Control Rod Reactivity Measurements in the Agesta Reactor with the Poised Neutron Method

Transcription

1 ÅE-364 UDC Control Rod Reactivity Measurements in the Agesta Reactor with the Poised Neutron Method K. Björéus AKTIEBOLAGET ATOMENERGI STOCKHOLM, SWEDEN 1969

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3 AE-364 CONTROL ROD REACTIVITY MEASUREMENTS IN THE ÄGESTA REACTOR WITH THE PULSED NEUTRON METHOD Kjell Björéus SUMMARY An extensive series of control rod measurements was made in the Ågesta reactor during the low power experimental period following the first criticality. This report describes the part of these investigations made with the pulsed neutron method, comprising nearly 300 measurements. The main objective was the determination of control rod reactivity worths for different rods and groups of rods, but some supplementary measurements were also made, e.g. a determination of the prompt neutron decay constant for the delayed critical condition and four different cores. The cores consisted of 20, 32, 68, and 140 fuel elements respectively, and measurements were made at room temperature and with the moderator level close to critical for each core, and for the 140-element core also with full moderator height and at the temperatures 140 C and 215 C. Both fully and partly inserted control rod groups were investigated. The measurements at critical water level give directly the control rod reactivity worths, whereas those with full water height give the shut-down reactivity. A comparison was made between measured reactivity worths for a number of rod groups and those calculated with the HETERO code.

4 The prompt neutron decay constant at delayed criticality en =p/l, o -1 for the full core at 215 C was found to be _ sec, corresponding to I = _ msec. The shut-down reactivity with 16 coarse control rods in pos. A-D 22, 40-04, 44, 26 is -5% at 25 C and -13% at 215 C. The relative error is usually around 8% in the reactivity worths, originating mainly from the higher harmonics content in the measured curves.

5 LIST OF CONTENTS Page 1. Introduction 1 2. Theory 3 3. Measurements and equipment Core configurations and higher harmonics content in the spatial flux distribution Equipment Measurements Measurements during the first approach to criticality Fundamental mode decay constant at delayed criticality, a Control rod measurements Analysis and results Method of analysis a -determinations and the variation of I with p 15 r o o 4.3 Control rod reactivities Comparison with calculated reactivities Discussion Acknowledgements References 25 Tables Figures Appendix 1

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7 INTRODUCTION Pulsed neutron techniques have been used for reactivity determinations in multiplying systems since about 1955, when the method was introduced by Sjöstrand [ 1 ]. Essentially, a pulsed neutron measurement consists of introducing repetitive bursts of neutrons into the reactor and studying the decay of the neutron population created by the bursts. From the decay characteristics, mainly those of the fundamental spatial mode, the reactivity of the system can be inferred. Sjöstrand, in his analysis, essentially used the areas under the prompt and delayed neutron populations respectively, to get the quantity p/p, where p is the reactivity and P is the effective delayed neutron fraction. There are also some other ways of performing and analyzing pulsed neutron experiments. In 1958 Simmons and King [ 2] published a method in which they used the decay constant, a, of the prompt fundamental mode to obtain the reactivity from the relation p = P -j 1 - r where ex is the decay constant when the reactor is in the delayed critical state. One of the drawbacks of the method of Simmons and King, as well as that of Sjöstrand, is that the variation of the prompt neutron life time with reactivity is not inherently corrected for, but some explicit correction has to be applied when the measured reactivities are large, say p < -1%. More recent theories have been developed by Gozani [ 3] and Garelis and Russel [ 4]. Gozani's method actually represents a refinement of the original one by Sjöstrand, being less sensitive to the higher harmonic content of the flux and to the variation of the neutron life time with reactivity. These features are also included in the method of Garelis and Russel, where the quantity k p /l is determined from the shape of the total response curve, that is, both the initial sharp rise and the slowly decaying delayed neutron tail are utilized in the analysis. The requirements for the applicability of the latter method are that the pulsing rate, R, is large compared to the decay constant of the shortest lived delayed neutron precursor, and small compared to the prompt neutron decay constant. Neither of these conditions could be fulfilled in the present case, since the maximum pulsing rate obtainable with the equipment was 3 sec, which is the same as the

8 - 2 - decay constant of the shortest lived precursor, 3. 0 sec, according to [ 5], and since decay constants down to < 10 sec were to be measured. Accordingly, what is essentially the Simmons and King method was used for the performance and evaluation of the present measurements, this method requiring only that the pulsing rate be chosen small enough so that the induced delayed neutron background can be treated as constant during the decay of the prompt neutron flux. Most pulsed neutron measurements for reactivity determinations have been made in experimental reactors. The measurements to be described in this report, however, were carried out in the Ågesta power reactor, 65 MW, during the low power experimental period following the first criticality, and also during the approach to criticality. Control rod measurements were also made with other techniques, such as the determination of the critical moderator level for the clean core and for the core with rods, in combination with measurements of a level reactivity coefficient, and an integration of the latter quantity between the two levels. These measurements have been described in [6] and will not be further treated here. The performance of pulsed neutron measurements in a power reactor does present some experimental difficulties, especially because there are limited possibilities for optimum placement of source and detectors for the elimination of higher spatial modes, which may be rather disturbing in the kind of analysis used here. However, in spite of these problems the pulsed neutron method offers some definite advantages. 1. It is possible to measure relatively large negative reactivities, which is generally not the case when comparing two critical measurements, e.g. for the rodded and the unrodded core. In the present case reactivities down to «-15% were measured by the pulsed technique. 2. The measurements are made with a fixed core configuration which means that the flux shape of the fundamental mode should be the same in the experiments and in the calculations, facilitating the comparison of reactivity conditions. 3. Only negative reactivities are encountered, so there should be

9 - 3 - fewer safety risks than when a rodded core is made critical and is thus in a potentially supercritical state if the rods were withdrawn. 4. The measurements are relatively rapid. In a typical case, pulsing rate 0.5 sec, 100 pulses, the measurement takes five minutes in all and a preliminary result can be obtained in ten minutes by evaluating the decay constant from a plot. In all, nearly 300 pulsed measurements were made during the low power period, including reactivity checks as fuel was loaded into the core, determination of delayed critical decay constants at different core load-. ings, and control rod measurements with four different cores. The quantity measured is the reactivity worth by which the reactor can be shut down in a given situation, and this is equivalent to the actual rod worth only when the measurement is made at the critical moderator level of the clean core. In other cases the inherent excess reactivity produced by the increased moderator level must be taken into account. 2. THEORY Using two-group diffusion theory [ 2] one arrives at the following equation, relating the fundamental mode decay constant to reactivity: a = L-LJL (1) 4* Here ot is the fundamental mode decay constant, P the effective delayed neutron fraction, neutron life-time. p the reactivity and I * = I /k.., 4 being the prompt The reactivity is conventionally defined as k - 1 eff -, n s. eff and the effective prompt neutron life-time as: t 1 s I* = 2~2~ + 2~ < 3 ) k ' v(l + ITB Ä ) k (1 + 7B Ä ) eff a g 7 eff g'

10 - 4 - where all notations are the conventional ones. The first term signifies the thermal diffusion time, and the second one is the slowing-down time from fission energy to thermal energy, t in eq. (3) is in this case _ / s about sec, so the last term is much smaller than the first one, _3 which is of the order of 10 sec. In the accurate calculation of the prompt neutron life-time, [5], the influence of the reflectors, both radially and axially, has been taken into account, which is particularly important for the small cores of 20, 32 and 68 fuel elements. weight-function \ 4> 2 dv reactor 4> 2 dv core The, to which 4* is proportional, varies from for the 20- element core at critical moderator level to for the 140-element core at full moderator height. It is evident from eq. (l) that a measurement at p = 0 would give the ratio between the delayed neutron fraction and the prompt lifetime, since at k,,.= 1, 4* is equal to I. If this ratio is denoted by ot = s/t* eft o r ' o eq. (l) gives for the reactivity p = e(i-sr-ri) o o Index o means the value at delayed criticality. From (4) it follows that the reactivity is not only a function of o> but also of &*, which unfortunately is not independent of the reactivity state. To see this eq. (3) is rewritten as 1 1+TB 2 t (1 + L 2 B 2 ) "' ~ k v + k oo a oo From eq. (5) is is now clear that I * is dependent on the geometric buckling, which in turn is altered as control rods are introduced into the core. Using (5) for 4*, eq. (4) can be written as: [b) (4) P=P(l-f) + (B^-B 2 )-p - (6) s & o o

11 - 5 - where the variation of the second term of (5) has been neglected as it is much smaller than the first one, and where only the first two terms have been used in a series expansion of l/(l + TB ). In (6) B is the g ' 2 8 geometrical buckling with control rods in the core and B the same => & go quantity for the clean critical core, that is, the material buckling. Eq. (6) is somewhat inconvenient to use, since it contains explicitly 2 2 the material buckling B and the geometrical buckling B, quantities which are generally not measured in pulsed neutron experiments of this type. However, (6) can be rearranged and expressed approximately with a sufficient degree of accuracy by e <*- -> P- - (') 1 -"p o In (7) K ~ =, which is taken from calculated values, [7]. M eff Though a rather important parameter in pulsed neutron measurements, [8], the induced background from delayed neutrons will not be treated here. In the type of analysis applied here the background occurs only as a correction term to be subtracted from the raw data, and is not directly utilized in the analysis as in the Garelis-Russel method. Accordingly it was judged that a well-determined constant background would be an adequate correction, especially as the rather limited accuracy in the a-determination would mask any influence due to a varying background, and also because it was not possible during the measurements to study specifically this problem, which is most serious close to criticality. The analysis to obtain the fundamental mode decay constant is further discussed in section 4, and in the appendix a full set of formulae is given, explaining the modal behaviour of the' neutron flux used in that analysis.

12 MEASUREMENTS AND EQUIPMENT The measurements covered not only control rod reactivities, but also, in the first stages of the loading, the reactivity added to the core by the addition of new fuel elements. Further, for each configuration at which control rod measurements were made the delayed critical decay constant a also had to be determined, since this parameter is a very important one in the type of analysis applied here. 3.1 Core configurations and higher harmonics content in the spatial flux distribution The Ågesta reactor has been thoroughly described in [ 9 ] and here only those parts will be mentioned, which are essential to the pulsed neutron measurements. Control rod measurements were made on cores consisting of 20, 32, 68 and 140 fuel elements. Fig. 1 gives a schematic view of the different cores. In the position indications the letter signifies the quadrant and the figures the x- och y-coordinates in the quadrants. The modulus of x and y is sa.r 2 = 19.1 cm where S is the lattice pitch, 27 cm. The distance from the centre is accordingly given by N/X^ + y2' cm (see Fig. 1). In the 20-element core and in the first part of the 32-element core measurements the Neutron Pulse Generator, NPG, was placed in position C44 and the two detectors in position D04, and A40 respectively. These were also the settings during loading up to the first critical core, which comprised 23 fuel elements. For the rest of the 32-element core measurements and those on the 68-element core and on the room-temperature 140-element core the NPG and detector positions were C62 and C48, D84 respectively, as indicated in Fig. 1. During the measurements on the hot 140-element core the detector positions were changed to B48 and D48, for reasons further discussed below. The different configurations are listed in Table 1, including critical water heights, water heights during measurements, temperatures, and positions of NPG and detectors. 365 cm in the table means full water height. As can be seen from Table 1 the axial positions of the NPG and

13 - 7 - detectors have in most cases, especially in the more important ones with the full core, been 2/3 H or l/3 H and l/2 H, respectively. The reason for this was of course to eliminate as far as possible axial higher harmonics of the spatial flux distribution. Considering only the axial component of the flux distribution in eq. A9 of Appendix 1, one has n IT z., x. s. nir z. 2 n. n 9 ~ s m s in = s in r TT s m TT z H H 3 2 with z = 2/3 H and z = H/2, where z and z are NPG and detector positions. It is evident from the equation above that all higher axial harmonics containing either one or both of the numbers 2 and 3 as a multiple in the order number will in the ideal case be eliminated either by not being excited or by having a node at the detector position; see also Fig. 2. Concerning the radial positions of the NPG and detectors, the possibilities of choosing the optimum positions were limited by the lattice arrangements and the fact that the NPG as well as the detectors occupy ordinary control rod positions. The primary reason for using two detectors was the ability to eliminate azimuthal higher harmonics by adding the signals from two properly placed detectors before carrying out the time-analysis. This technique was used earlier in measurements in the RO reactor, [ 10], and had then proved to work quite satisfactorily. From Fig. 2 it can be seen that with an angle of 45 between the NPG and detector 1, and 90 between the two detectors, all azimuthal higher harmonics with order numbers 1, 2 and 3 will be eliminated either by having opposite signs and equal magnitudes at the detector positions or by being zero at both positions. Separating the azimuthal part of the flux distribution and summing as indicated above gives:. _ m IT m TT 9-2 cos r cos -r cp 2 4 The above azimuthal detector positions were used for the measurements

14 - 8 - on the 68- and room-temperature 140-element cores, but unfortunately the two detectors, nominally identical, proved to have rather different sensitivities and dead-times at the time of the measurements, so the arrangement did not work satisfactorily. However, since the detector positions C48, D84 were very unfavourable for the first higher azi - muthal mode, which according to Table 2 is by far the most serious one when only one detector is used, new positions were chosen for the hot measurements on the 140-element core. These were as close as possible to 90 from the NPG to depress the odd azimuthal harmonics. However, the lattice positions B48 and D48 are at angles 81 and 99 respectively to C62, so the odd harmonics were not even in principle completely eliminated. However, it is considered that the new positions were more favourable than the original ones, e.g. the relative amplitude of the first higher azimuthal mode was decreased by a factor of 5, as can be seen from Table 2. A theoretical correction was applied to decrease the influence of higher harmonics as described in Sect. 4 below. Table 2 gives the characteristics, decay constant and relative amplitude of the two first higher harmonics in z-, r-, and cp-directions respectively, together with the fundamental mode constants for three different configurations. It should be noted that the calculations have been made for cores uniformly poisoned to give the k -- indicated in the table heads. Accordingly, the large flux disturbances caused by the control rods are not taken into account. It is clear from the table that the azimuthal modes are the most important ones, whereas the radial higher harmonics are more important than the axial ones only for low water heights. With full water height, the configuration at which most of the measurements were made, the radial harmonics have much less influence than the axial and azimuthal ones. Further the control rods can be estimated to cause more severe flux distortions in r- than in z- and cp-directions, since usually the control rods were fully inserted and the rod configurations were symmetric.

15 Equipment The experimental equipment used in the Ågesta reactor has been described in [ 11 ] and the pulsed neutron equipment more specifically in [12] and [13], so only some main characteristics will be given here. The pulsed neutron generator, NPG, was a very compact one, Kaman NT60-7, that could easily be introduced into the core, and had n an output of 10 n/pulse. The pulsing rate was limited to a maximum -1-1 of 3 sec. Usually, however, a pulsing rate of 0.5 sec was used to depress the induced background, and close to criticality it was as low -1 as 0.2 sec. The detectors were BF,- counters with a nominal sensitivity of 3 c/nvt. As mentioned earlier they proved to have quite different sensitivities, however, and the dead-times were also rather different, being 18 isec and 2.3 fxsec respectively during the room-temperature measurements and 4. 2 (asec and 2. 0 fxsec respectively during the hot measurements for the two detectors used. The detector pulses were fed via conventional electronics into a TMC 256-channel analyzer with a pulsed-neutron plug-in logic unit. A block diagram of the set-up is shown in Fig Measurements The main objective of the measurements was of course the determination of control rod reactivity worths, preferably for the full cores, serving the dual purposes of providing data such as e.g. shutdown reactivities for the selected core configurations, and giving a reasonably solid basis for comparisons to theoretical calculations for a realistic power reactor lattice with different rod groups and a large number of rods. For smaller cores the critical experiments give more reliable results for theoretical comparisons. Accordingly, the full core measurements have been more fully analyzed than the others, but in order to give a complete description of all the pulsed neutron measurements carried out in the Ågesta reactor, the initial measurements on the smaller cores are also included here.

16 Measurements during the first approach to criticality During the loading of the first core, 20 fuel elements, the reactivity added to the core by the addition of fuel elements, 4 at a time, was measured by both the pulsed neutron and the inverse multiplication techniques,. The interpretation of the pulsed neutron measurements is in this case rather doubtful for the following main reasons. 1. There are no calculated values of the prompt neutron life-time, I, for cores with less than 20 fuel elements, and as the ratio p/i appears in the equation relating the decay constant to reactivity, extrapolation of values from [ 5] had to be used. 2. It is difficult to define the core in those cases, as the assembly consisted of a few fuel elements in a practically infinite reflector. 3. Both the NPG and the detectors were located far away from the fuel region and possibly a large portion of the detected flux did not originate from the core, but was merely the directly thermalized source flux in the moderator. The results appear in Table 3, which also includes a measurement without any fuel or control rods in the moderator. Table 3. Results from reactivity checks during loading of the first core No. of fuel Decay -p Prompt lifeelements constant time used in Note g(sec, -1\ ) (%) the analysis } msec Fine control rods B62 and D62 in " Coarse control rod A00 in

17 Unfortunately, the coarse control rod A00 was inserted during the measurement on the 8-element core, so no quantitative conclusions concerning the addition of reactivity and interaction between fuel groups can be drawn from the table. However, the pulsed neutron measurements were found to be very valuable at this stage, especially as a fairly fast and accurate mean for reactivity control. They also gave reference points for the inverse multiplication measurements, where small amounts of reactivity were to be measured and "differential" worths were of interest Fundamental mode decay constant at delayed criticality, ex This quantity could not be determined for the 20-element core, which could not be made critical, and there was no means of estimating the subcriticality except by pulsed neutron measurements combined with a calculated value of I. For the 32-, 68- and 140-element cores, however, ot for the critical water levels was determined at room temperao r ture by extrapolations from measurements at some known subcritical levels. This was done during the approach to criticality with the respective cores in connection with inverse counting, which took place to determine the critical water level for each core. Later level-coefficient measurements enabled the determination of the degrees of subcriticality at which pulsing was performed. For the full-height and high temperature cores another technique had to be used, and it was decided to change the reactivity by varying the moderator temperature. In these cases control rods had to be inserted into the core to counter-balance the excess reactivity. Two series of such measurements were made, one before commencing the hot control rod measurements and one after. The temperature drift during t»he measurements was around 6 C/h and a measurement took 5 minutes to perform, so the reactivity variation during pulsing was in the worst case, i.e. at 200 C with 8p/8T~35 pem/'fc, less than 20 pcm. The reactivity worths at which pulsing took place were derived from the critical temperatures and 3p/9T, and as before, extrapolations were used to obtain a. Unfortunately, some of the ca o o measurements were unsuccessful, especially the last series of high

18 temperature full level measurements. As a consequence all a :s for full cores have been based on the value obtained from the first 200 C- series, and for the temperature dependence a theoretical correction has been made via the calculated prompt neutron lifetimes. (See further sec. 4 and table 5) Control rod measurements The control rod configurations investigated in the different cores are listed in Tables 7-9. As can be seen from the tables, measurements were made on both fully and partly inserted control rods. For the small cores, 20, 32 and 68 fuel elements, all measurements were made close to the critical water level for the clean cores, whereas for the fully loaded core investigations were made both at critical and full water heights. It should be noted that "fully inserted control rods" means that their lower end is 66 cm above the bottom plate, which is considered as the lower boundary of the core. In the tables, control rod positions are given as withdrawal in cm from in-position, 0 meaning fully inserted and 300 fully withdrawn. Intermediate insertions are accordingly given by: Lower end (cm above bottom plate) = 66 + position indication. Typically, there had to be about 100 pulses in each measurement to give a theoretical statistical error of around 1 % in the decay constant. All full-core configurations were measured at least twice, once with each detector, in order to make the higher harmonics correction as reliable as possible. In some cases entirely independent measurements were made on identical configurations, with the only difference that the detector positions were changed from C48, D84 to B48, D ANALYSIS AND RESULTS Some results from the full-core measurements, of a preliminary nature, have been published in [ 14]. The method of analysis for the fullcore measurements will be outlined below and the results will be given

19 with special emphasis on the full-core measurements and the ot -determination. 4.1 Method of analysis The relation between the measured prompt fundamental mode decay constant, en, and reactivity is given by eq. (7) in Section 2. Its application is fairly straightforward and unambiguous, provided that the variation of the prompt neutron lifetime with reactivity is correctly predicted. It is also clear that eq. (7) gives negative reactivities, as a is in all the measurements greater than a, and that this negative reactivity is the worth by which the reactor is shut down at the moment of measurement. Thus no direct information is obtained about the control rod reactivity-worth unless the initial state is the critical one, preferably with the moderator at the critical level. To get the control rod worths for cores with full water height, it is necessary to add to the measured value the excess reactivity, represented by the excess of water from critical to full height. The excess reactivity has been directly measured for the room-temperature core and estimated from measurements for the 215 C core [14] whereas an interpolated value must be used for the 140 C core [ 15]. It should be noted that the temperaturebound reactivity of the clean core is not given by the difference between two measurements of subcriticality for identical configurations at different temperatures, unless there are no control rods, since the effectiveness of the control rods is also temperature-dependent. The following excess-reactivities have been obtained, [14] and [15]. Table 4. Excess reactivities Core Excess reactivity (P cm ) 140 fuel elements, 30 C 9000 " 140 C 7300 " 215 C 5400

20 The main difficulty during the analysis has been'to obtain the fundamental mode decay constant, due to the comparatively high content of higher harmonics in the decay curves. As the detector arrangement for elimination of azimuthal higher harmonics did not work satisfactorily, because of differences between the two detectors, a theoretical correction had to be applied to the measured curves to suppress the higher harmonics content. This was done by calculating for each NPG detector water-height configuration the ratio between the fundamental mode flux and the sum of higher harmonic mode fluxes (see Appendix 1) as a function of time after pulsing. Denoting this ratio by y, the fundamental mode flux by 9,., the higher harmonics flux by 9, and the measured flux by 9, one obtains: 9 = 9, + 9, m f h 9 f (8) ich gives 9, = 9 f m Y 1 + v (9) Note that the 9 's as well as \ are all functions of time and also of.geometry, as seen from the appendix. It turns out that "V (t) for a given configuration is practically independent of reactivity on an absolute time scale, although the ratio between higher harmonic decay constants and the fundamental mode decay constant converges as the subcriticality increases. Eq. (9) was programmed as a pre-program to the ANPEX-code which performs a least square fit of one or more exponentials to the measured points, [16], and all the full-core measurements were corrected in this way, taking properly into account the actual configurations but disregarding the influence of the heterogeneous control rod arrangements.

21 The curves were fitted by least-squares analysis to one exponential plus a constant background. Some restrictions were applied to the part of the curves to be fitted, namely that the dead-time correction was not to exceed 20%, which is in fact a relatively high correction, and that the higher harmonics correction was not to exceed 20%. An example of the function. J is given in Fig. 4 for the configuration: Full water height, NPG in pos. C62 and the detectors in pos. C48 and D a -determinations and the variation of I with p As described in Section 3, the measurements were made at some known subcritical levels, close enough to criticality, however, to justify the neglect of the variation of the prompt lifetime with reactivity. Through the relation a=^j- ~ (10) o which is a fair approximation close to criticality, the value of I be determined if p and p are known and a is the measured decay constant. Four or five different p-values in the range pcm negative give an adequate average value of I and hence of a - (3/t. The reactivities in the case of water-level variation are with sufficient accuracy obtained from can and in the case of temperature variation from p= -(T-T c ) (12) where H = critical moderator level c H = level at which the pulsed measurement is made (Q H ) = level coefficient at H c

22 against l/h T = critical temperature c T = temperature at which the pulsed measurement is made (8p/8T) = mean value of the temperature reactivity coefficient between T and T c Another method of obtaining a is to plot the measured a-value or T for water level and temperature measurements, respectively, and extrapolate to the critical state. One advantage of the last method is that (3 is not explicitly involved in the determination of a, but of course it is if I is to be determined. Generally both ways have been used, and they seem to give very consistent results. The extrapolation to a in the 190 C, 140 fuel element core is shown in Fig. 5. As mentioned above, some of the o> -measurements were unsuco cesful, and for the full cores all values are based upon the determination of the value at C. They are related to the measured value through calculated I -values according to [5], with lattice parameters from [7], This of course introduces an extra error, but though the error in the absolute value of the calculated t may be rather large, it is considered that the relative error in the difference between the calculations for different conditions of the full core is not larger than 3 %. Table 5 lists the en - and I -values for the cores investigated, & o o and it also contains the calculated prompt neutron lifetimes for the different cores. It has been assumed that the introduction of control rods does not change the macroscopic properties of the cores, which appear to be reasonable according to what has been found in [ 6 ]. The listed values are averages of the two ways of evaluation mentioned above.

23 Table 5: a -value for the cores investigated Core 20 Core condition H T (cm) ( C) Full 20 I (msec) o v ' Normalized I Measured Calc., \ (msec) Not meas a (sec ) ) 322) Full 140 Full 140 Full ) Full ) ) ) ) ) 1) NPG in position C44, detectors in position A40, D04 2) NPG " " C62, " " " C48, D84 3) The same values are valid for the 136- and 140-element cores 4) Derived from the measured value at C and calculated I :s ' o For the full-core measurement the agreement between measured and calculated values is excellent and also for the 68-element core it may be considered satisfactory. The low value for the 32-element core, however, is someqhat curious. Actually, there is no significant difference between ot -values for the 32- and 68-element cores and it appears that there must be a systematic error in one of the measurements. might also be suspected, however, that the calculations have a tendency to overestimate the influence of the reflector. The limits of error in Table 5 do not account for an estimated systematic uncertainty of about 4 % in P.-, the value of which is The temperature dependence of P f, is very small and can thus be neglected. The dependence mainly comes from the change in the yield of photo-neutrons from the heavy water as the density changes. It

24 The correction term due to the variation of I 2 o with p in the de- nominator of eq. (7) contains the constant K = T/M, f. This correction has been applied only for the full-core measurements, using lattice parameters from [7] to obtain K. The reason for not applying the correction to the small core measurements was the difficulty of making reasonable 2 2 estimates of T and M rr for cores with so thick reflectors. M,, is eff eff written M eff = r + T~T ( 13 ) e±± 1+TB^ m 1 + l/b Z m Table 6 below gives the K :s for the full cores at 3 different temperatures. Table 6: K -values for the full core Temp. ( C) T (cm 2 ) M 2 (cm 2 ) K = T/M 2 eff v ' ~ ' e f f Control rod reactivities The results of the control rod measurements are presented in Tables 7, 8 and 9 for the small cores, completely inserted rods in the full core and partially inserted rods in the full core, respectively. The reactivity worths are calculated from eq. (7), except for the small cores, where the denominator has been neglected as mentioned above. The order of magnitude of the effect of this neglect is clear from the fact that when p is pcm, the correction is -500 pcm and that it increases with p. The limits of error listed in the tables are due to the uncertainties in the decay constant determination. In practically all cases two or more independent measurements of a have been made, using one detec-

25 tor at a time and with a higher harmonics correction applied as described in 4.1. In spite of this correction, however, there generally exist differences between different»-determinations on identical configurations which fall outside the ANPEX-calculated individual uncertainties (generally of the order of %). The limit of error appearing in the tables is the one representing the spread between different determinations. The uncertainty in (3,, has not been taken into account in evaluating limits of error in the reactivities calculated from the decay constants. eq. (7), The formula for the error is, neglecting the denominator of Aa 2. 2 Ap=±(P- p)^ (-;-2.) +(^) (14) o where p must be taken with its sign, always negative. As seen from (14), small reactivities are inherently more uncertain than large ones as far as relative values are concerned, even if en has the same accuracy. Generally, however, it is more difficult to determine accurately the decay constant for a small reactivity, say ] pj < 1000 pem, than for a large one, 1500 pem < p < 6000 pem, due to the high background close to criticality. It is also doubtful whether a constant background approximation is justified for small reactivities, as has been assumed in this report. For the measurements close to the critical water level for the respective cores, the reactivity tied up in the small deviations from critical levels has been corrected for by (11), so that the p-values are valid at H = H. The measured p-values are temperature corrected by (12), so as to be valid at 24 C, 140 C and 215 C respectively. The coefficients used for this have been taken from [6], and as the corrections are usually small no errors have been assigned to them. The results for partially inserted control rod groups are also graphically presented in Figs. 7 and 8. It is evident from Table 8 that the errors are usually relatively large, on the average around _+8%, and it is judged that the main reason is the influence of higher harmonics. Originally there existed even

26 larger discrepancies between the values from the different detectors but the correction described in 4.1 eliminated most of them. The effect of the correction can be seen from Fig. 6, where the decay curves from the two detectors before and after the correction are shown. The shut-down reactivity with 16 control rods is % at 215 C and -5% at 24 C. With 12 control rods in positions A-D22, and 44 the values are -10% and -3% at 215 C and 24 C respectively. The interaction between different rod groups can be found from Table 8, though the large uncertainties there can mask some effects. For instance, the rod A00 added to A-D22 would, according to Table 8, give a positive contribution of 90 pern at the critical level and 24 C, which is of course nonsense. (Note that to get the control rod worths from measurements at full water height the excess reactivities listed in Table 4 have been added to the column - p of Table 8). Nevertheless, some examples of the interaction effect will be given, illustrating the large difference in effectiveness of a control rod or a control rod group in different surroundings. A00 added to A-D22 at 215 C has a value of 340 pem; ~ = A00 added to A-D40-04 at 215 C has a value of 1300 pem; % = o z A00 alone at the critical level at 24 C has a value of 1210 pem; = A-D40-04 by themselves at 215 C have a value of 6080 pem A-D40-04 added to A-D22 have a value of 3920 pem A-D40-04 added to A-D44, 26 have a value of 7800 pem A-D22 by themselves at 215 C have a value of 6530 pem A-D22 added to A-D40-04 have a value of 4370 pem A-D22 added to A-D40-04, 44, 26 have a value of 5330 pem A-D22, at 215 C have a value of pem A-D22, added to A-D44, 26 have a value of pem The temperature dependence of the control rod effectiveness can also be found from Table 8, using the column p R, which represents the control rod worth, i. e. the clean core temperature effect has been eliminated using values from Table 4. The fractional increase in control rod effectiveness due to increased temperature, 6, is thus defined as rl

27 - 21-6= AP (T2-T1) = PT2-PT1. T1 < T2 P T1 P T1 Table 10 below shows the temperature effect for 3 different rod groups in 3 different temperature intervals. Table 10. Temperature coefficient of control rod effectiveness Control rod group 24 C-140 C 140 C-215 C 24 C-215 C A-D40-04, 44, 26 A-D22, 40-04, 44 A-D22, 40-04, 44, Average The control rod effectiveness as a function of insertion depth in the case of a large bank of rods is seen from Fig. 7b, representing the reactivity of the system as a function of the insertion of the rod bank A-D40-04, and 26. The same figure also shows the curve obtained from simple perturbation theory: sin 2ir p A {fr 2, H ) + B < 15 > where A and B are constants. The reactivity is normalized to the extrapolated measured curve at relative insertions 0 and 1.0. In Fig. 7a the same is shown for the control rods A-D26 and here the deviation from simple calculations is much smaller than when a large number of rods are moved, in fact practically negligible. Figs. 8a and 8b show the reactivity versus rod insertion for 16 and 8 rods moving from maximum insertion, 0.82, to close to critical insertion at 0.51 and 0.58, respectively. No calculated curves are given in these cases.

28 Comparisons with calculated reactivities The last column of Table 8 lists calculated control rod reactivity worths. They were calculated with the HETERO code, [17], which treats the fuel elements as sinks for thermal neutrons and as sources of fast neutrons. The control rods are considered as sinks for both thermal and fast neutrons. The distance inside the rods at which the control rods are "black" is of course different for neutrons in different energy groups. A comparison between the control rod reactivity values appearing in the last two columns of Table 8 shows that there is a systematic difference between the measured and calculated values. The calculations have given reactivity worths of the control rods that are on the average 11 % smaller than the measured ones. As can be found from the table this falls outside the limits of error of the measured control rod reactivities for almost all cases. The limits of error are taken as those appearing in the -p column, the quantity that is actually measured. As a consequence of the systematic difference found here, the HETERO code has subsequently been modified to take account of the differences found. 5. DISCUSSION Control rod measurements have been carried out on different core configurations in a heavy-water moderated power reactor. It has been found that this method of measurement is valuable for reactivity determinations, especially when large negative reactivities are to be determined. Most of the measurements were concerned with the determination of control rod reactivity worths, but it was also possible to check the reactivity added by individual fuel elements or groups of elements -when fuel was loaded into the reactor. A comparison between measured and calculated reactivities is less doubtful when pulsed measurements are considered than in many other cases, since the measurements and calculations are made for

29 the same core configurations. The result of such a comparison in the case treated here led to a modification of the calculation program, since a systematic difference between measurements and calculations of about 10% was revealed. As a necessary complement to the control rod measurements the ratio between the effective delayed neutron fraction and the prompt neutron life-time, 3, rr/l = <x, has been determined for the cores inefr o o vestigated. Good agreement was found between measured and calculated I -values, except for the 32-element core, where the calculations give too high a value. As a consequence of detector malfunctions the accuracy of the measurements is not as high as would otherwise have been obtained. However, the higher harmonic flux correction that has been applied to remove some of the errors resulting from the asymmetric flux detection has been found to reduce the differences between registrations on identical core configurations with different detectors to a large extent. On the average, the accuracy of the full core measurements, which are considered to be the most important ones, is _+ 8%, and it is considered that much better accuracy cannot be reached in a large power reactor with the relatively weak pulsed neutron source available at the time of the measurement. The limited accuracy obtained may seem to be unsatisfactory, but the experiments have nevertheless for several reasons been very useful. Also the experience gained should be quite valuable. For instance, in pulsed neutron measurements of this kind it was found that great care should be taken in placing the pulsed neutron source properly. The best position for the source is on the center axis of the core, since in that case no azimuthal higher harmonics are excited. Further, if two or more detectors are used to eliminate higher flux modes, one should make sure that they are equal at least within 10% with regard to sensitivity and dead-time. Also, a monitor should be used to terminate the pulsing cycle at equal numbers of collected pulses for different measurements, and thus reduce the consequences of possible irregularities of the pulsed source. With such precautions, it should be possible

30 to obtain a- values with an accuracy of better than 1 % and accordingly control rod reactivities with a relative uncertainty of around % in the region j p ] > 1500 pern. 6. ACKNOWLEDGEMENTS The measurements were suggested by Pehr E. Blomberg and performed by the Group for Physics Measurements in the Ågesta reactor with the assistance of the reactor staff. Much of the planning of the experiments was done in cooperation with Olof Nylund, ASEA, which is highly appreciated, as well as the valuable discussions and suggestions by P. E. Blomberg and O. Nylund during the analysis. Many thanks are also due to Torfinn Skardhamar, who performed the HETERO calculations, as well as to Mrs Ingegerd Gullberg who typed the manuscript.

31 REFERENCES SJÖSTRAND, N.G. Measurements on a subcritical reactor using a pulsed neutron source. Ark. Fys. 11 (1956') SIMMONS, B.E. and KING, J.S. A pulsed neutron technique for reactivity determination. Nucl. Sci. Eng. 3 (1958) GOZANI, T. A modified procedure for the evaluation of pulsed source experiments in subcritical reactors. Nukleonik 4 (1962) GARELIS, E. and RUSSEL JR, J. L. Theory of pulsed neutron source measurements. Nucl. Sci. Eng. 16 (1963) APELQUIST, G AB Atomenergi, Sweden. (Internal report. RFR-236, R In Swedish). BERNANDER, G. Measurements of the reactivity properties of the Ågesta nuclear power reactor (AE-289). APELQUIST, G AB Atomenergi, Sweden. (Internal report. RFR-171, R In Swedish). SASTRE, C. and WEINSTOCK, E.V. A note on delayed-neutron effects in pulsed-neutron measurements on multiplying assemblies. Nucl. Sci. Eng. 20(1964) The Ågesta Nuclear Power Station. AB Atomenergi, Stockholm BJÖRÉUS, K. and NYLUND, O AB Atomenergi, Sweden, (internal report. RFX-237, R In Swedish). BERNANDER, G., BLOMBERG, P. E. and DUBOIS, P-O. Experimental equipment for physics studies in the Ågesta reactor (AE-269).

32 BJÖRÉUS, K., PERSSON, R. and WIKDAHL, C-E. Measurements of control rod worths in critical and exponential assemblies. Physics and Material Problems of Reactor Control Rods Symposium, Vienna, Nov., IAEA, Vienna 1964, BJÖRÉUS, K AB Atomenergi, Sweden, (internal report. RFX-216, R In Swedish). APELQUIST, G. et al. Reactor physics studies and comparisons between reactor physics data from calculations and mock-up studies and from measurements in the Ågesta nuclear power plant. U.N. Intern. Conf. on Peaceful Uses of Atomic Energy. 3. Geneva Proc. New York Vol. 3, p APELQUIST, G. (State Power Board). Private information. NYMAN, K AB Atomenergi, Sweden, (internal report. RFN-157. In Swedish). JONSSON, A. et al. Theory and applications of heterogeneous methods for heavy water reactor calculations. U.N. Intern. Conf. on Peaceful Uses of Atomic Energy. 3. Geneva Proc. New York Vol. 3, p. 139.

33 Table 1. Core configurations Number of fuel elements Critical ' height H c v (cm) ' Height at measurem. H (cm) Temp, at measurem. ( c) Position (coordinate in fig. 1/ height above bottom plate in cm) NPG Det. 1 Det ii Not meas. II it C44/246 C44/246 C62/150 C62/124 C 62/124 C 62/124 C 62/244 C62/244 C 62/244 D04/183 D 04/105 C48/105 C48/95 C48/84 C48/183 B48/183 B48/183 B48/183 A4 0/183 A4 0/120 D84/120 D84/95 D84/84 D84/183 D48/183 D48/183 D48/183 1) Taken from ref. [6]. Note: From reactivity point of view there is no essential difference between the 140- and 136-fuel element cores, which may accordingly both be considered fully loaded.

34 Table 2. Some higher harmonics characteristics for the clean full-core configurations Mode indices I m n "(s" 1 ) k e f = V /H 101 H=165 cm «(s _1 ) Detector position C48 (D48) k..=0. 88 eff y /Y 101 «(s _1 ) k eff = Y /Y 101 H=365 cm a(s _1 ) k rr=0.88 eff y /V 101 ^s" 1 ) Detector position B48 (D48) k eff = y H=365 cm /y ioi a(s" ) k, =0.88 eff /Y Notes: 1. Calculated from the formulae given in Appendix 1 2. Detector height = 183 cm; NPG position C62; height = 124 cm

35 Table 7. Control rod worths for 20-, 32- and 68-element cores Fuel elements Core H (cm) T ( c) Control rods a (sec ) - P (pcm) 20 Full Full Full Full B22 1 B+D22 2 B,C,D22 3 A-D ) 2) 1) 2) 1) 2) A A-D22 4 it 4 A00;A-D22 5 " A A-D Full 24.0 ii A00;A-D NPG in position C44; detectors in positions A40, D04 NPG in position C62; detectors in positions C48, D84

36 Table 8. Reactivity worths for fully inserted control rods in the full core Control rods Positions No. of rods Core condition at meas. H (cm) T ( C) - P (pcm) 1)2) p CR (pcm) 3) p CR HETERO (pcm) A A-D Full A-D Full A00.A-D Full A00.A-D Full A00.A-D44 5 Full A-D22, Full Full A-D Full A00.A-D22, Full Full _ A-D22, 40-04, Full Full Full A-D40-04, 44,26 12 Full Full Full A-D22,40-04, 44, Full Full Full A-D22,40-04, 44,26,A00, A62 18 Full As above + fine control rods 18+2 Full ) The worth by which the reactor is shut off at a given situation 2) The measured a-values are not quoted since the values listed are sometimes averages of several measurements 3) The reactivity worth held by the control rods, p rr = - p + excess reactivity ace. to table 4

37 Table 9. Reactivity worths for partially inserted control rods in the full core Maximally inserted Rel. insertion=0. 82 Control rods Partially inserted Rel. * insertion Core condition a (sec ) - P (pcm) A-D22, 40-04, 44 A-D26 (4) H = Full T = 24.0 C A-D22, ,26 (16) H = Full T = A-D22 A-D ,26 (12) H = Full T = A-D22,40-04 (8) H = Full T = * The relative insertion is defined as: (300 - z)/366, where z is the reading on position indicator.

38

39 AE-364 ("} Control rod positions 0 Fuel element positions 1 NPG position, 20 and 32 element cores II la, lb NPG position, 32, 68 and 140 element cores Detector positions, 20 and 32 element cores 2a, 2b Detector positions, 32, 68 and 140 element cores at room temp» 3a, 3b Detector positions, 140 element core at room- and elevated temps. Fig» 1, Lattice configurations for the 20-, 32-, 68-, and 140-fuel element cores.

40 1.0.. j.. n ir 2 9 sm ax H AE l <t> az cos m cp T m=0 <P 1 * Fig. 2. Axial and azimuthal harmonics of the spatial flux distribution, NPG and detector positions in the 140-core indicated.

41 AE-364 Equipment in the control room "testart TMC V 256 channel time analyzer; TMC-CN110 Mixer > " «V J^ V Meas. bg Start NPG Open delay Delay ^ V Control unit NPG Pulse NPG Equipment in the reactor hall Preampl. HT Preampl. HT Detector signal (M fc> Other signals Reactor Fig. 3. Block diagram of the experimental set-up.

42 AE-364 Y/I+Y, Configuration: H = 365 cm NPG: C62/124 p = -5% 1.80 Detector in position: D84/ " t (msec. ) 0.80" ^\ Detector in position: C48/ " 0.40" Corresponding channel number with ch. width " H I I 1 1 I I 1 1 I I 1 h At=1280 [Jisec At=2560 jlsec Fig. 4. Example of the higher harmonics correction function y /l + y.

43 (sec ) AE " / a = s o I = msec if (3 r o T ( C) eff 190=T Fig, 5. Extrapolation of a vs. T for the 140 fuel element core to get a T c = 190.0"C.

44 Configuration: 136 fuel elements H = cm; T = C Control rods: A-D22, in pos. 0 Channel width: 1280 (xsec. AE or position: C48/ _. higher harmonics correction After higher harmonics co a = 71. cps 10 Channel No. H h "- rmonics _. After higher ha correction a Note: The left 10 chann relative should st H h » Channel No. H 1»" Fig. 6. Decay curves for two different detector positions before and after higher harmonics correction.

45 AE Max. insertion Configuration H = Full T = 24, 0 C Control rods Maximally inserted A-D22, 40-04, 44 at rel. insertion 0.82 Partially inserted A-D26 Measured curve Simple perturbation theory 4000 \j p = 2350 { s in 2 ir 77 JL} o 1 \ \ 1 1 *- Rel. insertion Max, insertion Configuration H = Full T = C Control rods Maximally inserted A-D22 at rel. insertion Partially inserted A-D 40-04, 44, 26 Measured curve Simple perturbation theory 2000 p = { H s in 2 IT 77 0^ H )+800 2TT Rel. insertion Figs. 7a and 7b. Reactivity worths of partially inserted control rod banks. Calculated curves normalized to meas. at rel. insertions 0 and 1.0,

46 -o (pcm) Fig. 8a AE C onf iguration H = Full = C Control rods A-D22, 40-04, 44, 26 withdrawn stepwise from maximal insertion to close to critical position Max, insertion, 1 h_ P (pcm) Fig. 8b Rel. insertion 5000 Configuration H = Full T = 215 C Control rods A-D22, withdrawn stepwise from maximal insertion to close to critical position Rel. insertion Figs. 8a and 8b, Reactivity worths of partially inserted rod banks. No fully inserted rods.

47 APPENDIX 1 The following formulae, based on homogeneous two-group diffusion theory, have been used to calculate the fluxes by which the measured decay curves have been corrected for higher harmonics content. k " Z a 2 -O z B 2 (A2) (k eff ) 101 (1 + TB^) B? m "f ) 2+ ( > z < A3 > (>W* m ' D,"": 8 " < A4» a< 1+ -r- B tmn)< 1 + T B Ln> a 1 + B? t 4 m n + -S (A5) ooo ao (k,,). (1 + TB. ) v eff t mn x I mn' a imn=t {k~t ( A6 ) I mn v eff'& mn P = *-= (A7) 1 + TB, I mn ^ 1 if m = 0 ^ i f t n / O (A8),* P 4N v,.. _sv r A m n "irr 2 H(i + 6 )j' 2 (j.) ^ v om' m"mi' W R ; mr z nit z sinf-jj-s-) J m (j mi * f) * cos(mcp) sinf-^) (A9)

48 <"»"' l > = 2 i,m.n<m.n- ^ "" ' < A1 > In the equations all notations are conventional, the indices I mn denoting r-, cp- and z-directions respectively. In eq. (A9) index s on r and z signifies source position and N is the yield from the pulsed source in neutrons per pulse, which might of course have been chosen arbitrarily. The flux modes that were treated, 38 in all, are listed below: Table A I. Spatial flux modes used in the higher harmonics correction Mode index i, m n. n. Fundam mode Mode index I m n Mode index I m n From eqs. (Al) and (A2) the corresponding to a given reactivity, (k,.).., is calculated, (k..) _. being the free parameter. On the input list the values of (k,,).. of interest are given, together with geometrical quantities and lattice parameters, and the program, on a Ferranti-Mercury computer, computes and prints out e.g. eq. (A10) for times from 0 to 200 msec., the ratio of the fundamental mode flux

49 to the sum of the fluxes from higher harmonics as a function of time, decay constants for the I-, m-, n-combinations specified in the programme and also the initial fluxes according to eq. (A9) for the same I-, m-, n-combinations. This is done for the actual core configurations investigated, except that the influence on the flux distribution from the control rods is not taken into account, since the latter according to eq. (A2) are treated as homogeneously distributed 1/v-absorbers, changing effectively only and k,.,.. It is realized, of course, that this is a simplification, but as it is mainly the azimuthal higher harmonics that are believed to disturb the measurements, and as in most cases symmetric control rod configurations have been investigated, this simple flux correction appears justifiable. Taking explicitly into account the flux disturbance caused by the control rods would have required a three-dimensional heterogeneous program, which can by no means be justified for this kind of calculation. The ratio between the fundamental mode flux and higher harmonic mode fluxes, denoted by "y, has been used to correct the measured flux decay curves for the higher harmonics content as described in sec. 4.

50

51

52 LIST OF PUBLISHED AE-REPORTS (See the back cover earlier reports.) 291. Separiaion of "Cr by means of the Szilard-Chalmers effect from potassium chromate irradiated at low temperature. By D. Brune p. Sw. cr. 10: Total and differential efficiencies for a circular detector viewing a circular radiator of finite thickness. By A. Lauber and B. Tol lander p. Sw. cr. 10: Absolute Ml and E2 transition probabilities in >"U. By S. G. Malmskog and M. Höjeberg p. Sw. cr. 10: Cerenkov detectors for fission product monitoring in reactor coolant water. By O. Strindehag. 1967, 56 p. Sw. cr. 10: RPC calculations for K-forbidden transitions in 18J W. Evidence for large inertial parameter connected with high-lying rotational bands. By S. G. Malmskog and S. Wahlbom p. Sw. cr. 10: An investigation of trace elements in marine and lacustrine deposits by means of a neutron activation method. By O. Landström, K. Samsahl and C-G. Wenner p. Sw. cr. 10: Natural circulation with boiling. By R. P. Mathisen p. Sw. cr. 10: Irradiation effects at C in some Swedish pressure vessel steels. By M. Grounes, H. P. Myers and N-E. Hannerz p. Sw. cr. 10: The measurement of epithermal-to-thermal U-23B neutron capture rate (P2s) in Agesta power reactor fuel. By G. Bernander p. Sw. cr. 10: Levels and transition rates in 1 "Au. By S. G. Malmskog, A. Bäcklin and B Fogelberg p. Sw. cr. 10: The present status of the half-life measuring equipment and technique at Studsvik. By S. G. Malmskog p. Sw. cr. 10: Determination of oxygen in aluminum by means of 14 MeV neutrons with an account of flux attenuation in the sample. By D. Brune and K. Jirlow p. Sw. cr. 10: Neutron elastic scattering cross sections of the elements Ni, Co, and Cu between 1.5 and 8.0 mev. By B. Holmqvist and T. Wiedling p. Sw. cr. 10: A study of the energy dependence of the Th232 capture cross section in the energy region O.I to 3.4 ev. By G. Lundgren p. Sw. cr. 10: Studies of the reactivity effect of polythene in the fast reactor FRO. By L. I. Tirén and R. Håkansson p. Sw. cr. 10: Final report on IFA-10, the first Swedish instrumented fuel assembly irradiated in HBWR, Norway. By J-A. Gyllander p. Sw. cr. 10: Solution of large systems of linear equations with quadratic or non-quadratic matrices and deconvolution of spectra. By K. Nygaard p. Sw. cr. 10: Irradiation of superheater test fuel elements in the steam loop of the R2 reactor. By F. Ravndal p. Sw. cr. 10: Measurement of the decay of thermal neutrons in water poisoned with the non-1/v neutron absorber cadmium. By. L. G. Larsson and E. Möller p. Sw. cr. 10: Calculated absolute detection efficiencies of cylindrical Naf (Tl) Scintillation crystals for aqueous spherical sources. By. O. Strindehag and B. Tollander p. Sw. cr. 10: Spectroscopic study of recombination in the early afterglow of a helium plasma. By J. Stevefelt p. Sw. cr. 10: Report on the personnel dosimetry at AB Atomenergi during By J. Carlsson and T. Wahlberg p. Sw. cr. 10: The electron temperature of a partially ionized gas In an electric field. By F. Robben p. Sw. cr. 10: Activation Doppler measurements on U238 and U235 in some fast reactor spectra. By L. I. Tirén and I. Gustafsson p. Sw. cr. 10: Transient temperature distribution in a reactor core with cylindrical fuel rods and compressible coolant. By H. Vollmer p. Sw. cr. 10: Linear dynamics modal for steam cooled fast power reactors. By H. Vollmer p. Sw. cr. 10: A low level radioactivity monitor for aqueous waste. By E. J. M. Quirk p. Sw. cr. 10: A study of the temperature distribution in UOi reactor fuel elements. By I. Devoid p. Sw. cr. 10: An on-line water monitor for low level /^-radioactivity measurements. By E. J. M. Quirk p. Sw. cr. 10: Special cryostats for lithium compensated germanium detectors. By A. Lauber, B. Malmsten and B. Rosencrantz. 19GB. 14 p. Sw. cr. 10: Stability of a steam cooled fast power reactor, its transients due to moderate perturbations and accidents. By H. Vollmer p. Sw. cr. 10: Progress report Nuclear chemistry p. Sw. cr. 10: Noise in the measurement of light with photomultipliers. By F. Robben p. Sw. cr. 10: Theoretical investigation of an electrogasdynamlc generator. By S. Palmgren p. Sw. cr. 10: Some comparisons of measured and predicted primary radiation levels in the Agesta power plant. By E. Aalto, R Sandlin and A. Krell p. Sw. cr. 10: An investigation of an irradiated fuel pin by measurement of the production of fast neutrons in a thermal column and by pile oscillation technique. By Veine Gustavsson p. Sw. cr. 10: Phytoplankton from Tvären, a bay of the Baltic, By Torbiörn Willén p. Sw. 10: Electronic contributions io the phonon damping in metals. By Rune Jonson p. Sw. cr. 10: Calculation of resonance interaction effects using a rational approximation to the symmetric resonance line shape function. By H. Häggblom p. Sw. cr, 10: Studies of the effect of heavy water in the fast reactor FRO. By L. I. Tirén, R. Håkansson and B. Karmhag p. Sw. cr. 10: A comparison of theoretical and experimental values of the activation Doppler effect in some fast reactor spectra. By H. Häggblom and L. I. Tirén p. Sw. cr. 10: Aspects of low temperature irradiation in neutron activation analysis. By D. Brune p. Sw. cr. 10: Application of a betatron in photonuclear activation analysis. By D. Brune, S. Mattsson and K. Liden p. Sw. cr. 10: Computation of resonance-screened cross section by the Dorix-Speng system. By H. Häggblom p. Sw. cr. 10: Solution of large systems of linear equations in the presence of errors. A constructive criticism of the least squares method. By K. Nygaard p. Sw. cr. 10: Calculation of void volume fraction in the subcooled and quality boiling regions. By S. Z. Rouhani and E. Axelsson p. Sw. cr. 10: Neutron elastic scattering cross sections of iron and zinc in the energy region 2.5 to 8.1 MeV. By B. Holmqvist, S. G. Johansson, A. Kiss, G. Lodin and T. Wiedling p. Sw. cr. 10: Calibration experiments with a DISA hot-wire anemometer. By B. Kjellström and S. Hedberg p. Sw. cr. 10: Silicon diode dosimeter for fast neutrons. By L. Svansson, P. Swedberg, C-O. Widell and M. Wik p. Sw. cr. 10: Phase diagrams of some sodium and potassium salts in light and heavy water. By K. E. Holmberg p. Sw. cr. 10: Nonlinear dynamic model of power plants with single-phase coolant reactors. By H. Vollmer p. Sw. cr. 10: Report on the personnel dosimetry at AB Atomenergi during By J. Carlsson and T. Wahlberg p. Sw. cr. 10: Friction factors En rough rod bundles estimated from experiments in parti-; ally rough annuli effects of dissimilarities in the shear stress and turbulence distributions. By B. Kjellström p. Sw. cr. 10: A study of the resonance interaction effect between 333 U and "'Pu in the lower energy region. By H. Häggblom p. Sw. cr. 10: Application of the microwave discharge modification of the Wilzbach technique for the tritium labelling of some organics of biological interest. By T. Gosztonyi. 1968, 12 p. Sw. cr. 10: A comparison between effective cross section calculations using the intermediate resonance approximation and more exact methods. By H. Häggblom p. Sw. cr. 10: A parameter study of large fast reactor nuclear explosion accidents. By J. R. Wiesel p. Sw. cr. 10: Computer program for inelastic neutron scattering by an anharmonic ciysla). By L. Bohlin, I. Ebbsjö and T. Högberg p. Sw. cr. 10: On low energy levels in "! W. By S. G. Malmskog, M. Höjeberg and V. Berg p. Sw. cr. 10: Formation of negative metal ions in a field-free plasma. By E. Larsson p. Sw. cr, 10: A determination of the m/s absorption cross section and resonance integral of arsenic by pile oscillator technique. By E. K. Sokolowski and R. Bladh p. Sw. cr. 10: The decay of " 1 Os. By S. G. Malmskog and A. Bäcklin p. Sw. cr. 10: Diffusion from a ground level point source experiment with thermoluminescence dosimeters and Kr 85 as tracer substance. By Ch. Gyllander, S. Hollman and U. Widemo. 19S9. 23 p. Sw. cr. 10: Progress report, FFN, October 1, september 30, By T. Wiedling p. Sw. cr. 10: Thermodynamic analysis of a supercritical mercury power cycle. By A. S. Roberts, Jr., p. Sw. cr. 10: On the theory of compensation in lithium drifted semiconductor detectors. By A. Lauber p. Sw. cr. 10: Half-life measurements of levels in "As. By M. Höjeberg and S. G. Malmskog p. Sw. cr. 10: A non-linear digital computer model requiring short computation time for studies concerning the hydrodynamics of the BWR. By F. Reisch and G. Vayssier p. Sw. cr. 10: Vanadium beta emission detectors for reactor in-core neutron monitoring. I. ö. Andersson and B. Soderlund p. Sw. cr. 10: Progress report 1968 nuclear chemistry p. Sw. cr. 10: A half-life measurement of the kev level in,,s Lu. By M. Höjeberg and S. G. Malmskog p. Sw. cr. 10: The application of thermoluminescence dosimeters to studies of released activity distributions. By B-l. Rudén p. Sw. cr. 10: Transition rates in >"Dy. By V. Berg and S. G. Malmskog p. Sw. cr. 10: Control rod reactivity measurements in the Agesta reactor with the pulsed neutron method. By K. Björeus p. Sw. cr. 10:-. List of published AES-reports (In Swedish) 1. Analysis be means of gamma spectrometry. By D. Brune p. Sw. cr. 6:-. 2. Irradiation changes and neutron atmosphere in reactor pressure vesselssome points of view. By M. Grounes p. Sw. cr. 6:. 3. Study of the elongation limit in mild steel. By G. Östberg and R. Attermo p. Sw. cr. 6:-. 4. Technical purchasing in the reactor field. By Erik Jonson p. Sw. cr. 8:-. 5. Ågesta nuclear power station. Summary of technical data, descriptions, etc. for the reactor. By B. Lilliehöök p. Sw. cr. 15:-. 6. Atom Day Summary of lectures and discussions. By S. Sandström p. Sw. cr. 15:-. 7. Building materials containing radium considered from the radiation protection point of view. By Stig O. W. Bergström and Tor Wahlberg p. Sw. cr. 10:-. Additional copies available from the library of AB Atomenergi, Fack, S Nyköping, Sweden. EOS-tryckerierna, Stockholm 1969