The feed-out process: Rayleigh-Taylor and Richtmyer-Meshkov instabilities in thin, laser-driven foils Page: 42 of 193
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into an almost isotropic state. If the radiation is anisotropic, then the diffusion
approximation may not be used. Caution must be exercised in the application of
diffusion to radiation, as the LTE assumption, isotropy, and therefore diffusion,
may not be valid for all frequencies. For example, the peak of the hohlraum radia-
tion spectrum used to drive the feed-out packages is about 150-200 eV. For most of
the plasma, LTE at this temperature is a good assumption, but not for the ablated
material. In addition, there are high energy components to the spectrum in the
keV range. These photons stream through the packages with e-folding distances
on the order of the size of the package, breaking the LTE assumption. As they rep-
resent only a small portion of the total energy in the radiation field, diffusion may
still be used.
Diffusion in a radiation field in LTE may be written as:
S = JIv2(dQ)dv = 41( 3aT3) VT, (2)
stating that the flux of radiant energy of all frequencies, S, is proportional to the
gradient of the temperature, T. The symbol 1 is the average mean free path for a
Planckian distribution over all frequencies and is commonly termed the Rosse-
land mean free path. The total energy lost or gained per unit volume of fluid, per
unit time due to radiation transport, q, is now simply q = V.5. Thus, by assum-
ing LTE and diffusion, the radiation transfer problem has been reduced to a prob-
lem very similar to heat transport. This approximation and is frequently known
as the radiation heat conduction approximation [Duderstadt].
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Smitherman, D.P. The feed-out process: Rayleigh-Taylor and Richtmyer-Meshkov instabilities in thin, laser-driven foils, report, April 1, 1998; New Mexico. (https://digital.library.unt.edu/ark:/67531/metadc699271/m1/42/: accessed April 19, 2024), University of North Texas Libraries, UNT Digital Library, https://digital.library.unt.edu; crediting UNT Libraries Government Documents Department.