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Title: Bent Marshak waves

Abstract

Radiation-driven heat waves (Marshak waves) are ubiquitous in astrophysics and terrestrial laser-driven high-energy density plasma physics experiments. Generally, the equations describing Marshak waves are so nonlinear, that solutions involving more than one spatial dimension require simulation. However, in this paper it is shown that one may analytically solve the problem of the two-dimensional nonlinear evolution of a Marshak wave, bounded by lossy walls, using an asymptotic expansion in a parameter related to the wall albedo and a simplification of the heat front equation of motion. Three parameters determine the nonlinear evolution: a modified Markshak diffusion constant, a smallness parameter related to the wall albedo, and the spacing of the walls. The final nonlinear solution shows that the Marshak wave will be both slowed and bent by the nonideal boundary. In the limit of a perfect boundary, the solution recovers the original diffusion-like solution of Marshak. The analytic solution will be compared to a limited set of simulation results and experimental data.

Authors:
;  [1]
  1. University of California, Lawrence Livermore National Laboratory P.O. Box 808, Livermore, California 94551 (United States)
Publication Date:
OSTI Identifier:
20860400
Resource Type:
Journal Article
Journal Name:
Physics of Plasmas
Additional Journal Information:
Journal Volume: 13; Journal Issue: 11; Other Information: DOI: 10.1063/1.2388268; (c) 2006 American Institute of Physics; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 1070-664X
Country of Publication:
United States
Language:
English
Subject:
70 PLASMA PHYSICS AND FUSION TECHNOLOGY; ANALYTICAL SOLUTION; BOUNDARY LAYERS; COMPUTERIZED SIMULATION; DIFFUSION; ENERGY DENSITY; EQUATIONS OF MOTION; HEAT; LASERS; NONLINEAR PROBLEMS; PLASMA; PLASMA SIMULATION; RADIATION TRANSPORT; TWO-DIMENSIONAL CALCULATIONS; WALL EFFECTS

Citation Formats

Hurricane, O A, and Hammer, J H. Bent Marshak waves. United States: N. p., 2006. Web. doi:10.1063/1.2388268.
Hurricane, O A, & Hammer, J H. Bent Marshak waves. United States. https://doi.org/10.1063/1.2388268
Hurricane, O A, and Hammer, J H. 2006. "Bent Marshak waves". United States. https://doi.org/10.1063/1.2388268.
@article{osti_20860400,
title = {Bent Marshak waves},
author = {Hurricane, O A and Hammer, J H},
abstractNote = {Radiation-driven heat waves (Marshak waves) are ubiquitous in astrophysics and terrestrial laser-driven high-energy density plasma physics experiments. Generally, the equations describing Marshak waves are so nonlinear, that solutions involving more than one spatial dimension require simulation. However, in this paper it is shown that one may analytically solve the problem of the two-dimensional nonlinear evolution of a Marshak wave, bounded by lossy walls, using an asymptotic expansion in a parameter related to the wall albedo and a simplification of the heat front equation of motion. Three parameters determine the nonlinear evolution: a modified Markshak diffusion constant, a smallness parameter related to the wall albedo, and the spacing of the walls. The final nonlinear solution shows that the Marshak wave will be both slowed and bent by the nonideal boundary. In the limit of a perfect boundary, the solution recovers the original diffusion-like solution of Marshak. The analytic solution will be compared to a limited set of simulation results and experimental data.},
doi = {10.1063/1.2388268},
url = {https://www.osti.gov/biblio/20860400}, journal = {Physics of Plasmas},
issn = {1070-664X},
number = 11,
volume = 13,
place = {United States},
year = {Wed Nov 15 00:00:00 EST 2006},
month = {Wed Nov 15 00:00:00 EST 2006}
}