Verifying the Authenticity of Nuclear Warheads Without Revealing Sensitive Design Information

Transcription

1 Verifying the Authenticity of Nuclear Warheads Without Revealing Sensitive Design Inforation Steve Fetter and Thoas B. Cochran Verifying the disantleent of nuclear warheads will require reconciling two conflicting obectives: the desire of the onitoring party to insure that the obects slated for disantleent are bona fide warheads of the declared type, and the desire of the onitored party to protect sensitive inforation about the design of the warhead. A possible solution would involve visiting a deployent site on short notice and randoly selecting a given nuber of warheads for disantleent. The warheads would then be placed in tagged, sealed containers for transport to the disantleent facility, where the integrity of the tags and seals would be verified. If the nuber of warheads to be disantled is a sall fraction of the entire inventory, then the onitoring party would be reasonably sure that the warheads are genuine, for the only way the onitored party could defeat the schee would be to deploy large nubers of fake warheads. Still, the process of on-site tagging and sealing for each warhead is tedious, and the onitored party would have no assurance that all the warheads were genuine, since the onitored party could easily replace 0 or 0 percent of the warheads slated for disantleent with decoys. A uch better solution would involve gathering only a sall saple of warheads during an initial rando on-site inspection and establishing a unique fingerprint or signature for this warhead type. An ecellent eaple of a fingerprint would be the warhead's characteristic gaa-ray eissions. Subsequent warheads could siply be brought to the disantleent facility at the convenience of the onitored party, where a warhead's fingerprint would be copared with those of the reference warheads to establish its authenticity. 3 For a ore general discussion of verifying reductions in nuclear warheads, see Ending the Production of Fissile Materials for Weapons; Verifying the Disantleent of Nuclear Warheads: The Technical Basis for Action (Washington, DC: Federation of Aerican Scientists, June 99). Other types of fingerprints can be iagined, but we have identified none that have convincing advantages over intrinsic gaa-ray eissions. One could, for eaple, radiograph the warhead, but the algorith to copare radiographs would be far ore cople than the algorith to copare the intensity of gaa-ray eissions, the inforation contained in the radiographs would be far ore sensitive than that contained in the gaa-ray spectra, and the possibility of cheating by substituting non-weapons-grade uraniu and plutoniu for weapons-grade uraniu and plutoniu, which would lead to identical X-rays, would require the use of gaa-ray and/or neutron detection as a suppleent in any case. 3 Alternatively, one could copare the fingerprints of disassebled coponents leaving the facility, to verify that a given nuber of a given type of warhead had been disantled. One could, for eaple, place the plutoniu pit in a given container and verify this fingerprint, although the gaa-ray fingerprint described below would presuably reveal ore sensitive inforation in this case if the design of the container was known.

2 All nuclear warheads contain radioactive isotopes of uraniu and/or plutoniu. 4 Most of these isotopes eit gaa rays and neutrons at rates that can be detected outside the warhead. For eaple, plutoniu-39 the ost iportant plutoniu isotope eits over two dozen gaa rays that can be detected outside of typical warheads. Since the energies of the gaa rays are deterined by the characteristics of the eitting nucleus, detecting ust one or two of these gaa rays perits the unabiguous identification of the radioactive aterial. And since the intensity of each gaa ray depends on the quantity and geoetry of the radioactive aterial and the thickness, geoetry, and atoic nuber of all surrounding aterials, it would be etreely difficult if not ipossible to replicate the gaa-ray spectru with a saller aount of aterial in a different configuration. The fingerprint should be based on eissions that would not be epected to vary by ore than a few percent fro warhead to warhead. Ecellent choices would be the gaa rays eitted during the decay of uraniu-35 and plutoniu-39. The aount of uraniu-35 and plutoniu-39 in a given type of warhead, and the intensity of their gaa rays outside the warhead, should vary very little fro warhead to warhead, and would not depend on the age of the aterial. 5 Gaa rays are eitted during the decay of other isotopes of uraniu and plutoniu (e.g., uraniu-3, uraniu-38, plutoniu-4, etc.), but the concentration of these isotopes could easily vary by ore than 0 percent fro warhead to warhead. Copious neutrons are eitted by plutoniu-40, but the percentage of this isotope in weapon-grade plutoniu ight vary by ore than 50 percent fro warhead to warhead (e.g., fro 3 to 6 percent or ore). The energy and intensity of the gaa rays eitted by plutoniu-39 are such that one can epect to receive a detectable signal outside any warhead that contains plutoniu. It is, however, possible to build warheads that use uraniu-35 for fissile coponents, and which contain no plutoniu. The gaa rays eitted by uraniu-35 are considerably less energetic than those eitted by plutoniu-39; if the uraniu is surrounded by thick aterials with high atoic nubers, these gaa rays ay be undetectable outside the warhead. Shielded counting chabers and long counting ties will help, but ay not guarantee detection of these lowenergy gaa rays in soe conceivable warhead designs. We do not believe that such designs are coon in the superpower arsenals, but they are a possibility that ust be considered. To deal with the possible failure of gaa-ray detection, one could illuinate the warhead with bursts of high-energy neutrons. The neutrons would penetrate to the fissile aterial, causing a certain nuber of fissions and the consequent eission of propt and delayed neutrons and gaa rays. Like the gaa rays eitted during radioactive decay, these eissions would depend on the quantity and geoetry of the fissile aterial, the thickness, geoetry, and isotopic coposition of all surrounding aterials, and the incident neutron energy. Inelastic absorption of 4 For a ore general and coplete discussion of warhead detection, see Steve Fetter, Valery A. Frolov, Marvin Miller, Robert Mozley, Oleg F. Prilutsky, Stanislav N. Rodionov, and Roald Z. Sagdeev, "Detecting Nuclear Warheads," Science and Global Security, Vol., pp (990). 5 An eception ight be non-fissile uraniu coponents, in which the concentration of uraniu-35 is low (between 0. and 0.7 percent). The concentration of uraniu-35 in such coponents could vary by ore than a factor of two fro warhead to warhead if coponents were fabricated fro depleted uraniu of different assays, or if soe coponents were fabricated fro natural uraniu and others fro depleted uraniu. One could deal with such cases by easuring the uch stronger gaa rays eitted during the decay of uraniu-38.

3 neutrons by surrounding aterials would also lead to the eission of characteristic gaa rays that could be used in the warhead signature as well. Although a neutron source would greatly increase the cost the syste, it would guarantee obtaining a fingerprint that would be etreely difficult to counterfeit. A aor obection to radiation fingerprinting is that it ay reveal sensitive inforation about the design of the nuclear warhead. By working backwards fro the gaa-ray spectra, it ay be feared that the onitoring party could reconstruct previously unknown aspects of the warhead design, which could then be used to iprove warhead design or strategic defenses. Although it sees highly unlikely to us that valuable inforation can be derived fro such fingerprints (in the sense that it would allow eaningful iproveents in nuclear offense or defense), it is reasonable to anticipate and deal with such obections whenever possible. In the following eaple, we outline an autoated syste that would return a siple yes or no answer to the question: is the radiation fingerprint of this warhead significantly different fro the fingerprints of the reference warheads? First, the onitored party would provide a list of all locations where warheads of the type to be disantled are deployed or stored. The onitoring party would then visit several of these sites on short notice, and randoly select a sall nuber (e.g., a total of ten) warheads. (Selecting ore than one warhead allows the natural variability in the warheads to be estiated, which will be valuable in iniizing false accusations of cheating.) Each warhead would be placed in a tagged and sealed container, which would be shipped to the disantleent facility. Upon arrival, the authenticity of the tags and seals would be checked to ensure that the arriving warheads are the sae as those selected fro the declared sites. Net, the warheads would be placed, one by one, on a turntable in a shielded chaber. (Rotating the warhead with respect to the detector would ake it unnecessary to reproduce the eact orientation of the warhead.) While the warhead is rotated in the chaber, gaa rays eitted by the warhead are detected by high-purity geraniu detectors located at different heights above the turntable. 6 The counting tie should be long enough so that statistical counting errors are sall (e.g., percent, or saller than the natural saple variability). [As entioned above, a neutron source could also be used to produce propt fission, fissionproduct, and neutron-absorption gaa rays and propt and delayed fission neutrons. For siplicity, only gaa rays fro radioactive decay are discussed below, although the techniques are easily generalized to include neutron-induced eissions.] Iediately before and/or after each easureent, background easureents and calibration easureents would be ade. The calibration sources would ideally include a sall quantity of uraniu-35 and plutoniu-39. Note that it is only necessary to easure changes in the relative efficiency of the detectors. These easureents would also serve to indicate the proper functioning of the equipent. 6 Alternatively, a single detector could be used and the elevation of the turntable varied. Also note that warheads and bobs will probably require different shape counting chabers. 3

4 Each spectru would then be analyzed by a peak-finding progra to deterine the energy and intensity of each gaa-ray eission (e.g., significant at the 3-standard-deviation level), the uncertainty in these quantities, and to identify those eissions that are due to the decay of uraniu-35 and plutoniu At this point, uncertainties are due ainly to counting statistics. For eaple, if 00 gaa rays of a given energy were detected, then (neglecting background) the uncertainty in the easureent would be the square root of the nuber of counts in this case, 0 counts. A percent uncertainty would require 0,000 counts (assuing the background is sall). This nuber of counts per peak ight be achievable in less than an hour for plutoniu-bearing warheads. 8 After the spectra are corrected for variations in detector efficiency, we have a library of gaaray energies E i, observed gaa-ray count rates i, and uncertainties in these count rates s i (including uncertainties fro counting statistics, background, and relative detector efficiency) for each warhead i and gaa ray at each detector location. The ean count rate, averaged over the group of reference warheads, is given by i i s = s i i () If statistics are poor, the siple average ay be a ore robust easure of the ean than the weighted average. The variance in the count rate is given by σ = () ( ) i i = Before proceeding, we should ask two questions about the group of reference warheads: () are these warheads nearly identical, and () if they are not identical, are they all of the sae type? Answering the first question is iportant because it deterines the type of statistical analysis that should be used in coparing fingerprints. If the warheads are nearly identical (i.e., if variations in the count rates due to variations in anufacture are uch saller than variations due to counting statistics), then we can assue that deviations fro the ean count rates are statistically independent, and we can use the uch sipler (and ore powerful) χ statistic to test whether fingerprints atch. If, however, anufacturing tolerances lead to variations in the count rates that eceed those due to counting statistics, then differences in count rates probably 7 An eaple of such progra is HYPERMET. See G.W. Phillips and K.W. Marlow, Progra HYPERMET for Autoatic Analysis of Gaa-ray Spectra fro Geraniu Detectors (Washington, DC: Naval Research Laboratory, Report NRL-398, 976). 8 In easureents ade on a Soviet warhead, count rates for 4 different lines varied fro 0.05 to.6 counts/s. [Steve Fetter, Thoas B. Cochran, Lee Grodzins, Harvey L. Lynch, and Martin S. Zucker, "Gaa-Ray Measureents of a Soviet Cruise Missile Warhead," Science, Vol., 48, pp (8 May 990).] The easureents were, however, ade about 75 c fro the center of the warhead, through a steel launch tube about 7 c thick. At a distance of 50 c and without the steel launch tube, count rates would have been 5 to 400 counts/s enough for over 0,000 counts per peak in less than an hour. 4

5 will be correlated and the ore coplicated and less powerful T statistic ust be used to test the equivalence of two fingerprints. Nuclear warheads are perhaps the ost carefully constructed ites on the planet, and we doubt that anufacturing and assebly tolerances are so la that they would result in large variations in gaa-ray eissions. 9 It is, nevertheless, a possibility that ust be anticipated in advance. One way to deterine whether the warheads are nearly identical is to copare the variance calculated in equation () with the variance the would be epected based solely on counting statistics, which is given by S = s i (3) If the observed variance in the count rate is uch greater than what would be epected fro counting statistics alone (i.e., if σ S ), then warhead-to-warhead variations are iportant and ust be taken into account. Unlike errors fro counting statistics, which are independent of gaa-ray energy, variations in anufacture will lead to differences in count rates that are correlated with each other. For eaple, a sall decrease in the aount of plutoniu in a warhead will cause all count rates to decrease, though soe will decrease ore than others. A ore robust ethod of deterining whether differences in count rates are correlated is to test the hypothesis that the correlation is zero. The coefficient for the correlation between the count rates for gaa-ray eissions and k ( k) is given by r k = ( )( ) i ik k ( ) σσ k (4) The statistic z k, which is given by z k + r log k = e rk (5) is norally distributed with a standard deviation of about ( 3) ½. Therefore, the probability that the statistic is greater than z k given that the correlation is zero is given by 9 To note an etree eaple, the ean-free-path of a 86-keV gaa-ray (the ost intense eission fro U-35) is only 0.36 in uraniu. If the thickness of a uraniu coponent between the source and the detector varied by as little as one-thousandth of an inch ( il) fro warhead to warhead, the intensity of the gaa ray at the detector would vary by over 0 percent. In the U.S., heavy-etal weapon coponents are typically achined to tolerances of ± to ± ils, and there ight be five to si heavy-etal layers in a typical assebly. (Richard Hatfield, Lawrence Liverore National Laboratory, personal counication, 6 August 99.) 5

6 P -3 z = erfc z k (6) ( k ) where erfc ( ) = π e t dt (7) There will be a total of n(n )/ covariances; if q is the probability that no one of these covariances appear non-zero fro rando variations, then P(z k ) should satisfy the condition ( ) ( ) nn ( ) k P z q (8) If q = 0.05 and n = = 0, then P(z k ) 0.00 and z k 0.87 for any and k to reect the null hypothesis that the count rates are uncorrelated. A better procedure ight be to use a ore la criterion (e.g., P(z k ) 0.05, z k 0.66), and siply require that ore than, say, 0 percent of the z k eceed this criterion in order to reect the null hypothesis. If the null hypothesis is accepted (i.e., the reference warheads are nearly identical), then we can safely assue that they are all of the sae type. If they are not identical, then we ust check to see if the data are consistent with the assuption that the reference warheads are all of the sae type (i.e., that none of the warheads are draatically different fro the others). This is iportant because it could reveal an attept by the onitored party to fool the syste into accepting a large saple variability, which would ake cheating uch easier. To account for this, one could copare the count rates for ( ) warheads with the count rates for the reaining warhead, for all warheads; then copare the count rates for ( ) warheads with count rates for the reaining two warheads, for all cobinations of two warheads; and so on. The probability that the two groups of warheads are different is given by the T statistic developed below. The coputer progra could alert the onitoring party of a significant difference between two subgroups of warheads, which could then request additional inforation fro the onitored party before proceeding. Let us assue that we accept the hypothesis that all the references are of the sae type, and that the observed variations between warheads are due to counting statistics and variations in anufacture. When the onitored party brings a new warhead to the disantleent facility, the onitoring party would attept to verify its authenticity by coparing its radiation fingerprint to that of the reference set of warheads. Once again, the peak-finding and peak-fitting progra would identify all lines associated with the decay of uraniu-35 and plutoniu-39 and would estiate the count rate of each eission y and the associated uncertainty s. If we have also accepted the hypothesis that the warheads are nearly identical, then a siple chisquare test can be used to deterine if a new warhead belongs to the sae set as the reference warheads: y 6

7 χ = n ( ) y σ = + sy (9) [Equation (9) assues that the sae gaa-ray eissions are detected in each case. If this is not true, the analysis could be restricted to only those peaks found to be significant in both spectra, or the spectra could be reanalyzed to deterine the possible agnitude of "issing" peaks. The preferred technique probably depends on the nuber of such cases and the quality of the data in each case.] The probability that the chi-square observed for the new warhead will eceed the value χ by chance (i.e., the probability that the warhead is drawn fro the population represented by the reference warheads and that the observed deviations in the spectra are due to rando variations) is given by the incoplete gaa function: χ n t t (0) Γ n t P( ) = e d χ n Before aking use of this equation, we ust decide what probability of a false alar is tolerable. If, for eaple, we reect warheads for which P(χ n) < 0.0, then on average one out of every 00 legitiate warheads would reected. Since disantleent capaigns ight involve over,000 warheads, this is clearly unacceptable, since false accusations of cheating could be very daaging. The total nuber of warheads that will be disantled by the superpowers in the coing decades is probably between 0,000 and 50,000. If we require that the probability of a false alar during the entire disantleent capaign is fairly reote (e.g., to 5 percent), then the criteria for reecting a warhead should be P(χ n) < 0 6. The following table gives the required χ for a given n and P(χ n): P(χ n) = 0 5 P(χ n) = 0 6 P(χ n) = 0 7 n χ χ /n χ χ /n χ χ /n

8 To see that false alar rates as low as 0 6 ay be possible while preventing significant diversion of aterial, assue, for the sake of siplicity, that sy y, s i i and σ, where and y are now the total nuber of counts; then Assuing that ( y ) = n χ () + y y, the allowable root-ean-square (rs) relative difference in the count rate is approiately equal to ( χ )( + ) n ; if we detect an average of ust,000 counts in each of four lines, the allowable rs error would be less than percent for a false alar rate of 0 6. If, on the other hand, we reected the hypothesis that the warheads are nearly identical (i.e., that warhead-to-warhead variations lead to correlated differences in count rates), the statistic we should copute is T, which in vector notation is as follows: T T - = ( -y) c ( -y ) () + The eleents of the vector ( ) -y are ( ) y. Note that this differs fro the noral twosaple proble in that the second saple contains ust one set of observations, y. Therefore, the covariances are estiated fro the observations of the reference group of warheads (and are assued to equal the covariances fro the group that y was drawn fro). The eleents of the covariance atri c are as follows: c = ( )( ) k n i ik k i = (3) It can be shown that the T statistic is distributed according to the F distribution: F n n n + n, n = T = ( ) ( n ) ( )( ) ( ) T - ( ) -y c -y (4) The probability Q that the F observed will eceed the value F' by chance (i.e., the probability that the new warhead is drawn fro the population represented by the reference warheads) is given by n n n Q( F n, n ) = I,, n + nf (5) where the function I is equal to 8

9 ( a b) ( a) ( b) Γ + (,, ) = ( ) d Γ Γ a b I ab t t t 0 (6) Note that the nuber of gaa-ray eissions used coputing the T statistic (n) ust be less than the nuber of warheads in the reference set (). If n, then n should be reduced by choosing only the ost significant eissions, taking care to space the as evenly as possible with gaa-ray energy. It should be fairly straightforward to design an algorith to autoatically select the best eissions for such an analysis. Without actual data on different warheads of a given type, it is ipossible to estiate the power of the T statistic to discriinate between phony warheads and warheads with significant correlated differences. We believe that it should be possible to liit the acceptable difference in the count rates to less than 0 percent, at least in plutoniu-bearing warheads. If this is insufficient, discriination power could be increased considerably by storing the spectra fro each warhead and using this inforation to refine the estiates with each new warhead. By adding the spectra of each acceptable warhead to the set of reference warheads, estiates of the covariances could be iproved substantially, and ore lines could be added to the analysis. In addition to asking whether the new warhead is statistically different fro the set of reference warheads, the coputer could ask whether any subgroup yet eained is statistically different fro any other subgroup. This would eliinate the possibility of, for eaple, reoving 0 percent of the plutoniu fro a large fraction of the warheads to be disantled; even though a 0 percent difference ay not be noticed in single warhead, a disproportionately large fraction of warheads showing a 0 percent difference would be noticed. Such techniques ay be especially valuable in cases where few gaa-ray eissions are detectable (e.g., uraniu-only warheads). Note that all the data analysis discussed above could be perfored autoatically by a coputer, without huan intervention. Algoriths have been developed that can autoatically and reliably find and identify statistically significant peaks in gaa-ray spectra; it would be relatively straightforward to analyze and store this inforation in a secure anner for coparison with future data. The coputer could be prograed to provide a siple yes or no answer to the question, Is the warhead under eaination statistically different fro group of reference warheads?, or it could provide the probability that the observed difference is due to rando variations. The coputer could also answer the question, Is any subgroup of warheads eained so far statistically different fro the other warheads, and if so, which warheads and by how uch? There would be no need to reveal any aspect of the spectra theselves, although such revelations would aid greatly in building confidence in the syste and resolving abiguities. At a iniu, the coputer could indicate the presence of uraniu-35 or plutoniu-39 and the nuber of statistically significant peaks detected. In addition, the energy of the peaks ight be given, along with the count rates for a few of the strongest eissions. A great aount of attention obviously would have to be given to red-teaing, or finding out if and how the syste could be fooled into accepted illegitiate warheads. While it sees to us highly unlikely that the gaa-ray fingerprint of a legitiate warhead could be atched by a duy warhead containing less fissile aterial, this possibility could be better evaluated by those knowledgeable in weapon design. 9