The result is the formation of a crater with a considerable amount of close-in fallout and throwout. Since in cratering the cavity never stabilizes, a significant amount of fused rock will be present in the fallout, as well as species that are volatile, primarily present as a surface coating on many of the particles formed during the fracturing and spallation of the overburden. The fraction of activity, including transuranics, released to the fallout field depends on the yield and the depth of burial (scaled to 1 kiloton). The optimum emplacement depth of the device for producing the largest crater is approximately that depth for which spallation and gas acceleration contribute about equally to crater formation. This depth is not necessarily the depth at which the maximum amount of radioactivity appears in the fallout, however. When the emplacement of the device is at shallow depth so that the cavity or even the fireball breaks through the surface, the characteristics of a surface burst are approached. However, fallout from a surface burst and from bursts above the surface is better understood by an approach starting with a consideration of free-air bursts. For a more extensive discussion of free-air bursts, see Glasstone (1962). A free-air burst is defined as a burst in which the fireball does not interact with the land or water surface beneath it. Here, we limit the definition to include only those bursts occurring at an altitude such that no surface materials enter the fireball before it has cooled to at least the solidification temperature of the vaporized species resulting from the chemical interaction of the device materials with the air. As the fireball increases in size and cools, the vapors condense and form a cloud of solid particles of device debris. Thus, the solid contents of the cloud consist almost entirely of highly radioactive device debris in the form of small, generally smooth, round particles having an approximately lognormal size distribution with a geometric mean (median) diameter of about 0.14 pm and a geometric standard deviation of about 2.1 (Nathans, 1976a). The radionuclide concentrations more or less follow the radial distribution theory of Freiling in the particle size range above several micrometers; that_is, the concentrations have a particle size dependence as (diameter) , where m lies between 0 and -1, depending upon the volatility of the radionuclide species condensing in the fireball. However, in the particle size range below a few micrometers, the radionuclide concentrations increase quite sharply with decreasing particle size (Nathans, 1971). Because of the small size of the particles that are formed, a free-air burst leaves virtually no local fallout. Usually, as the cloud rises, some of the particles are left behind to form a "stem.'' There is some evidence that the mean size of the parti-~ cles in this "stem" is a little larger than that of the particles in the main cloud (Nathans, 1971). In addition, the cloud rise causes the appearance of a strong updraft in its wake with inflowing winds ("afterwinds"). 552