braginskii, in Reviews of Plasma Physics, edited by M. A. Leontovich (Consultants Bureau, New York, 1965), Vol. 1, p. 205.
23. Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, edited by M. Abramowitz and I. A. Stegun (Wiley, New York, 1972), Sec. 25.4.30.
24. The Coulomb logarithm is independent of (Formula presented) in the presence of a laser electric field 192021.
25. Due to the periodic nature of the ray motion, there is a fortuitous cancellation of accumulated trajectory error each time the ray reaches a point that is an integral number of half-wavelengths from its starting point that leads to an apparent error scaling (Formula presented) Conversely, the error is largest at odd numbers of quarter-wavelengths from the starting point and scales as expected there.
26. For simplicity (Formula presented) was fixed at its value at (Formula presented)
27. The same result can be derived from a more lengthy algebraic analysis of all the coefficients of (Formula presented) See W. H. Beyer, CRC Standard Mathematical Tables, 28th ed. (CRC, Boca Raton, FL, 1989), pp. 210–211.
28. Gary Kerbel (private communication).
29. J. J. Thompson, C. E. Max, and K. Estabrook, Phys. Rev. Lett. 35, 663 (1975).
30. J. Harte and G. Zimmerman, LLNL Report UCRL 79860, 1978.
31. Note that summing individual ray energy densities presupposes that the rays are statistically independent.