A New Look at the Fission-Product Gamma-Ray Component of Nuclear Weapon Initial Radiation*

Paper 13

A NEW LOOK AT THE FISSION-PRODUCT GAMMA-RAY COMPONENT OF NUCLEAR WEAPON INITIAL RADIATION*

L. G. Mooney and R. L. French Radiation Research Associates, Inc. Fort Worth, Texas

*RRA-M-7102; based on work sponsored by the Defense Nuclear Agency and performed under subcontract for the Oak Ridge National Laboratory.

251 253

ABSTRACT

A new model has been developed for predicting the fission- product gamma-ray component of the initial radiation exposure during the first minute following a nuclear detonation in air. The model incorporates Monte Carlo air transport data, fission- product source spectra, cloud rise approximations, air-ground interface effects, and hydrodynamic enhanc€iment treatments from the work of a numbar of previous investigators. Fission-product gamma-ray doses calculated with the model,, when combined with secondary gamma-ray doses based on StrakerTs air-over-ground neutron transport calculations, give results that generally agree with weapons test data within 25% for low-yield weapons and 50% for high-yield weapons. Calculations performed with the model show that the fission-product component of nuclear weapon initial radiation is often much more important than is generally indicated in the weapons effects literature. 254

INTRODUCTION

The fission-product gamma-ray component of the initial radiation exposure from nuclear weapons has been mentioned in a number of publi- cations dealing with initial radiation.l*z*3However, the importance of fission-product- gamma rays during the first minute or so following a detonation has generally been underestimated in both the unclassified and the classified literature. The relatively poor understanding of the fission-product gamma rays has been due largely to the fact that, in the absence of a systematic approach for calculating this component from theoretical considerations, most information has been based on data measured in weapon tests where the distinction between the fission- product and the secondary gamma-ray components is often not clear. (The integral dose from prompt fission gamma rays is negligible compared to the other components because they are emitted and largely absorbed by the weapon while it is still intacti)

The recent availability of accurate data5 describing the pro- duction and transport of air- and ground-secondary gamma rays and techniques6 for applying these data to specific weapons has provided new incentive for calculating the transport of fission-product gamma rays from basic principles. Knowing the portion of the measured initial gamma-ray dose which may be attributed to secondary gamma rays, one can compare calculated fission-product doses with the remainder. With this opportunity in hand, a reasonably successful method has been developed essentially from basic principles which permits calculations of the fission-product dose. These doses, when combined with those resulting from secondary gamma rays, have been found to give good agreement with measured data for a wide range of weapons.

The number of gamma rays emitted from fission products, their energies, and the decay rates are well known. Gamma-ray cross sections are relatively easy to handle in transport calculations. Several methods are available with which gamma-ray transport in an air or 255 air-over-ground geometry may be calculated to a high degree of accuracy. In spite of these facts, there is a dearth of reliable quantitive calculated data on the magnitude and spatial distributions of the gamma dose from the decay of fission products during the first one or two minutes after the detonation of a nuclear weapon. This situation results largely from a combination of source and media dynamics that is probably unique in transport problems. These dynamics include the formation and evolution of the fireball, the cloud expansion and rise, the decay of the fission products with time, and the severe pertubation of the air through which the radiation penetrates.

The formation of the fireball and the expansion and rise of the cloud depends upon weapon yield, weapon design, atmospheric conditions, and other parameters. The distribution of fission products in the cloud as a function of time is not well known, and, consequently, the attenuation of fission-product gamma rays within the cloud can only be approximated.

The sudden release of energy in the form of blast and shock produces an immediate increase in temperature and pressure thus pro- ducing hot, compressed gases from the weapon material. The gases ex- pand rapidly and, in so doing, initiate a pressure wave, called a "shock wave" in the surrounding medium. The characteristic of a shock wave is that there is a sudden increase of pressure at the front with a gradual decrease behind it. Associated with this pressure change is a much more severe change in the density of the heated air behind the shock front. It is the large reduction in the air density or optical depth between the rising source and the receiver which produces the enhancement of gamma-ray intensities from hydrodynamic effects. These effects may last for several minutes and reach out to large distances from the detonation. The intensity and duration of hydrodynamic effects increase with weapon yield. 256

A fission-product gamma prediction model capable of considering all of these factors in full detail is impossible to for- mulate with existing technology. However, there are adequate data and techniques available for treating the most important considerations and there are reasonable approximations available for the remainder. The principal objectives of the study upon which this paper is based were to develop the available treatments into a single comprehensive fission-product calculation model and to evaluate the model through compairsons with weapon test data. The study was performed in 1969 and was originally reported in the classi fied literature. During the preparation of the present paper, the authors learned of another formulation7 which is similar in many details to the one described herein. 257

METHODS DEVELOPMENT

In developing the model to calculate the fission-product gamma exposure from weapons, the effects of cloud rise (assuming a point source of radiation), source decay with time, and hydrodynamic enhancement were studied in the order mentioned. The final model in- cludes these factors plus an accurate definition of the predetonation environment and geometry. Limited sensitivity studies indicated that the effect of cloud expansion and attenuation within the cloud and associated debris could be assumed negligible for separation distances of practical interest. Hence the cloud is treated as a point isotropic source.*

The model is unique in that all factors considered in the dynamics of the problems with the exception of the cloud-rise formula, are based on data or methods obtained from basic considerations, either from theoretical calculation or from data generated in the laboratory. The model employs the predetonation geometry and environment (i.e., the detonation height, detector height, air density, air pressure, etc.). The gamma-ray attenuation in air following detonation is obtained from Monte Carlo transport data8 using an energy spectrum measured in the laboratory9. The formalisms giving the original source intensity and decay with time were also obtained from laboratory measurements9. The hydrodynamic enhancement is based on empirical expressions fitted to data obtained from a mathematical treatment of idealized shock front behavior.

Air Transport Data Development of the model for calculating the fission-product gamma exposure starts with consideration of the transport of gamma rays from an idealized point isotropic source of gamma rays in air. Monte Carlo data giving the dose versus distance in an infinite air medium for monoenergetic gamma-ray point sources with energies of 0.5, 1, 2, 4, 6, 8, and 10 MeV have been reported by Marshall and Wells8. These data were folded with the fission-product energy spectrum in the 0.2 - 0.5 second-time interval following fission. This energy spectrum was taken

* Studies reported in Reference 7 further substantiate the point source approxitaation. 258 from t.he measurements of Engle and Fishet* and is representative of all gamma rays emitted during the first minute following fission*

As the next step, the resulting data were plotted in the form of R* dose per source photon from fission-product decay versus range R expressed in mass thickness or optical depth (gn»/cra2). This curve was fitted by the expression

R2D(R> - Aa~R/A where

A « 3.611 X 10~17 and A « 97.04 for R < 21.28 gas/cm2, and A - 5.826 X l 21.28 gta/cm2.

Source Strength

Since R2D(R) is the dose (rad) per fission-product source photon, it must be multiplied by the source strength of fission products. 23 Assuming 1.45 X 10 fissions/KT, a fission fraction F (i.e., fraction of the total yield attributed to fission), a total yield of W(KT) and a time-dependent fission-product gamma-emission rate of G(T) photons/sec- fission, the total source strength (photons/sec) at time T after fission is

S(T) « 1.45 X 1023 F W G(T) • (2)

The decay rate

G<*> - 1 +°0887 T • <3>

Application of these terms to Equation (1) and rearrangement gives the equation for the time-dependent dose (rad/sec) from a stationary point fission-product source in unperturbed homogeneous air (i.e., without 259 the hydrodynamic effect and air-ground interface effect)

1.16 x 10 J F W A -R/A D(T,R) = (4) (1 + 0.87T)R2

Three modifications of Equation (4) are required to consider the air- ground interface effect, the cloud-rise effect and the hydrodynamic effect.

Air-Ground Interface Effect

A systematic method for adjusting fission-product gamma-ray data for air-grcund interface effects is not yet available. However, gamma- ray interface effects are relatively small and, consequently, no adjustment or a very crude adjustment may suffice for many purposes.. 60 Analysis of BREN measurements10 and related calculations for Co gamma rays indicates, for example, that at a separation distance of 2400 feet and a source height of 300 feet, the dose at a detector at the ground surface is 80% of the corresponding infinite air dose. On the basis of these data, a factor of 0.8 was incorporated into Equation (4) as an approximate air-ground interface adjustment.

Cloud-Rise Effect

To account for cloud rise, a time-dependent separation distance, R(T), is substituted for R. R(T) is developed starting with the fitted equation

fG.19 T0.82 HC(T) - 66.7W (5) which gives the cloud height Hc in yards (with reference to the burst height) as a function of time (seconds) following the detonation of a weapon with a yield of W(KT). For a burst height ^ (yards) and horizontal range R^ (yards) to a detector located at the ground surface, the geometric separation distance (in yards) between the center of the rising cloud and the detector is

(6) 260

For use with Equation (6), R_ must be converted to mass thickness 2 (gm/cm ):

R(T) = 91.44 p RG(T) (7)

3 where p is the ambient air density in gm/cm .

Hydrodynamic Effect

The final modification to Equation (4) is the substitution of a modified mass thickness R'(T) in the exponent to account for the change in mass thickness of air between the source and detector caused by the hydrodynamic effect. Rf(T) is calculated from R(T) as described below. (Note that R(T) must be retained in the numerator of Equation (4), since the geometric distance is not changed by the hydrodynamic effect.)

The modified mass thickness or optical depth is a function of time, yield, ambient air density and pressure, source-detector distance before detonation, and distance at time T after detonation. Several steps are required to calculate Rf(T),

First, a scaled distance, J (yards), is given by

J = 3.798 x 104 fe^3 , (8)

2 where P is the ambient air pressure in dynes/cm and q = 1 for an air 2 1/3 burst (i.e., burst height >10 W ) and is equal to 2 for a surface burst (burst height <10 ! w1'3). (A value of q = 2 was used in the calculations presented in this report.) W is the yield (KT). The scaled distance, J, is used to calculate a scaled unitless time, L, from

P 1/2 T L = 0.012938 - ^ (9) P J where p is the ambient air density. Two additional quantities, C and 261

V, are calculated from J and L:

31278 1 00025 C = J(0.55974L°- + 0.9510L ' )

when L < 6.55, (10)

C = J(L + 0.67279) when L > 6.55, (11)

V = 0.95134 + 0.17507lT0,68722when L < 6.55, (12) and V = 1, when L > 6.55. (13)

A third parameter, Y, is calculated from V by

v - 1Q5(V2-l) 2 • 7V +35 2 The effective optical depth (in gm/cm ) due to enhancement is then calculated from

R'(T) = R(T) 2lV I when R < C (15) 56V -351 C I °

When R > C <16) R.(T) . R(T) ( 1 - SS^ll) (lM ' o 56V -35 / I o where R(T) is the optical depth at time T but neglecting enhancement, as given by Equation (7) and Rq is the original source-detector separation distance.

Final Equation

The final equation for the total fission-product exposure (rad) during the first T seconds following a detonation, including source decay, cloud rise, the interface effect and the hydrodynamic 2 effect at a range of R(gm/cm ) is

22 f -R?(T)/A D(R) = 9.28 x 10 F W A J = d'T. (17) J (1 + 0.87T) R(T) 0 262

CALCULATIONS

Equation (17) and the equations for the various terms were coded for numerical solution by computer. The coded version of the model was used to calculate the fission-product gamma-ray exposure as a function of range, air density, weapon yield, and burst height. These calculations were made with and without hydrodynamic enhancement to better determine the importance of the effect.

An example of the output of the code is shown in Figure 1, which illustrates the effects of cloud rise and hydrodynamic enhancement for a nominal 1-KT weapon. It is noted that even for this low yield, the hydrodynaroic effect increases the fission-product gamma dose by approximately 50%. However, by coincidence, this increase is almost exactly ofi>et by the cloud-rise effect.

Figure 2 shows the hydrodynamic enhancement factor for a range of weapon yields at ranges up to 6000 meters in air with a density -3 3 of 1.225 X 10 " gm/cm . The factors are also strongly dependent upon air density for high yields and weakly dependent for low yields* 263

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10"

WITH ClOUD RISE AND HYDRODYNAMIC EFFECT

>*o 10'

WITH CLOUD RISE EFFECT

10' MS!

10"

10*0 500 1000 1500 2000 2500 3000 R, SLANT RANGE (metcri)

Figwre 1. Effect of Cloud Rise and Hydrodynamic Enhancement on Fission-Product Gamma Exposure vs Slant Range from Nominal 1-KT Device 264

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Figure 2. Fission-Product Gamma-Ray Hydrodynamic Enhancement Factors vs Slant Range 265

COMPARISONS

In cases where both the air-ground secondary and fission- product gamma-ray dose are important, both field test data for the weapon and the leakage neutron energy spectrum for the same (or similar) weapon must be available in order to make comparisons. The neutron spectrum is required to calculate the secondary gamma- ray component. Sixteen different test events including 9 low- yield devices and 7 high-yield devices (>100KT) were identified which met these conditions* The low-yield devices include those used in the previous evaluation of neutron predictions.6

Initial gamma-ray calculations were made for each of the 16 devices for the geometrical and meteorological conditions reported during the field tests. The calculations included the fission-product component as given by Equation (17) and secondary gamma-ray component as given by the data and techniques described in Reference 6.

Figures 3 through 7 show comparisons of the calculated air- ground secondary gamma dose, the fission-product gamma dose and the total calculated dose with the measured total doses for five representative low-yield weapons, all as a function of the slant range from the detonation. The yields of these devices range from approximately 1 to 40KT.

For all weapons except Device No. 10, the fission-product dose is seen to be higher than that resulting from secondaries. The total measured and calcu?ated doses differ most for Devices No. 6 and 10 although the slopes agree favorably. The measured and calculated slopes appear to be somewhat different for Devices No. 11 and 14 although most measured points are well within 50% of the calculated totals. The calculations and measurements for Device No. 18 are seen to be in generally excellent agreement both in magnitude and slope. The largest area of disagreement is at the 266

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Figure 3. Calculated and Measured Gamma-Ray Exposure vs Slant Range for Device No. 6 267

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Figure 4. Calculated and Measured Gamma-Ray Exposure vs Slant Range for Device No. 10 268

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Figure '/. Calculated and Measured Gamma-Ray Exposure vs Slant Range for Device No. 18 271 short ranges where the neglect in the calculations of cloud expansion and fission-product dispersion through the cloud is least justified.

The overall agreement between the measured and calculated total exposures is quite good. Considering all cases compared, approximately 80% of the measured points are within 25% of the calculated totals. As implied by measurements made at different azi- muthal angles (see Figure 7, for example), the measured data probably have uncertainties on the order of 25% or more. The differences between the measurements scarcely exceed 50% in the worst cases.

Figures 8 through 11 show comparisons of the calculated fission- product gamma exposure with measurements for four representative high- yield weapons. In every case the secondary exposure is seen to be less than some 15% of the fission-product exposure. It should be noted that the calculations of the secondary gamma data are for air- over-ground rather than air-over-water, whereas all of the high-yield tests were in the Pacific.

It is noted that the measured data for the high-yield devices are generally more sporadic than was the case for the low-yield devices. In spite of this, considering all cases compared, approximately 80% of the measured points are within 50% of the calculated total exposures and over one-third agree within 25%. Within the yield range of the high-yield comparisons (approximately 200KT to 5MT), neither total yield nor the fission-to-total yield ratio appears to have a systematic effect upon the agreement between the measurements and the calculations. The fission-to-total yield ratios vary from less than 0.1 to 1.0.

Unlike the low-yield devices, the high-yield calculated exposures tend to be higher than the measurements. Consequently, although less accurate than predictions for low-yield weapons, the high-yield predictions are more conservative. 272

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Figure '/. Calculated and Measured Gamma-Ray Exposure vs Slant Range for Device No. 18 273

Figure '/. Calculated and Measured Gamma-Ray Exposure vs Slant Range for Device No. 18 274

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Figure '/. Calculated and Measured Gamma-Ray Exposure vs Slant Range for Device No. 18 276

CONCLUSIONS

Of the important initial radiation components, the fission- product gamma rays have generally been the most neglected and adequate predictive models have not been available. The new model developed and evaluated herein shows that in almost every case the fission-product gamma-ray dose during the first one minute is greater than the other gamma-ray components of the initial radiation from nuclear weapon detonations.

Fission-product gamma-ray doses calculated with the model, when combined with secondary-gamma doses based on Strakerfs air- over-ground neutron transport calculations,5 give results that generally agree with weapons test data within 25% for low-yield weapons and 50% for Mgh-yield weapons. 277

REFERENCES

1. Samuel Glasstone, editor, "The Effects of Nuclear Weapons," U. S. Atomic Energy Commission (1962).

2. Harold L. Brode, "Review of Nuclear Weapons Effects," Annual Review of Nuclear Science Vol. 18 (1968).

3. R, H. Ritchie and G. S. Hurst, "Penetration of Weapon Radia- tion; Application to the Hiroshima-Nagasaki Studies," Health Physics 1, 390-404 (1959).

4. R. L. French and M. B, Wells, "Calculations of Weapon Radia- tion in Air," Health Physics 5, 108-118 (1961).

5. E. A. Straker, "Time-Dependent Neutron and Secondary Gamma- Ray Transport in an.Air-Over-Ground Geometry," 0RNL-4289, Vol. II, Oak Ridge National Laboratory (1968).

6. R. L. French and L. G. Mooney, "Prediction of Nuclear Weapon Neutron-Radiation Environments," Nuclear Technology 10, 348-365 (1971).

7. V. I. Kukhtevich, et al., "Protection from Penetrating Radiation of a Nuclear Explosion," Atomizdat Press, Moscow (1970).

8. J. D. Marshall and M. B. Wells, "The Effects of Cut-Off Energy on Monte Carlo Calculated Gamma-Ray Dose Rates in Air," RRA-M67, Radiation Research Associates, Inc. (1966).

9. L. B. Engle and P. C. Fisher, "Energy and Time Dependence of Delayed Gammas from Fission," LAMS-2642, Los Alamos Scientific Laboratory (1962).

10. F. F. Haywood, "Spatial Dose Distribution in Air-Over-Ground Geometry," Health Physics 11, 185-192 (1965).