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BNL2094 Subject Category: PHYSICS ATOMIC ENERGY COMMISSION UNITED STATES EXPONENTIAL EXPERIMENTS ON LIGHT WATER MODERATED 1 PER CENT U235 LATTICES By H. J. Kouts J. Chernick I. Kaplan November 28, 1952 Brookhaven National Laboratory Upton, New York Technical Information Service, Oak Ridge, Tennersse J'r L Z*SSIIED UNCLASSIFIED This report was prepared asa scientific account of Govern mentsponsored work. Neither the United States, nor the Com mission, nor any person acting on behalf of the Commission makes any warranty or representation, express or implied, with respect to the accuracy, completeness, or usefulness of the in formation contained in this report, or that the use of any infor motion, apparatus, method, or process disclosed in this report may not infringe privatelyowned rights. The Commission assumes no liability with respect to the use of,or from damages resulting from the use of, any information, apparatus, method, or process disclosed in this report. Date Declassified: October 31, 1955. This report has been reproduced directly from the best available copy. Issuance of this document does not constitute authority for declassification of classified material, of the same or similar content and title by the same authors. Printed in USA, Price 140 cents. Available fzem the Office of Technical Services, D~epartment of Commerce, Wash ington 2T, D. C. Exponential Exp*eriments on Light Water Moderated, 1 Per Cent U23r Lattices BNL2094 Report Written by H. J. Kouts J. Cherniok I. Kaplan Work Done by H. J. Kouts K. Downes R. Shor G. Price V. Walsh November 28, 1952 Work performed under Contract No. AT302Gen16 Brookhaven idotional Labora~tory Upton, New Ylork Dlcg'lzed by the Inte nel AIChive in 2012 with funcllng Irom University of Florida, George A. Smathers Libraries with sulpport from LYRAASIS andj me Sloan Foundation http://archive.org/details/exponentialexpe99broo Contents I. Introduction, 2 II. Experimental Facilities. 2 III. Buckling MIeasurements. 6 A. Theory 6 B. Experimental Techniques 8 C. Analysis of Measurements and Results 11 D. Cadmium Retios 13 IV. Anrisotropy Measurement. 1 A. Introduction 13 B. Theory 14e 0. Experimental Methods 16 D. Results 17l V. Migration Area Measuremaents, 27 A. Lu~troduction 27 B. Theory 27 C. Experimental Methods 28 D. Analysis of Data and Resulta 29 VI. Intracell Flux Traverses. 38 ..Introduction 38 B. Experimental Procedure 38 0. Analysis of Data and Results 40 VII. The Effect of Absorber Rode. 43 IIII. The Effect of a "Gap" on1 the Azil Relazation Length. 45 Eyponential Experiments on Light Water M3oderated. 1 Per Cent U235 Lattices 1.Introduction. At the request of the Division of Reactor Developmnent of the UI.S.A.E.C., the Phsics Division of the N~uclear Engineering Department at Brookhaven under took a program of exponential experiments on ordinary water moderated, slightly enriched uranian lattices. The purpose of the measurements was to provide nuclear design information for the core of a reactor for the production of plutonium and power. In particular, nuclear data were to be provided on tile basis of which the Atomic Energy Division of the H. K. Ferguson Co. now the Walter Kidde Nuclear Laboratory could prepare a feasibility report on such a reactor. Consequently, th~e program of the expe~riments was planned in close cooperation with members of the WKNJL and cooperation was maintained during the course of the experiments. The present report is a sumrary of the exponential experiment neasure ments which were made during the period November 15, 1951 to June 30, 1952, as part of a broader Reactor Components Testing Project. The experiments to be des oribed include measurements of the critical buckling, the migration arse, intra cell flux traverses, effectiveness of control rod materials, the effect of re moving uranium rode from the assembly, ete. II. Experimental. Facilities. The facility for the exp~onential assembly was planned with great care in view of the difficulties met in earlier experiments on ordinary water moderated natural uranium lattices at Oak Ridgel. 1. GP2842. The measurements were carried out in a water tank placed on a thermal column which occupies a portion of the top of the` Brookhaven pile shielded The thermal column consists of five one1Boot thick layers of graphite,. stepped from la 4' x 4' size at the bottom to 5' x 5' at the top. This~ stepped construction prevents fast neurtron leakage up the side of the thermal columnj and the well machined surfaces of the graphite blocks which manke up the structure provide tight packinggyhich ensures a wellmoderated source of neutrons at the. top sur face. The cadmium ratio of this source as measured with five mil thick indium foils was better than 105. The water tank is cylindrical, six feet in diameter and six feet high. Surrounding it is a makeshift shield of threeinch steel armor plate and assorted blocks of Brookhaven concrete. Inside the large water tank is a perforated aluminum cylinders four feet in diameter =nd four feet high, which serves as a vertical support for the top tube plate system, from which the uranium rods are suspended. This top is a' ring of three inch thick arnor plate which holds the circular aluminum top tube plates. The inner tank with a tube plate is shown in Fig. 1. The tube plates are made of 28 aluminum, the upper plate being 1*5n thick, and the lower plate *75" thick. In eadb are drilled 275 holes for the uranium rods, and 20 holes for the insertion of foils. C~are was. taken to locate these. holes accurately, the tolerance being Os *5 mils for each hole dianeter, and 5 mils overall for the distance between holes. These low tolerances were main tained largely because we did not know the effect of variations of individual rod positions on, reactivity and the positioning of foils, and we preferred working with conditions which could be trusted The uranium was prepared at KC2r, and was rolled into rods of .750n dia. at the St. Louis plant of the iMalinekrodt Chem~ical Corporation. Th~e Brookhaven metallurgy group then straightened the rods to within 15 nile lateral deviation in four feet of length, and clad than with 30 mil thick aluminum. Most rods are single fourfoot lengths of uraniun. A few are slightly under four feet in lengths and a few are made of shorter aeotions matched to provide approximately four foot lengths. Analyses of the uranian composition were made at Oak Ridge. The average composition is 1.027 per cent f .001 per cent by weight. Distilled water purchased commnercially was used throughout the experiment. Occasional spectroscopic tests of purity were supplemented by tests of reproduci bility of the data. In fact, the criterion of reproducibility was used constantly as a check: on the possibility that other factors might be influencing the measure nents. For a large part of the time the water contained boric said in solution. At all tines the tank contained cadmiumn from the shutter (see below). There was always the possibility that boron or cadmium coatings might form on the aluminum cladding of the roday thus changing the reactivity. For this reason, particularly, reproducibility of the data was held to be important. This reproducibility was mraintained throughout the excperimenmts. Best results from an exponentia~l experiment are obtained if the source of 2. Lack of accurate positioning of rods and lack of straightness of rods have been suggested as the source of errors in the Oak Ridge measurements (see reference 1). Best results from an exponential experiment are obtained if the source of thermal neutrons feeding the reproducing lattice is made about the sam~e size as the lattice itself. In this event the decay vertically of the flux harm~onics is most rapid, and the region of flux harmonies corrections is smallest. For this reason the bottom of the large water tan~k was covered with a cadmium sheet having a central circular orifice. The holein the cadmium had a radina about 7 st larger than thg) of the max~i~umu uraniua loading. This defines the source size most suitable for rapid decay of harmonica, because the radial extrapolation dis tance of the thermal neutron flux in the reproducing lattice was found to be close to seven centimeters for those loadings investigated. A shutter system of oadmium covered aluminum plates was designed to fit under the lattice assembly, to make possible turning off tihe source flux when irradiations were not being mazde. Because of corrosion and working under the weight of' the uranium and support assanbly, this shutter system never worked prop erly. In practise, the source flux was always turned off by the dropping of a saduium sheet into the water tank, over the disc source, after the inner tank with its uranium loading was removed by crane. The water tank contains a system of steam pipes which allow heating of the water. Thus the equipment has provision for finding temperature coefficients of the various quantities mleasured. No temperature coefficients have yet been measured, but it is planned to determine some in the near future. III. Buckling Measurements . A. Theory. We have used throughout the course of the measurements a onegroup view of the diffusion problem in the lattice. Accordingly, we suppose the neutron flux satisfies the relation (1) 2q +B2dy = 0, and the critical equation is simply (2) kno=1 + 29 2 The standard exponential experiment involves obtaining the Laplacian by differentiation of the measured thermal flux distribution. For a cylindrical array such as we used the space dependence of the flux can be written as a series of Bessel functions: ** r where r and z are cylindrical coordinates in the lattice. h is the reflector savings, and a, are the successive roots of (4) Jo(r) = 0 The coefficients f, have the form (5 )a, En 3n ex (g) / s+D s [i (n ) B 1/ the exponents being real for a subcritical assembly. C, is small compared with Dn,, since the first term is only important near the upper boundary of the lattice. Furthernores since the rate of decay of the higher harmonies is greater than that of the fundamental, above some value of z', tle, flux can be repressented closely by the fundamental alone: (6) ~ sIg f~), a>2s ' Ordinarily, one would measure the radial and axial flux distributions in the region of validity of (6). The radial distribution would be fitted to Jo(al r/ro), the axial distribution fitted to 01 ep s/L + D1 expjBF s/ ad the buckling wquld be (7) B /o21L Unfortunately, thle small loadings we were working with did not permit accurate measurements of the radial flux distribution. Syamnetry conditions mrade only five positions available for flux measurtsments on any one radius, and the outenrost of these was so close to the essentially infinite water reflectors as to make it useless. TIhe effect of the reflector can be seen from a typical radial traverse, shown in Fig. 2. Thlus only four points were. available along any one radius, and a curvofitting to these points was not accurate enough for our purpose. On the other hand, the axial flux distributions showed in every case the behavior characteristic of the presence of the fundamental only, from about 10 amn 3. The decision to use reflected lattices was made mainly because of the small amount of uranium available for the oxperimont. .The reflector sa~ving~s was equivalent to about 0.7 tons of extra uranium. L. The lack, of accuracy does not rise simply from the fewness of points. Rather, it is caused by the feet thlat these points are on the flat pa~rt of the Jo. curve, and ame~ll experimental errors in thea values of the foil activities cause largo variations in the extrapolated endpoint. upward from the bottom of the lattice. Mbreoverl the end corrections were small below about 70 as front the bottom of the lattice. Thus there existed about 60 an of variation of a over which the flux decaiy was simply exponential, and so quite good measurements of L could be made. He therefore decided to try basing mteasure mIents of B2 fin measurements of L alone. For such a determination of B2, one would nee~sure L for a wide range of rod loadings. Each such loading would be idealized to a cylinder with the sese loaded radius the case would have if the uranium were uniformly distributed at the same watertometal ratio. Least squares fits would then be made to X and B2 in ( 8) ( al/R+1)2 L/2 1 =B Such an analysis contains of course an assumption that A and B2 have the same value for all loadings used. This is perhaps no worse than the assumption ordinarily made in an exponential experiment on an inhonog~eneous lattice that the results can be interpreted in terms of fudged calculations liodeled after homno geneous reactor theory, with a value of the buckling which does not depend on the size of loading. Nevertheless we have kept in mind the fact that this assumption underlies the measurement, and later in this report present experimental evidence that the assumption is probably not far wrong. This problem is also being in vestigated from a theoretical viewpoints B. Experimental Techniques. The measurements of neutron flux distributions were made with indium foils, 0.220" in diameter and five mile thick. Each foil was counted in from three to six counters, to a total of more than ten thousand counts,, (1 per cent statistical accuracy) per fail. Counter resolving times were found by the twosource mesthod, and in all counts resolvingtime corrections were kept below 3 per cent. He believe that in this vwa we have kept to about .1 per cent of the total counts per fail the error introduced by having to make resolving time corrections. Count times were controlled by a preset thmer which was accurate within .3 seconds (at most *5 per coalt per count), about half systematic and half random. The estimated error due to timling is ~uns about .25 per cent. The overall estimated error in the activity of an individual foil is then about 1.3 per cent about the means when thd conditions for accuracy are worst. The foils were positioned in foil rods inserted through the top tube plate. At first thinwalled aluninue tubes were used, with slots to hold the foiled punched at ten centimeter intervals. The foiled were placed in thin aluminum foil covers, each being held together with Duco cement. The cement was removed by two washings in acetone before foil counting was begun. The meadata error in vertical positioning of the individual foils was about 1 rmn. For thel shortest Tolaixation length we measureds the maimrum error in foil. activity measured was thus about 0.7 per cent f'rom this source. Each foil ves used only once, so there were no errors from the presence of longlived activities. The aluminum foil positioning tubes were later replaced by machined lucite rods. Positioning error was thus reduced (to about 0.2 per cent at most). The use of Duco canent was avoided, and the replacenant rate of foil rods which had been large because of bending of the aluminum and rapid enlargement of the holes for foils, was naterially reduced. Because of large local variation of flux, it was necessary that all foils be centered accurately in a lattice cell. Ths was accomplished through the use of lucite spacers located at one foot intervals in height throughout the lattice. The foils were weighed to within 0.1 ag each. Their weights averaged 0.027 gma, with not aauch variation about the mean. Measurements of activity as a function of foil weight showed that corrections to the activity due to weight variation are about 20 per cent of the weight correction. MYatched sets of foils, with weight variations limited to ?: .1 mg, were used at every stage. Th~e esti mated error caused bty individual, variationns in foil weight was at vost about .05 per cent. This contribution to the total error is negligible.5 The value of the indium half life was taken as 54.05 minutes for foil activity calculations. At the end of the buckling apoperien~ts a careful determination of the halflife was masdes and gave a result T1/2 5i4.14 .0 m4linutes. The error in all the bucklings introduced by this discrepancy would be about 0.3 per cent. A measurement of the indiumn halflife was suggested to us by A. Mattenberg, who pointed out the lack of agreement in previously published values. The compounding of all these errors indicates inaccuracies of individual foil activities of at mnost 1.5 per cent about the nean. Statistical variations in 5* The variation with weight of the weight correction to the activity was measured. It was found that al1 per cent weight variation was accompanied by only a 0.2 per cent change in foil sensitivity. This is much less than the direct pro portionality usually easumeod. 10 the mleasured quantities were consistent with this estimated error. C. Analysis of Messuirements and Results. The relaxation lengths listed in Table 1 are obtained from least squares fits of excponentials to the axal fliix traverses. Watertometal ratios of 1.5:1, 1.75:1, 2:1, 2*5:1, 3:1, end 1:1 are reported. These ratios are really those of water plus alumrinus to uraniuml. Also given in Table 1 are the residuals of the least squares fits of B2 and h. Table 2 gives .the values of B2 and X which resut from the least squares fits. Fig. 3 is a plot of B2 vs wsat~rtometal ratio fron Table 2. Fig. 4 is a plot of X vs watertometal ratio from Table 2. The estimated errors in every case refer to reproducibility of data. Thus they do not include systematic errors or limitations to the validity of the method. The effect of having ignored end corSrections was considered. To determine the magnitude of this effect the following procedure was used. Values of L vere calculated from flux mecasuremnents over a range of 60 an, beginning 10 an fron the bottom of the lattice. Least squares fits of B2 and A were made for this set of data. The calculation was then redone leaving out the points at 70 as from the bottom of thle lattice. Since end corrections are greatest at this points the changes in computed values of B2 and X may be attributed to than. Small abanges in B2 were observed; they everagod about 0*5 per cent, in the direction consistent with the presence of end corrections. Since these changes are of an order of magnitude smaller than the accuracy of the measurements, it is felt that end cor rections are not of sufficient importance to warrant further investigation. The  11 values given in Tables 2 and 3 refer to the six point axial attenuation Ieasure ments, which have the smaller and effect corrections. At no stage were arUy effects observed which might be attributed to thle presence of the harmonies in (3). Since the method used to find the buckling is not standard, it was con sidered advisable to make some radial traverses in order to be able to compare results with those which would normally have been obtained. TIhe best radial traverses were made with the 3:1 watertometal ratio, at a loading of 265 rods. At this loading the lattice was approximately an elliptic cylinder, the distance to the edge of the metal loading being different for the two directions along which radial traverses were made. The effective radii vere found by fitting tho measured foil activities to Jo(al ig i)* The values of the reflector savings for the two radii were then found as the difference betwoon values of Reff and the actual distance fromu the lattice center to the edge of the letal loading. The average of six radial traverses gave in this way a value of 6.65 + *50 an for the reflector savings. This is to be compared with the value of 6.9L f .11 a~n de termnined by the method of exial bucklings only. The agreement of these values to within three millimeters is strikingly good. a single measurement of thle reflector savings was carried out in the LS5:1 lattice, in connection with the anlisotroply measura~nant discussed later in this report. The measured value of k in this case was 7.67 anu, with somewhat uncertain accuracy. The value given in Table 2 is obtained by the method of axial bucklings is 7.71 i .14 an. Agair the agreement is exceptionally good. 12 As a further check on the validity of tle assLumption of constant B2 and 1, the buckling for the 3:1 lattice was recoq.luted, using only loadings between 181 and 263 rods. B2 and h woro unchanged within the expericantol error roportod in Tablo 3. Thus the orperiDontel data available tends only to bear out the accuracy of the assumption underlying the method we have used. It would still be interest ing to see thes results of critical experiments made on these lattices. If the slowingdowsn and diff~usion of neutrons does not take place iso tropically in the reactor core, thG exponential experiment must be modified con sidera~bly. The effect of such anisotropy has been discussed by Young and Wheelor they showed that if the anisotropy is large it is possible to draw grossly in accurato conclusions froll a simple exponential exper~iment. D.Csadium Hatios. To a certain extent, information on the energy distribution of low energy neutrons m~yr be detorcined front the coduium ratios. Therefore accurate usesure nocnts of tho codduin:. ratio were made at thle center of a lattice coll, .uaing indiun and gold fails. The indium: foils were five uils thick; the gold foils were 1.2 mnils thick. Moosured values of the cadmaiun ratio are listed in Table 3 and.plotr ted in Fig. 5* IV. Anisotrop~y M\Ioouronente >.. Introduction. As will be seen in Part V of this report, the migration area which we have measured is essentially a constant over the range of watertometal volume ratios investigated, and is in this region quite close to them~igration area of fiesion 6. C90* 13 neutrons in water alone. TIhus it appears that because of high inelastic scatter ingr uranium in water may be considered quite closely oquivalont volumnewisG tOn the average) to the water it displccos, for the purposes of neutron alo~ingdown. It might be suspected that this condition mafkes the~ existence of anisatropic of foots unlikely. Nevertheless, the situation socluod to warrant a sac~reh for such an anisotropic character of th :;igrction area. Young and Whoolor also roportod and analysod the sugestion by Wigner that a doubleo exponential exporimant" would yield the degree of anisotropy. It is such a double exponential experiment which vo have carried out for the 1.5:1 waterto)metal volume ratio lattice, which~ should have the greatest anisotropy of the lattices we have used. For the general theory of the double exponential experiment, one should see the p~aper by Young and Whleelor. We give here a discussion suitable for :.me purposes . We consider our subcritical lattice in the shape of a rectangular paratl lelopiped, with edges Px$ y The fulel rods are supposed to lie in the a direction. If the ~thermal neutron source activating this array is placed at oneJ end of the lattice (the side with odges 1x and a ) thu onogroup critical equation will. bc (9) : 1 = M (B~ 8 ) MB .i k_ is of course the infinite pile preproduction factor. 14 (10) Bx=~ 7 2 (11) Bs = 1/L . L is the relaxation length for decay of the fundamental in the st direction, X is the reflector savings, and M~ and M have physical meaning aassciated with the mean equere distanco a fission neutron travels ~in dirootions parallel to the rods and normal to the rods, respectively. If, on the other hand, the source is placed on one of the side of the lattice (that defined by y and a), we shall have in place of (9) (12) kz1 = M~b~ M (b2 2) where (13) bj = R s 5/2 + X)2 2 2 (14) b = B (15) b = 1/(Lt)2 L' is now the relaxationl length of' the fundamental in the x direction, neasured in this geometry. From (9) and (12) we obtain H2 (B2 + B ) MB2a = M 2 + M2 (2 or (16) M /M2 = (B2 + b2)/(Bx ~) In practise, we took tkbo first geometry to be cylindrical, so that instead of (9) one has 15 (17) k 1 = ZB 11 B2 with (18) B1 = (a R+b)2. al being the first root of the Beasel function of order soro, and R boing tho radius of the loading cylinder. The relation which corresponds to (16) is do rived fron (12) and (17): (19) 11~ /di = (Bq + b2)/(B2 + b2~ ~ 0. ~ExJporiuentall MeIthods. B1 and B2 can be found froml the buckrling noTauroancnts in cylindrical geonotry described earlier. Thus to find the anisotropy it was only nocossary to carry out the second u~ousurcment abovo the determination of b2t, by2 and b2. F~or this purpose a set of lucite support piooos was constructed; these permitted a horizontal layered construction of the lattice in a 16 x 16 rod array thus a loading of 256 rods. Support was provided by the lucito at four points along the length of the rods, to prevent sagging, and the foils which were used to measure the neutron distribution were placed in maachined holos in the surface of the lucite support structure. The cadmina which defined the shape of the thermal neutron source had out in it a rectangular hole about 14 c7 larger on each side than that of the array. This source shape was most suitable for the appearance only of the fundamontal. The gold foils which were used throughout were .220 inches in dienneter, and were about one mil thick. They wore chosen as a set matched in eight to about .5 per cent. The foil counting techniques are the same as those described earlier. 16 D. Rosults. Equation (17) does not refer to any particular radius of the lattice, and Sas a result B2 andi B m~ay be taken in (19) for any loading. We have chosen Prather arbitrarily to base the analysis on tbo 235 rod loadings, the results ij. of which are given in T'able 2. Here, L is 17.72 an by mloasuromuent. Analysis of the least squares meth~ods used to obtain L show an expected accuracy of about .10. We allog, for each of the two muoasurements double this error, so SL (the error in L) is assumlod about i .14. The loaded radius at 265 rods is 23.087 cm. The reflector savings given by buckling measurements is 7.71 emn. Allthough this number is here being questioned (its derivation is based oh use of the isotropic critical Gquation rather than on (17)), it is doubtful that it is wrong by more than *: 5 em. Thus vo may take Rth = 30.80 r ,50 can with some confidence. So far we have (20) B = 1/L2 = 3.18 x 10"3 & .052 x 103 cmd" B2 = (al/R+1) = 6.09 x 103 t .055 x 103 ad"^. Wiith the lattice placed horizontally, a set of seven foils was placed in the~ yr direction, to provide a determination of the flux distribution in that direction* A least squares fit to A cos bx gave b = .0513 t .0046, or,@/2 + h = 30.62 ex f 2.75 cn. Since Py = 32*95 on, we have h = 7.67 an 2*75 an. Inr spection of thG least squares fit to the plot of the flux distribution given in Fi6* 6 shows that the cosine curve was actually shifted somewhat from the assumed center of the lattice. If all foils are translated slightly in the same direction, :. the error is considerably reduced. During the acasurement such a displacement seems to have occurred. We prefer therefore to accept the above value of X, but i 1'7 vith an error closer to about *5 an. Thus (21) = 2.63 x 103 *043 x 103 an". The flux values obtained from this traverse are listed in Table 4. ALlso, be can be obtained accurately enough from just the rod length (four feet] and this reflector savings; we have then 2 3 .a 03 m2 (22) be = 53x1 .0 0 c The thirteen foils which were used to neassure bx2 seemed to separate into two groups) the syaPnetry of the triangular lattice cell. in which a given foil was placed determining its group. Those in lattice colle with a vertex upward lay on a different curve from those with a vertex downward. These two curves seemed to have quite different end corrections, but apparently could be fitted byr the same value of L'. Least squares fits to oeah of A exp x/L B oxp x/L; agred fairly well with LI = 100 f 30 an. The large error is caused b7 the presence of sizceable and corrootions, the thicknzess of the lattice in the x direction being only 45.90 emn. The results of the x traverse are given in Table 5 and shown in Fig. 7. From the value of L' we have (23) = 10"A t 104~ am"^ Substituting the values from (20), (21), (22), and (23) in (19), we obtain (24) M~ /~ = 1.039 . An estimate of accuracy can be obtained by differentiating (19). Putting for the inoment we get 18 dB2 + db2 JdB2, +d2 d2) d3 The uncertainties in the various values can be considered as randy; the un certainty in 5 is then given by (dB2) + db2. 2 2 dB2)2 + (dbp2)2 (dbY) 1/ .2 (25) af = B + b b Insertion of the uncertainties given in (20), (21), (22), and (23) gives (26) AT~ ~ .0as The anisotropy indicated by (26) is just barely outside the error limits set by (26); we conclude that within experimental error it is negligible. Thus there appears to be too little anisotropy to influence the validity of the ex ponential experiment too greatly. Another search for anisotropy could be made, based on the recasting of (19) in the form (27) =1 3B2 B~ with a thre~e constant fit of 51, and k1/M~ to measurements of B2~ as a function of loading The agreasont of values of X obtained fron the two constant fit with the values obtained froml radial traverses indicate though that such a procedure would also show negligible anisotropy. 19 Tablo 1. Relaxetion Loggthes L (an~) In Water81ightlyEnriched Uranina Lattices Rosiduals of L (an) let nrn 2nd run L (1st run) L (2nd nrn) No. of Rods 1.5:1 Lattice 19*793 18.492 17 .723 16*564 15*741 14.996 13*997 13.129 12.259 11.282 9.665 1.75:1 Lattice 22.168 20*391 18*757 17.744 16.623 15.237 Us*203 13.062 12.134 10,030 19*559 18.733 17 .722 16.892 15.865 15.154 14.13 13*200 12.271 10*435 8.801 .156 .012 .009 .121 .006 .183 .043 .037 .104 .097 .026 *105 .044 .125 *045 .097 .024 .023 .037 .065 .126 .132 .093 .111 .012 .040 .020 .020 .014 .094 .095 .161 .057 .268 .034 .143 *080 .002 .068 .060 .019 .068 21.935 20*287 18.811 17.666 16.285 15.215 17.257 13.118 12.071 11.060 10.012 2() Table 1. (Continuad) Residuals of L (an) let run 2nd run No. of Riods L (1st run) L (2nd run) 2:1 Lottico 29.087 26*539 23947 21. 510 19.612 18.252 16.781 14.905 14.102 2.5:1 Lattice 30.021 28.091 25.062 22.763 29.688 18.444 16.867 15.317 13.932 12.400 11.119 271 265 253 235 217 1991 181 169 163 15 127 109 *122 .262 .010 .080 .100 *372 *266 *453 .1465 *352 .312 *332 *333 .073 .249 .137 .108 .002 .060 .022 27.297 25.955 23.424 21*551 19.631 16.815 15.109 14*557 13.028 30.472. 27.800 24*737 22.886 20*330 18.761. 16.950 15.147 13.793 12.341 11.058 .282 .180 .135 .180 .113 .14t5 *341 .156 .011 .097 .041. .032 .037 .152 .214L .154 .037 .003 .045  21 Residuals of L (anI) let rnm 2n~d run No. of trods L (1st ru) L (2nd nru) 9:1 Lattice 33.437 29*4d60 26.296 23.669 21.419 19*438 17 .653 16.016 L:1 Lattice 36.&647 33*592 29*448 26.152 23.754 21.577 19.547 17*.311 15.821 .13.006 9*933 26.845 24*396 22.546 21*315 20*342 19.019 17.525 16.016 .153 .145 .104 *134 .211 *287 .139 .051  .127 *300 .180 .199 .280 *145 .139 .100 .022 .174 25*521 24.333 22.808 22.888 21*390 20.150 .18*580 17.690 16*589 .15*999 16.237 13*936 .347.021 *350 .017 .019 .105 .062 .001 .027 .307 .076 .224~ .203 .060 .160 *307  .379 .069 235 217 199 181 163 145 109 22 Table .1. (Continued) TIable 2. Results of Loast Squares Fits to B2 and X Latice 1stRun 2nd Run Avon 1st Run 2nd Rlun Avseraa 1.5:1 2.85 *62.94 + .05 2.89 + .05 7.56 & .14 7*56 &t .11 7.71 + .14 1.75:1 *~ 3.453 2.034 3.486 t.053 3.L70 af c033 7.16 .08 7.15 .12 7.16 &t .10 2:1 3.65 &.09 3.86 *.07 3*75 1.08 7.23 .26 6.75 .20; 6.94 *23 2*5:1 3.700 t.055 3.647 ',025 3.673 f.048 6.81 &.17 6.99 &.09 6.90 & .16 3:1 3.304 2.028 3.271 +.006 3.28g &.018 6,82 .11 7.05 f .09 6.94 f .11 :11.76 + .10 (1.88 + .04 [1.86 + .06+ 6.83 F *52 6.37 f .19 6.42 *f .22 # Aveircages for this lattice are weighted because one mecasureme~nt is Iluch poorer than the othor. 23 Table 3. Cadmnium Ratios Gold Gadmiumu Ratios 1.918 .052 2.~292 + .038 2.88, t .025 3.307 &t *045 Lattice 2:1 3:1 4:1 Indium Cadmuiumn Ratios 2*576 2 .014 3.044 ;t .16 4*30 & .033 5*7462 t .092 24 Table I. Neutron Flux Moasuremeonts fronl yTraverse Last Squarea* Fits Residuals ~(5A~ctivityv) 17.9 4.6 1.8 3.5 4.7 11.6 S.0 Distance From' Assumed Center teu) 15.776 10.039 4.303 1.4t34 7.171 12.908 18.645 Measured Foil Activity (units arbitrary) 583.3 718.1 798.3 821.2 760.2 634.9 464.7 SThe residuals are those resulting fray fitting column 2 to A cos Bx. The best values, on which the residuals are based, are A = 819.9 28.0 B = .0513 j: .00~46 ca1 25 Table r. Neutron Flug Moasure m xTraverso Distance From First Foil (cu) 0.0 4*970 9.940 14.910 19 .880 24.850 29.820 0.0 4*970 9*940 14.910 19.880 26.850 Measured FEoil Activity (arbitrary unit) 1160 1028 882*S 758*3 570.5 4646.9 316.6 1107 962.9 Lost 652.1 490.2 350.7 Least Squares Fit Residuals ( A\ activity) 8* 2*7 21.6 23*5 4*5 6.9 15 20.4 9.2 2.9 0000?P 1 GRlOUP 2 "Columnu 2 was fitted to A e'aX + B o+0%. Although points made boat values somewhat uncerttain, these the scattering of tho few are about a[am1) *010 A GROUP 1 2083 B 911.5 GrouP 2 2162 1041 .010 26 IV. Migration Area iMeasurem~ents. A. Introduction. The values of the migration area are based on weasuranlents of the buckling in lattices with boron poisoned water, as a function of the boron concentration. The theoretical basis for the rmoasurem~ent is discussed in the next section. B. Theory. We ma g express he in two wellknown ways, either by the critical equations (1) 1= 1 + B2(T + L2) or by the fourfactor formula ( 2) ~= f pE P B2 is the buckling, 7 the age to thermal of fission neutrons, L2 the thermal dit fusion area, so 7 + L2 9i2 is the adpgration area; f is tbo thermal utilization, '1the number of noutrona captured in uranian; which cause fission (per neutron cycle), & is tho fast fission factors and p is the resonance escape probability. If the moderator is mado anna neutron absorbing bry means of the addition of a poison, those quantitios in (1) and (2) which will be changed are ~, B22 f, and L2, the other remaining constant; 20~ msain effect of the poison is to de crease f. Hence, if the measured values of B2 are plotted against f, a straight lino should bo obtained, the slope of whidb gives Mi2. For fs theoretical values calculated by the Kidde group, were used to get preliminary values of M2. These will eventually be corrected by the use of nexperimeontaln' values of f obtained from measurements of intracell flux distributions. 27 0. Experimental Mothods. A typical mlecauromeont of the migration area involved dissolving succas sively increasing amounts of 8203 in the water, and Ileasuring the values of the buckling of a lattice in these poisoned mcoderators. At each stako the boron con celntration was determined by the analytical group in the Brookhavon chemistry department. The bucklings were mleasured at three different boron concentrations for each lattice. When the measuroments with unpoibroned water are included, the dependence of B2 on boron concentration is thus found at four values of the boron concentration for each watertometal vrolumeo ratio. The buckling was found by measuring the axial relaxation length as a function of toe number of rods loaded, a method described earlier. For each poisoned lattice, measurements were made at only five loadings, because of the large number of balcklings which had to be measured in a short tiuo. Thermal neutron flues were measured with foils of five mil thick indian .220 inches in diameter. The techniques used to position foiled in the lattice and to measure their activities are described in Part III of this report. Because of the possibility that boron might plate out of solution and onto the aluminum cladding of the rods, tests of reproducibility wore made when possible. Thoso consisted of neasuronents of the relaxantion length in an un poisoned lattice, and comparison of the buckling it indicated with previous measuranants. The results of theso test exials are given in Appendix 1. They lead to the conclusion that no important change in reactivity of the lattice occurred during the buckling and emigration area measurements.  28 An earlier effort to Yoasure the migration area by another means was un successful. In this attempt, the uranium rods were covered with cadmian sleeve, !:to suppress neutron multiplication. A measurement of the thermal neutron flux ~distribution due to a known fission source was to have yielded the uigration aron. SLow values of the flux fro, tbo fission source kept this measurement from being successful. This method of determining the migration area was used at Oak Ridge I in an ocrlior investigation of this reactor typo. The Oak Ridge result differ a;~iguificantly from ours, particularly at the lower watertometal ratios. These discrepancies will be discussed in a later section D. Analysis of Data and Results. The values of the relaxation lengths, as found from least aquarea fits to the axial flux measure~ments, are given in Table 6. Also given are the residuals resulting from last squares fitting to the buckling and reflector savings. The best values of B2 snd h are listed in Table 7. The boron concentrations; calou lated values of f, measured values of! B anddeduced values of M12 are listed in Table 8, for watortomotal volume ratios of LS5:1, 2:1, 3:1, and 11:1. The values of B2 when plotted against f for a given lattice yielded good straight linas; the value of M~2 was obtained by a least squares fit. A typical plot of B2 against f is shown in Fig. 8. Also shown in Table 9 are the values of k indi cated by the values of N12 and B2 for the four lattices. The values of migration area and a~given by this report aust be considered as tentative, because they are based on calculated values of f. There is some uncertainty about the results of the calculations because of the simplifying 29 assumptions about the geomnetrzy, the angular distribution of the flux, and the creassectiona. The value of the.mitration area as obtained from a poisoned lattice experiment is quite sensitive to the values of f used and it appears that accurate measured values of f must be obtained before the migration areas reported here can bon~aldeo trustworthy. A preliminary estimate of the "experi mentala values of for the unpoisoned lattices is given in section VI of this report. These values differ significantly from the values provided by Kiddes and theoretical work on this problon is in progress at BNL. For these reasons, the errors eited with the values of the emigration area must be considered to represent only measuoes of the internal consistency of the experiments and the possibility of a systematic error must be borne in mind. The most striking result of these experiments is therefore the apparent constancy of M2 over the range of value of the watertometal ratio studied. This result is quite different from that predicted by present theory, as can be seen front Fig. 9. When calculated values of L2 are enbtractod from M2 (and L2 is small in these lattices), the age is obtained. The resulting ages are plotted against watertometal volume ratio in Fige 9, and compared with the theory of Soodak and Forman. 30 Table 6. Measured Values of Axial Relaxation Lenetth for Various Boron Concentrations. Nwuber of Rods Rlelayation Length L~an) L Residual (an) 1.rj:1 Lattice. .216 Boron atoms/103 water molecules 262 16.898 .023 229 15.686 .063 193 14.21) .011 157 12*735 .085 *121 11.430 .056 1.5:1 Lattice, .563 Boron atomus/LOS water molecules 263 14.960 .101 229 13.879 co054 193 12.823 .090 157 11.710 .124 121 10.828 ,l60 1.551 Lattfoo, .860 Boron atoms/103 water muoleculos 263 13.677 .002 229 12.976 .020 211 12* 538 .015 193 12.121 .013 175 11.710 .013 2:1 Lattice, *359 Bornn atoms/10 water molecules 265 18*744 *073 229 16*750 .254 193 15.288 .438 157 13.597 .181 121 12.085 *059 2r1 Lattice. .590 Boron atomafl0 water molecules 265 16.367 .061 229 14.867 .261 193 13.899 .392 157 12.568 .090 121 11.205 ,108 31 Relazation Longth L(cm) , ~~~~~~~~~~~ ~ ' ~ ~ ~ S ~Ei L:1 Latticel r071 Boron atoas/10 water molecules Table 6, (Continued) Numnber of Rods 2:1 Lattice, .8214 Boron atomaf/l03 265 14.700 229 13.902 193 12.862 157 11.8C8 121 10.850 3:91 Lattice. .171 Boron atoms/103 water molecules .003 .064 ,048 .057? 0061 water molecules .081L *131 .041 .086 *005 vater molecules 263 22*519 229 19.97 8 193 17 .794 157 15.7 67 121 13*579 1 :3 Lattice .145 Boron atens(103 18.128 16.825 15.467 13.910 12.225 .043 .001 .089q .028 .014 3:1 Lattice. .512 Boron atoms/LOS vater molecules 263 229 193 157 121 15.659 14.856 13.871 12.794 11.582 *036 .C0ei .013 .026 .008 265 193 ly? 121 21.287 17 .790 16.010 13.939 ,005 .069 .101 .084, 323 L Residual (an) Table 6. (Continued) Numiber of Rods Relaxation Longth L(em) L Residual (cm) 4:1 Lattico, .146 Boron atoms/103 water molecules 265 18.895 *008 229 17 .626 .033g 193 16 .203 .022 157 14*571 .136 121 13.202 .091 4:1 Lattice, .218 Boron atoms/103 water molecules 265 17.097 .020 229 16.187 .064 193 15045 .001 157 13.745 .114 121 12*595 *073 333 Tqble 7. Buckling and Reflector Savingeo qe a Function of Boron Concentration Boron C neentration Lattice (B atoms/10~ 190 molecules) 82 2) x 103 Acam) 1.5:1 .216 2.164 i .082 7 .61 i .18 1*5:1 563 1.107 a .217 7.61 i .46 1*S:1 .860 .24;3 t .05 7.75 2 .12 2:1 *359 2.045 i .255 7 .45 .67 2:1 .590 1.212 *314 7.11 .78 2:1 .826 .326 i .094r 7.32 t .22 3:1 .174 2.086 i .052 6.79 i .20 3:1 *345i 1.137 1 .057 6*37 + .19 3:1 *512 .019 ;r .049 6.59 t .17 4:1 .074 1.103 i .050 7.16 i .26 1:1 .146 .596 i .067 6.60 *30 4:1 .218 .054 f .070 6.81 i .32 U 35 IlhY1__ I_ YC Table 8. Values of the Migr a Determined by the PoisonedLattice Method Boron Concentration (atomes per 1000 Lattice molecules of water) (an" x 10': eyperimental) Migration Area (cln2) The~rmal Utilization (Theoretical) 2.86 2.20 1.19 0*33 3.75 2.05 1.27 0.33 3.29 2.09 1.14 0.02 1.86 1.10 0.60 0.05 1.5:1 0 0.216 *563 .860 0 0.359 .590 0 0.174 c345 .512 0 0.074 .218 0.917 *900 .874 .852 0.889 .851 .828 .808 0,828 .803 *779 *758 0.774 .761 .?18 *735 28.99 ~0.37 30.06 1: 1.21 28.69 & 1.23 28.47 & 1*413 4:1 Tahlo 9.s Preliminary Values of 6 2.86 3.75 3.29 1.86 MiSgration Area (an2) 29.0 30.1 28.7 28*5 1.083 1.113 1.094 1.053 Lattice 1.5:1 2:1 3:1 4:1 36 APPENDIX 1 Results of Test of Axal Hensasuremnts of Reproducibili~ty The poisoned lattice measurements were performed on the 2:1, 4:1, 1.5:1, and 3:1 lattices, in that order. Immediately after the 2:1 poisoned lattice measurements, a single axial measurement was carried out with the Ic:1 lattice and pure water. Use of the measured rdiaxation length and the reflector savings from reference 1 gave a value of B2 = 1.816 x 10"3 om2, compared with the previously measured best value of 1.79 x 10 Lanediately after the 1.5:1 poisoned lattice measurementJ a single clean axial was measured with the 3:1 lattice. The value of B2 thus. indicated was 3.23 x 10 3, compared with. the best valuel of 3.287 x 10 Just after the 3:1 poisoned lattice runs, a clean axial flux measurement was made with the 2:1 lattice. This gave B2 = 3.62 x 10"3s compared with the best value of 3.75 x 103, Within the accuracy of the measurements, these results imply reproduci bility of the data throughout the course of buckling and migration area mueasure ments. VI. Intracel Flux Traversea. a. Introduction. The values of the migration area we have reported earlier depend on cal culated values of the thermal utilization f. Since there is some uncertainty about tbo theoretical method used to find these values, an attempt at measuring them seems useful. He have used the direct approach of measuring the thermal neutron flux distribution in the water and in the fuel raday thus thle values of f we obtain are still uncertain by an amount depending on the crosa sections used and hence on the assumed neutron temperature. Evaluation of f of courao also has motivation from the desire to check experimentally the methods need to calculate k through the fourfactor formula. B. Ejrperimental Procedure. Intracell flux distributions were measured for l*5:1, 2:1, 3:1, and 4:1 watertomretal volurme ratios. These are actually ration of water plus aluminan to uranium. Because these lattices are so tightly packed, it was necessary to nee very small detector foil, not only in the roda but also in the water, if any detail in the flux distribution was to be obtained. ~The foiled used were 1*5 miLImbeter diameter diace of lucite containing dysprosium oxide, about *5: millinueters thick. D~yaprosina vas considered ideal as a detector, because its lack of low energy resonances makes possible the measure muent of thermal fluxes without the need for making cadmium difference measurements. Foils of this type have been used by the reactor physical group at Argonne, with considerable auecess. The foils were punched out of a small sheet masde in a hot press from a powder mixture of lucite polymer and dysprosiumn oxide. Because the activity de 1/2 aired (T 140 minutes) was not reported in the literature with an accuracy sufficient for our purposes, a measurement of the halflife was carried out. The procedure and result, 51/2 = 139.17 14 minutes, are reported as a letter to the editor in the Physical Review. During the course of this measurement, it was found that no other activity which would interfere with the one desired was present in detectable amounts. Mass spectrographic analysis of the dysprosiuml showed only trace impurities, due mostly to,other~ rare earths. Flux traverses in the uranium were made using a split fuel rod, with nine Holes of about 1.6 millimeter milled on each of two diameters. A drawing of a iicross section of this rod is shown in Fig. 10. From the figure it is seen that the foils are quite close together compared to their diameters. They are re placing a medium (uranium) with nearly the same absorpjtions however, and so the influence of neighboring foils on each other is small. The use of finitesized foil of course introduces an error arising from the fact that the flux is not constant over their area. For tihe foil aises used and the fluxes observed, it can be shown that the observed activity can be at tributed to the flux at the fail center, with an error of at most .2 per cent. Since corrections for this effect would be anall compared to errors in measurement, they have not been made. The foila used in the water were positioned in a piece of lucite which ran through the lattice. The horizontal positions of these foils relative to those in the fuel rod were known to be within about five mils (.013 an). 39 Foils La the uranium were not placed at the same vertical level as those in the water. The difference in elevation was measured, however, and the known axial relaxation length made it possible to correct the observed activities to those they would have had if they had been at the same height. The error intro duced by this procedure is considered negligible. Each foil used was counted to about seven thousand counts in each of six end window counters. Thus there vae no need to make counter efficiency corree tions, the activity of a given foil being determined from the total counts ob served in all counters. In all, six complete intracell flux traverses were measured, one in the 1.5:19 one in the 2:1, two in the 3:1, and two in the 4s1 lattices. an additional partial traverse was also obtained (in the metal) in the l*Ssi lattice. C. Analvaia of Data ga :Results. The experimental data obtained from the intracell flux traverses are shown in Figs. 11 16. In view of the triangular syimmettry of the lattice the neutron flux in the moderator was measured along; two lines, the first joining rod centers and the second along: the median of the triangle. The most complete moderator data was obtained at the higher moderator to fuel volume ratios. Only a few points could be obtained at the 1*5:1 volume ratio because of the tightness of the lattice. The flux data uco the fuel rod were first fitted to the Bessel function lo(Ko~r) where r is the radial position of the foil from the rod center and Ko = 1/Lo is the reciprocal diffusion length. The function lo(Kior) represents the symptnotic form of the flux distribution in the fuelsl but in order to obtain a 40 good fit of the flux data, a value of Ko considerably higher than the theoretical value must be assumed. The results of the least square fit of the data are given in Table 10 below. Tablo 10. Bessel Function Pit of Flux Traverse in the Uranium Rod Vol. Ratio Ko (in1) L, (an) F l*5:1 2.970 0.855' 4*7 per cent 1.147 1.Fr1 2. 818 0.901 ~t6.0 per cent 1.133 2:1 2*585 0.982 8.0 per cent 1.113 3:1 2.659 0.955 5.4t per cent 1.119 3:1 2. 644 0.961' 7.0 per cent 1.118 4ll 2.988 0.850 54 per cent 1.149 4:1 3.152 0.806 2.9 per cent 1.165 The ratio F of the flux at the surface of the fuel rod to the average flux in the rod is given in the final column of Tablo 10. Thle values do not very significantly with moderator to fuel volume ratio. The average value of F=1.135 which corresponds to Ko = 1.116 em1 ausdipltnghefu uv lo(Kor) for the fuel rod in Figs. 11 16. The values of F obtained from the BNL experiments ear much higher than would be expected from elemnentary diffusion theory. These results are in con fornity with those obtained with uranium rods at other laboratories, notably at North Anerican Aviation. Kidde has estimated the thermal utilization of our water lattices (HKFlk92D151, Mar. 4J 1952) by the use of an elementary diffusion theory formula with the value of F corrected by means of a spherical harmonics calculation. Their estimates are given in Table 11. 41 Table 11. Vol, Ratio _g 1*5:1 0.917 2:1 0.889 3:1 0.828 4:1 0*775 These values of f were used in the preliminary estimates of th~e migration area (Section V of this report). The theoretical flux curves in the water obtained by the use of elementary diffusion theory are shown in Figs. 11 16,1 corresponding to a value of F = 1.135. The lower ourve in each figure corresponds to the currently acceptedl value of L1 3 2.85 cm for the diffusion length in water. On the basia of these flux dlistribu tions the relative absorption of thermal neutrons in fuel, cladding and moderator is shown in Table'12. Table 12. Thermal Neutron Absorption in a Unit Cell Yol. Ratio f fal ~fmod 1:1 .9169 .00)50 .0781 2:1 .8873 .0048 .1079 3:1 .8298 00045 .1657 4:1 37759 .0042 .2199 Although the values of f agree with the K~idde estimates it may be seen tbat the theory greatly underestimates the neutron flu~x in the inderator. The reason for this discrepancy is clear from the exp~erimen~tal flux data. Extrapolation of these data to the moderator fuel interface would indicate a discontinuity in flux in this region. The apparent discontinuity arises fran the neglect of the non asymptotic solutions of the transport equation which are important near such an interface. Ic2 The required refinements of reactor lattice theory are not within the scope of this report. However, to obtain a better fit of the experimental neutron flux curves in the moderator and hence more realistic estimates of the thermals utilization, we need to modify the value of the diffusion length 1 lsi the miod erator. Thle modified diffusion theory curves are also shown in Figa. 11 16. The corresponding values of the thermal utilization are given in Table 13. Table 13. .iodified Values of the Thermal Utilization Vol. Ratio f C ~1*5:1 .910o 2:1 .871 3:1 .1 4:1 *755 These values of f are preliminary and are being refined by a more exact analysis VII. The Effect of Absorber Rods. The effectiveness of a central absorber rod in lattices of the type under investigation was studied in another set of experiments. Cadhnium tubes of dif ferent dianmeters were tested; the change in the axial relaxation length caused by replacing the central uranium rod by an absorber rod was measured. Hollow cadniurm rods of different diameter were used; the wall thickness was 0.056 indb in each casse. In m~ost of the experiments, the rod was filled with water; in one case the rod contained a steel cylinder. The fractional change of the axial buckling was also calculated fran the relaxation lengths. 43 To test the effectiveness of an absorber rod as compared to that of the removal of a fuel rod, the central fuel rod in the 3:1 lattice was removed, and the change in relaxation length measured. The value of the relaxation length was 32*32 a~n with 254~ roda in the lattice; when the central rod was removed, theo relaxation length decreased to 32.25 em, or a decrease of 0.07 an. This decroase Corresponded to a fractional decrease in the axial buckling of 0.0)022 r 0).0017, or about 0.2 per cent. In the other experiments, the change in relaxation length corresponds to the replacement of the central fuel rod by the absorber rod. The results of the experiments are given in Table 14. Estimates of the precision has been shown in two cases, which seaned to be typical. No attempt has been made at BNL to treat the data from a theoretical standpoint. Table 1L. The Effect o~f Absorber Rods on the Asial Rolaxbtion Longth Rod Outer Dieamter of Type of Relazation Fractional Change in Lattice Loading Cadniumn Tube (in) Filling Length: L(on) the Azial Buckling~ 1.5:1 255 No tube  18.96 0.81 H20 16.93 0.253 2:1 263 No tube  26.89 0.95 H20 23.27 0*335' o .010 3:1 254 No tube  32.32 0.81 H20 26.77 0.461 253 No tube  32025 0.65 R20 26.88 0.439 1+:1 253 No tube  23.15 0.95 "20 21.11 0.203 0.81 H20 21.71 0.138 263 No tube  25.18 0*75 Steel 22.40 0.2522 f 0.004, 44 VIII. The Effect on the Agial Relaxation Lonath of a "Gap" in the Lattice. In the design considered by the Walter Kidde Co. for a powerplutonium reactor, the lattice is to be divided into several groups of rods. WJhen the fuel is ready for processing, the sub assanblies are to be separated before being removed fran the reactor. In this case, it is desirable to know what change in reactivity may be expected when two subassemblies are separated, and a series of experinent~p was made in order to obtain some information of this kind. In these experiments. the relazatioin lengths were measured for two different arrange ments of 160 rods; this was done for each of the four usual lattices. In the first arrangement, the 160 rods were in a rootangle with 16 rows, each containing 10 rods. To form the second arrangement, tho rodls in one of the two central rows were removed and placed at the end of the rectangle. This resulted in 2 rectangles each of 8 rows with 10 rods per row, the two rectangles being separated by one row without rods. The second lattice may be regarded as a split lattice separated by a water gap. The axial relaxation length was measured for each arrangement; the results ear listed in Table 15. The fractional change in the exial buckling is plotted against watertometal ratio in Fig~. 17. The fractional change in the axial buckling is defined as L2 12 L1 where the subscripts refer to the two arrangements. 45 Table ly Gau_ on the Relaxation Lenp~th Effect of a Central Relaxation Lengrth (an) 13.26 13.51 15.70 14.80 17 .73 15.37 16.48 14.16 Fractional Change in in Agial Buckling: 0.0367 (Gain in Reactivity) 0.12C (Loss) 0*331 (Loss) 0*354 (Loss) Lattice 1.5:1 2:1 3:1 4:1 Arranzerment No Gap Gap No Gap Gap No Gap Gap No Gap Gap In three of the four lattices the effect of the separation was to de orease the relaxation length (decrease the reactivity). In the tightest lettica, 1*5:1, there was a slight, about 2 per cent,, increase in relaxation length, indi cating that the separation caused a alight increase in reactivity. 46 ,~trv:*, :~?~r~kl d~Cr~ r ~"' (I, .: 9"; IE; JP Si~ ,~, *i :~SFF ;ri i: ,... ,; i f;g : .It i : ihi C::r 7i~F: :i"z z~c .r.:, i:Cr~ \~: Fi@lre 1 Ficture of Tsn~. Neati,e ~~o. ~?152 The inner tank with a tube plste nd fuel rods. 47 TYPICAL RADIAL FLUX TR AV ERS E IN 2:1 LATTICE, SHOWING FLUX m RISE NEAR REFLECTOR ac % o IrI FIG ~~  1 I O  O W> g O 0 0O I I I I  REFLECTOR SAVINGS VS. WA~TERTO METAL VOLUME RATIO .75" RODS OF 1.027% 25 URANIUM, LIGHT WATER MODERATOR 10 ;z hLJ ) C 4' WATERTOMETAL VOLU ME RATIO FIG. 4 5o O O (D J CD ~O M (U QIIVt~ ~nlWQ~3 51 110J I 1 i I I I I 1L"  O LLJ I/ lo 0 lo cu O O a) O O NU 52 O / D O OJO o +  O( O m CO W 53 x E OU O ak  a z< ON 20 \ Iro to CR u! a, NOlltlZnlln ~tlVUtl3HI O 3 000 .004 3 .0846 .0849 .086 I S.0841 .0 46 M ei a) O r0852. .0 8 45 .0839 .0060 c L/ \ IK/ \ IJ b ~L b~Lb Q) I aD I a> I a, P U1 U1 VI Q, O 00 .00 50 .0066 36 FOIL POS TIONS FO R INTRA CELL FLUX TRAVERSE FIG. IO E a 0 o a J 04 <1 OO ~90 E" o (3 L LL SO m to 4 O N  8 Os N (U O (11 1 E E WI u a 0 do D O o a QD IA O zz o a 0:0 Jz  W~ OO~ CE IIII com tr O 3 (UL \ Ic O (Z D g cu o N o o co  11 u00 O E mo aR O a a: o, 000 o Z O o c O z~ U trj ttIlll I62 I 2rU. S. GOVERNMENT PRINTING OFFICE : 1956 D 377~567 9N11)13n8 'ltllXtl NI 3~NtlH3 UNIVRSIT OF L O ID 3 26 82998 
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