Appendix A THEORY AND PREDICTION This appendix contains additional material used primarily for theoretical analysis and prediction of the radiation fields expected from the two underwater detonations. Since this same material ts also helpful in the interpretation of some of the results presented in this report, it has been summarized briefly in the following sections. A.1 FACTORS FOR THEORETICAL CALCULATIONS All factors used in the calculation of the relative contributions to the total gamma field have been tabulated in as compact a form as possible. may be found in the literature cited. A more detailed discussion of these factors A.2 THEORETICAL DEPOSITION FROM A RADIOACTIVE CLOUD Calculated values of the free-field dose expressed as a percentage of the gross gammafield are presented in Table A.8 for a number of cloud slopes (Section 1.3.1). The values for cloud slopes of 0.17 and 0.05 are also plotted in Figures 1.5 and 1.6. A.3 MODEL FOR AN INCLINED WALL OF APPROACHING BASE SURGE To analyze the gamma radiation fields due to the base surge, it is useful to deduce the radiation intensity at a stationary detector as it is approached by a radiating cloud of finite thickness whose leading and trailing edges are sloped away from the detector position at a specified angle. The theoretical considerations in Reference 46 and the base surge photography establish this angle at 60°. The direct solution of this problem leads to an intractable analytical expression; therefore, the following geometrical approximations are employed to obtain the desired solution. An inclined cloud of infinite height and breadth but of finite thickness approaching along the ocean’s surface is assumed to continue to infinity beneath the ocean surface (Figure A.3). The radiation intensity from both the real cloud and its imaginary extension below the ocean’s surface is exactly that which would be observed at a point a distance V3/2 h above a slab of homogeneously distributed radioactivity whose thickness is V3/2s, where h Is the distance along the ocean’s surface to the leading edge of the real cloud. The analytical expression for sucha slab is integrable (Reference 39), and the resultant radiation intensity may be computed. If now an imaginary ocean surface is drawn below the true surface so that the surface is a mirror image of the true surface, it is obvious that the radiation intensity due to the real cloud is exactly half that due to the slab of homogeneous activity less the radiation due to the infinitely long trapezoidal strip bounded by the true ocean surface and its mirror image. The radiation resulting from such a strip has been calculated in Reference 119, on the attenuation of gamma radiation by iron plates, if the special case of an iron piate of zero thickness is considered. Thus, by first calculating the radiation intensity from a slab of homogeneously distributed radioactivity then subtracting the intensity due to a trapezoidal strip whose width is h on the surface toward the detector, and finally dividing the difference by two, the radiation fields due to base surge approaching at an angle of 60° were computed for a number of distances from the leading edge to the detector. The results of these calculations are presented in Section 1.3.2. 347