Re: A Numeric Study of the Dependence of the Surface Temperature of Beta-Layered Regions

Originally posted by F-18 Hamburger
Beta-layering of deuterium-tritium (D-T) ice in spherical shell geometries is numerically and analytically considered to investigate the relationship between temperature differences that arise because of inner-surface perturbations and the absolute shell thickness. The calculations use dimensions based on a proposed design of an inertial confinement fusion target for use at the National Ignition Facility. The temperature differences are calculated within D-T ice shells of varying total thicknesses, and the temperature differences calculated in three dimensions are compared both to the one-dimensional results and to the expected limits in three dimensions for long- and short-wavelength surface perturbations. The three-dimensional numeric results agree well with both the long- and short-wavelength limits; the region of crossover from short- to long-wavelength behavior is mapped out. Temperature differences due to surface perturbations are proportional to D-T layer thickness in one-dimensional systems but not in three-dimensional spherical shells. In spherical shells, surface perturbations of long wavelength give rise to temperature perturbations that are approximately proportional to the total shell thickness, while for short-wavelength perturbations, the temperature differences are inversely related to total shell thickness. In contrast to the one-dimensional result, we find that in three dimensions there is not a general relationship between shell thickness and surface temperature differences.

Not my field, but phyics should apply…also you should tell people some backgrounds. Here’s what i think…
Well, as said by the first few sentences, this is used for laser (or energy beam) fusion studies. The problem with fusion is that a critical temperature must be achieved before it can be self sustaining during fusion (with proper shielding of course or else it’ll quickly cool down and turn itself off). Ok, now you start with D-T “ice” as they call it, most probably a cryotenetically cooled hydrogen isotopes to basically like an “ice” ball shell…quick searches tells you that the shell is basically “molded” by something else. Traditionally, AFAIK, a glass sphere of ~100um dia is used to hold high pressure D-T (~1-300kpsi)…but in this case they use “solid” phase shells of the fuel material probably to increase the initial fusion energy density deposited by the lasers. So, the question is all about heat transport. By focusing energy beams on it, the energy is transfered to the D-T…but the question is how much of it can be contained, hence you need to know the heat transport characteristics. Now it seems like the shell “smoothness” is highly critical since you don’t want the highly focused beam to hit the outside of the shell only to be diffracted due to the lack of smooth shell surfaces (both inside and out…outside should be controlled by the molding material). The high and low frequency “pertubations” caused by the shell have more to do with 1) the laser energy deposition step which might cause a loss of focused energy to the gas phase D-T inside the shell and hence reduced focus energy. So you want to know its characteristics. By the way Temperature difference should be mean dT (differential temperature difference) and in the context of dT/dx (heat transport)…however since the dimensions was stated to be based on some “standard”, the dx is deemed “constant” and you can compare things simply by using dT. 2) It seems like the temperature difference during the formation of these shells thru Beta-layering is controlling the inner surface smoothness of the shells. Beta should be referring to the radioisotope decay (hence generating heat, hence providing the perturbation energy for mass to transport and hopefully smooth out the shells automatically if done right). All in all, this is just some characterization study of mass and heat transport done between 1 and 3D analysis. Usually they are different in this kinds of scales…not really a surprise there.