A METHOD FOR DETERMINING MATERIAL ATTRIBUTES FROM POST- DETONATION FISSION PRODUCT MEASUREMENTS OF AN HEU DEVICE

Transcription

1 A MEHOD FOR DEERMINING MAERIAL ARIBUES FROM POS- DEONAION FISSION PRODUC MEASUREMENS OF AN HEU DEVICE Adrenne M. LaFleur and Wllam S. Charlton Nuclear Engneerng Department 3133 AMU exas A&M Unversty College Staton, X ABSRAC An algorthm was developed that uses measured sotopc ratos from fsson product resdue followng the detonaton of a nuclear weapon to compute the orgnal attrbutes of the nuclear materal used n the weapon. Whle more accurate (and more computatonally ntensve) methods are beng explored by others, the method descrbed here could serve as a preprocessng step to a more detaled methodology (potentally savng on computatonal tme). hs would, n turn, expedte the process of determnng where the devce came from, eventually leadng to whch terrorst group perpetrated the event. hs work was restrcted only to Hghly Enrched Uranum (HEU) devces; however, future efforts wll consder plutonum devces as well. he attrbutes determned nclude orgnal materal uranum sotopcs (at present consderng only U, U, and U) and the type of enrchment process used to create the materal (e.g., gaseous dffuson, gas centrfuge, etc.). he approach to developng ths algorthm nvolved a smulaton of the fsson products and actndes present followng a nuclear exploson and a detaled evaluaton to determne vald ratos that could be used to work backward and acheve the orgnal materal n the devce. he algorthm used was purely analytcal, derved drectly from burnup and radoactve decay equatons. hus, ths methodology provded solutons wth essentally no computatonal tme requred. INRODUCION One of the most crucal ssues to natonal securty n the Unted States s the ablty to safeguard our country aganst nuclear terrorsm. If natonal securty was breached and a terrorst nuclear devce was detonated n the Unted States, how quckly could we assess the ste to determne what type of devce was detonated, how powerful the devce was and where t came from? Nuclear threats are not wdely understood by the general populaton; therefore, f a terrorst devce was ever detonated n our country mmedate results must be produced n order to prevent mass hystera. he objectve of the algorthm developed here was to utlze post-detonaton measured sotopc ratos n order to determne the pre-detonaton materal attrbutes wthn reasonable accuracy. More computatonally ntensve (and admttedly more accurate) methods are beng developed elsewhere; however, these methods requre extensve computatonal tmes n order to produce acceptable results. In effort to reduce the computatonal tme requred to compute the orgnal materal attrbutes, the method developed here uses an analytcal approach whch conssted nversons of the buldup and decay equatons (all frst-order ordnary dfferental equatons). It s envsoned that ths methodology could serve as a preprocessor step to a more computatonally ntensve and more accurate system. NSSPI INMM Annual Meetng

2 hs work concentrated on the attrbuton of an HEU weapon post-detonaton. errorst devces may dffer from mltary nuclear weapons manly n the sophstcaton of constructed (e.g., type and grade of materal used and qualty of tamper/reflector). errorst nuclear weapons that use HEU are lkely to be gun-type weapons due to the smplcty of ts structure. Snce gun-type assembly s relatvely smple, ths s consdered to be a lkely scenaro for a nuclear terrorst attack. [4] Gven a measurement of the sotopcs of resdue post-detonaton, the nterest n ths work was to attempt to determne the followng characterstcs (n ths order of mportance): (1) pre-detonaton U enrchment, (2) pre-detonaton U/ U sotopc rato, (3) pre-detonaton U/ U sotopc rato, (4) enrchment method used to produce materal, (5) pre-enrchment U/ U sotopc rato, (6) pre-enrchment U/ U sotopc rato, and (7) source (mne or otherwse) from whch feed uranum was taken. It was acknowledged mmedately that steps (1)-(3) would have a lkely chance of success and the steps (4)-(7) would be sgnfcantly more dffcult (n fact step (7) s probably not possble, but s stll an nterestng problem to attempt to solve). For the purposes of ths study, we have so far lmted the analyss only to gaseous centrfuge and gaseous dffuson enrchment methods, snce these enrchment processes are very smlar n physcal process. It s expected that dstngushng most other methods (such as AVLIS or EMIS) would be much smpler. U Isotopcs n Mnes Dfferent uranum mnes throughout the world are characterzed by dfferent sotopc abundances of U whch may be used as a sgnature to ndcate the geographc orgn of the materal. U has a relatvely short half-lfe and exsts n secular equlbrum wth U. hus, the rato of U to U should equal to the rato of the half-lves (53.8 ppm). Varatons n the rato of U/ U may result from processes that dsrupt the decay chan of U to U [2]. able I shows some of these varatons n naturally occurrng uranum. ABLE I Varatons n natural uranum U sotopc abundances from mnes throughout the world. [2] Country Mne/Mll Faclty U / U Atom Rato Gabon Comuf Mounana E-5 Canada CAMECO Rabbt Lake Op E-5 Namba Roessng Uranum Mne 5.464E-5 Enrchment Methods Weapons-grade HEU s typcally enrched to about 9% U. he method of enrchment s a sgnature that may ndcate where the uranum was enrched. Methods used to enrch uranum nclude: gas centrfuge, gaseous dffuson, laser sotope separaton, chemcal/on separaton and electromagnetc sotope separaton. he two most common enrchment methods are gaseous centrfuge and gaseous dffuson both of whch separate the uranum sotopes n a gaseous state called uranum hexafluorde. Both gaseous dffuson and gaseous centrfuge rely on the dfferences n mass between U contanng molecules and U contanng molecules though they are based on dfferent physcal processes. Gas centrfuge s based on centrfugaton whereas gaseous dffuson s based on NSSPI INMM Annual Meetng

3 molecular effuson. Snce U s lghter than U t enrches even more n ether the gas centrfuge or gaseous dffuson process than the U. he followng equaton represents the U enrchment for gaseous centrfuge: [3] M.7731 M where M s the atomc mass of U and M s the atomc mass of U. he followng equaton represents the U enrchment for gaseous dffuson: [3] M.8 (2) * M Natural uranum contans essentally no U (though small quanttes are found n natural materal due to the actvaton of U from neutron background); however, enrched uranum of U.S. or Russan orgn ncludes a sgnfcantly hgher abundance of U due to the re-enrchment of naval fuel. he followng equaton represents the U enrchment n U.S. orgn fuel: (1) *.46 M M (3) * MEHODOLOGY he algorthm developed here conssts of two man parts: a forward model and an nverse model. he forward model conssted of smulatons to predct post-detonaton (actually post-rradaton) sotopcs gven the orgnal sotopcs of the materal and the number of fsson (or yeld) of the devce. he data from the forward model was manly used to test the vablty of the nverse model. he nverse model predcted pre-detonaton sotopcs usng analytcal nversons of the buldup and decay equatons and post-detonaton sotopc measurements. he nverse model also ncluded error propagatons to allow for predcton of uncertantes n the attrbutes as well as to determne the senstvty of the results to the nput data. Forward Model Development he forward model smulatons used the ORIGEN2 code [1]. ORIGEN2 calculates the buldup and depleton of sotopcs from rradaton and decay. he code possesses a large set of lbrares (each lbrary corresponds to a specfc type of reactor) wth cross-secton, decay, and fsson product yeld data. ORIGEN2 uses the matrx exponental method to solve a large system of coupled, lnear, frst -order ordnary dfferental equatons. Whle not a weapon burn code, ORIGEN contans suffcent capablty to allow for analyss of the feasblty of the method developed here. Four dfferent uranum sgnatures from gaseous centrfuge and gaseous dffuson enrched uranum, both wth and wthout U present n the orgnal materal, were smulated. he uranum was enrched to 95 atom% U and the U and U concentratons were calculated for both methods of enrchment usng equatons (1), (2), and (3). hen, ORIGEN was used to smulate the burnup of * hese equatons were taken from ransware Enterprses Inc., ransfx Computer Software Manuals, July 21. NSSPI INMM Annual Meetng

4 the materal n the devce gven a 2 k yeld. he resultant sotopcs from ths burnup were then decayed for 1. day (assumes that t wll take approxmately 1 day or more to acqure measured resultants from resdue post-detonaton). Inverse Model Development he nverse model equatons are all expressed n terms of atom ratos relatve to U (the U concentraton n the devce s roughly constant durng rradaton). he nverse model uses an teratve procedure where the pre-detonaton U/ U rato s set to an ntal guess nput by the user. he pre-detonaton U/ U and U/ U (f applcable) ratos were calculated usng Eqs. (1)-(3) and then combned wth the ntal guess for U/ U n order to calculate the U enrchment of the orgnal materal usng: 1 e (4) x where e s the pre-detonaton enrchment for step and N s the pre-detonaton atom rato of sotope x to U from step -1 (or from the ntal guess for the frst step). he number of fssons n the devce per unt mass was calculated usng the measurement of two fsson products: 95 Zr and 89 Sr. A sngle fsson product could have been used but by usng two fsson products, teraton between the two yelded a better predcton of the number of fssons. he followng equaton was used to calculate the number of fssons per unt mass n the devce: 1 89 N AER N F e 89 (5) M Y where F s the number of fssons n the devce followng rradaton (.e., at tme ) per unt mass 89 for step, N s the measured 89 Sr/ U atom rato post-detonaton (.e., at tme ), N A s Avagadro s number, E R s the recoverable energy per fsson, and Y 89 s the cumulatve fsson product yeld for 89 Sr. In usng Eq. (5) we assumed that the fsson product yelds and recoverable energy per fsson from U was adequate (.e., ths assumes that all fssons were from U). An updated U/ U value was then calculated usng measurements of 232 U/ U n the resdue and the followng equaton: 232 f 3n E F R N M A e where f s the one-group mcroscopc fsson cross secton for U and 3n s the one-group mcroscopc (n,3n) cross secton for U. hs equaton assumes that no 232 U exsted n the orgnal materal and the measured 232 U concentraton was produced only from the U(n,3n) 232 U reacton. (6) NSSPI INMM Annual Meetng

5 An updated U/ U value was then calculated usng measurements of U/ U n the resdue and the followng equaton: + 1 a f F E R M N where a s the one-group mcroscopc absorpton cross secton for U. hs assumes that the change n U s equal to ts loss rate from absorpton. hen, an updated U/ U value was then calculated usng measurements of U/ U n the resdue and the followng equaton: M N e A F E R A a f e a 1 2 f N 1 + (7) (8) hs assumes the change n U s equal to ts producton rate from radatve capture n U mnus the loss rate from the absorpton of U. Equaton (8) was obtaned by assumng that the rato of ( U / U) as a functon of rradaton tme was lnear and therefore was easly ntegrated. he new value for the enrchment can now be calculated usng Eq. (4). Equatons (4)-(8) can then be repeated untl the pre-detonaton U/ U rato converges to wthn some tolerance. RESULS AND DISCUSSION he methodology descrbed above was tested for a 2 k detonaton of a 95% enrched HEU devce. he measured values were produced from ORIGEN smulatons for four dfferent uranum sgnatures from gaseous centrfuge and gaseous dffuson enrched uranum, both wth and wthout U present n the orgnal materal. he algorthm was nsenstve to the ntal guess for U concentraton. In all cases less than 1 teratons (less than 1 second computatonal tme) were used to acqure a result. he results presented n able II verfed that for any postve ntal guess of any order of magntude nput nto the algorthm wll be terated to a reasonably correct answer. ABLE II Comparson of the values calculated by the nverse model wth varous ntal guesses for the U concentraton and the actual values for the orgnal materal attrbutes. Enrchment Process Intal Guess Orgnal Value Inverse Model Percent (N/N) (N/N) (N/N) Error Centrfuge (wth U) 1. x ± % Dffuson (no U) 1. x ± % he measured sotopc values generated from ORIGEN2 and the values computed n the nverse model for both centrfuge and dffuson enrchment processes (wth and wthout U) are presented n ables III and IV. he results from the nverse model were consstently hgher than the exact values for the orgnal materal attrbutes. he resultng error may be attrbuted to an assumpton made when developng the algorthm that the atomc densty of U dd not change wth tme. NSSPI INMM Annual Meetng

6 In order to determne vald sgnatures ndcatng the method of enrchment, the measured values for post-detonaton U concentratons were compared. For centrfuge enrched fuel, the U concentraton was approxmately 5. tmes greater than the U concentraton for dffuson enrched fuel. hese sgnfcant varatons n U were used as sgnatures ndcatng the enrchment process used. ABLE III Comparson of the nverse model calculaton and the exact value for the orgnal materal attrbutes for gaseous centrfuge and dffuson enrchment wthout U. Enrchment Process Centrfuge (no U) Dffuson (no U) Measured Value Orgnal Value Inverse Model Percent Atomc Rato ( 1.1 days) ( days) ( days) Error N / N ± % N / N ± % N / N ±.75 - N / N ± % N / N ± % N / N ±.26 - ABLE IV Comparson of the nverse model calculaton and the exact value for the orgnal materal attrbutes for gaseous centrfuge and dffuson enrchment wth U. Enrchment Process Centrfuge (wth U) Dffuson (wth U) Measured Value Orgnal Value Inverse Model Percent Atomc Rato ( 1.1 days) ( days) ( days) Error N / N ± % N / N ± % N / N ± % N / N ± % N / N ± % N / N ± % ABLE V Comparson of the nverse model calculaton and the exact value for the orgnal materal attrbutes for gaseous dffuson enrchment wth and wthout U. Enrchment Process Dffuson (wth U) Dffuson (no U) Atomc Rato Orgnal Values Inverse Model ( days) ( days) Percent Error N / N ± % N / N ± % N / N ± % N / N ± % N / N ± % N / N..273 ±.26 - NSSPI INMM Annual Meetng

7 After the enrchment process has been determned, whether or not U exsted n orgnal weapons materal must be establshed. he values computed n the nverse model for dffuson enrched fuel wth and wthout U are presented n able V. For dffuson enrched fuel (wth U), the U value from the nverse model was approxmately 4.5 tmes greater than the U value for dffuson enrched fuel (wthout U). In the dervaton of Eq. (8) t was assumed that the rato of U/ U was a lnear functon wth respect to tme and could therefore be easly ntegrated. he assumpton was verfed n the followng fgure whch depcts the rato as a functon of rradaton tme. A lnear trend lne was used to ft to the data ponts. ( U / U ) Concentraton y.119x +.45 R Irradaton me (days) Fgure 2. ORIGEN2 calculaton of ( U/ U) sotopc rato as a functon of rradaton tme for rradaton of 95% enrched uranum enrched. CONCLUSIONS In ths work, an algorthm was developed that uses measured sotopc ratos from fsson products and actndes present followng the detonaton of a nuclear weapon to compute the orgnal materal attrbutes of the weapon. he algorthm was comprsed of analytcal nversons of frst-order dfferental equatons derved drectly from burnup and radoactve decay equatons. he followng post-detonaton sotopc ratos were used: 89 Sr/ U, 95 Zr/ U, 232 U/ U, U/ U, U/ U, and U/ U. he prmary advantage ganed from ths methodology was t provded accurate solutons wth essentally no computatonal tme requred. he results computed n the nverse model for the orgnal attrbutes of the HEU fuel were compared for gaseous centrfuge and gaseous dffuson enrched fuel, both wth and wthout U present n the orgnal materal. he values computed n the algorthm were consstently hgher than the exact values; however, the resultng percent dfferences, rangng from.6631% to %, were always wthn the acceptable uncertantes. he determned sgnature that ndcated the use of a centrfuge enrchment process to create the weapons materal was based on the U/ U rato. A source of error that was not assessed exsts n the cross-secton data used throughout the algorthm from the ORIGEN2 lbrary for an FFFC reactor. In ths work, we were only testng the feasblty of the algorthm and dd not consder ts relatonshp to an actual weapon detonaton. hus, testng of ths methodology usng cross-secton NSSPI INMM Annual Meetng

8 data obtaned for an actual devce detonaton would mprove the vablty of the algorthm. Also, there was no testng of spoofng mechansms performed. hs work s mportant to homeland securty and a sgnfcant prototype to data protocol n the event of a terrorst attack n our country. he algorthm developed was restrcted only to HEU devces; however, future efforts wll consder plutonum devces as well. It s also necessary to analyze how elements dsperse n the envronment and what current technology s avalable to measure sotopc fsson fragments n the envronment. All of the above aspects wll affect the valdty of the algorthm and f t could n fact be used f a terrorst devce was detonated n the U.S. ACKNOWLEDGMENS hs research was performed whle on appontment as a U.S. Department of Homeland Securty (DHS) Scholar under the DHS Scholarshp and Fellowshp Program, a program admnstered by the Oak Rdge Insttute for Scence and Educaton (ORISE) for DHS through an nteragency agreement wth the U.S Department of Energy (DOE). ORISE s managed by Oak Rdge Assocated Unverstes under DOE contract number DE-AC5-OR2275. All opnons expressed n ths paper are the author's and do not necessarly reflect the polces and vews of DHS, DOE, or ORISE. REFERENCES [1] A.G. Croff, A User s Manual for the ORIGEN2 Computer Code, ORNL/M7175, Oak Rdge Natonal Laboratory (July 198). [2] S. Rchter, A. Alonso, W. De Bolle, R. Wellum, P.D.P. aylor, Isotopc fngerprnts for Natural Uranum Ore Samples, Internatonal Journal of Mass Spectrometry, 193, 19 (1999). [3] Uranum Enrchment, [ ]. [4] Robert F. Mozley, he Poltcs and echnology of Nuclear Prolferaton, Unversty of Washngton Press (1984). NSSPI INMM Annual Meetng