Analysis of the Neutronic Characteristics of GFR-2400 Fast Reactor Using MCNPX Transport Code

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1 Amr Ibrahim, et al. Arab J. Nucl. Sci. Appl, Vol 51, 1, The Egyptian Arab Journal of Nuclear Sciences and Applications (2018) Society of Nuclear Vol 51, 1, ( ) 2018 Sciences and Applications ISSN Web site: esnsa-eg.com (ESNSA) Analysis of the Neutronic Characteristics of GFR-2400 Fast Reactor Using MCNPX Transport Code Amr Ibrahim a, Moustafa Aziz b, S.U. EL-Kameesy c, S. A. EL-Fiki c and A. A. Galahom d (a) High Institute for Engineering and Technology, Cairo, Egypt (b) Nuclear and Radiological Regulatory Authority, Cairo, Egypt (c) Faculty of Science, Physics Department, Ain Shams University, Cairo, Egypt (d) Higher Technological Institute 10th of Ramadan City, Egypt Received: 21/5/2017 Accepted: 25/7/2017 ABSTRACT The 2400 MW Gas Cooled Fast Reactor (GFR2400) is a promising potential candidate for future sustainable and economic nuclear power systems. It is a highly innovative system with advanced geometrical design and fuel materials (Ceramic fuel pellets of mixed uranium plutonium carbide within fuel pins). The active fuel region of this reactor is divided radially into two core zones of different fissile plutonium enrichments namely, inner core fuel assemblies (IC), and outer core fuel assemblies (OC). Using MCNPX transport code, 3D heterogeneous model of GFR2400 core has been designed to study the neutronic characteristics of the GFR2400 concept and to simulate its operation during a fuel cycle of a duration 1443 effective full power days. The obtained results show good agreement with previous studies and confirm the capability of the GFR2400 concept to achieve sustainability. Keywords: Fast reactor- GFR2400- MCNPX- Plutonium- Minor actinides 1. INTRODUCTION The only fissile material occurring in nature is uranium, which contains 0.7% of the fissile isotope 235 U and 99.3% of the isotope 238 U. In most of thermal reactor fuel, fissile enrichment of uranium must be enriched from 0.7% to at least 3%. The tails of this enrichment process, so called depleted uranium (DU) are stored in large stockpiles, for which there is no much use. Furthermore, of the enriched uranium that is loaded into the reactor core, only about 5% is actually fissioned. However, to meet the increasing global energy demand it is important to achieve a better utilization of natural resources. Fast reactors are expected to allow for efficient utilization of uranium resources as it enables the fissile materials in the nuclear spent fuel to be reused. In a fast reactor, the non-fissile 238 U can be converted to the fissile isotope 239 Pu by neutron capture and subsequent decay, and 238 U is accordingly designated as a fertile isotope. The amount of the fissile materials that can be produced in the reactor core depends on the neutron economy and the fertile fraction in the fuel. If more than one fertile nucleus is converted for each fissioned nucleus, the net amount of fissile material in the reactor increases and the reactor is called a breeder reactor. In fast reactors, the neutron economy is such that during irradiation enough neutrons remain after each fission reaction to allow for a capture in a fertile nuclide. Hence, fast reactors can be used to reduce stockpiles of depleted uranium and nuclear waste by optimizing fuel efficiency. 177

2 Amr Ibrahim, et al. Arab J. Nucl. Sci. Appl, Vol 51, 1, (2018) The Gas Cooled Fast Reacor (GCFR) is one of the six advanced systems that have been chosen by Gen-IV iniatiative for research and developement of a relaible, economic, safe and proliferationresistant nuclear system (1). The GCFR is a fast neutron spectrum, helium (He) cooled nuclear system which combines the advantages of fast spectrum systems with those of high-temperature systems (2). The neutron spectrum of the GCFR is considered to be the hardest among fast spectrum systems. This hard spectrum allows the GCFR to contribute to fuel sustainability in two ways: on one hand actinides are more likely to be fissioned and less likely to capture neutrons and form heavier isotopes, and on the other hand, the average number of neutrons produced in fission is higher and hence more neutrons are available for breeding. During the last decade, the design of GCFR concept has been under development. This development included designs of different considered fuel forms such as coated fuel particle, silicon carbide blocks with dispersed microparticle fuel inside, and silicon carbide plates with fuel pellets arranged in honeycomb structure, finally arriving to the current design of a hexagonal fuel assembly composed of cylindrical rods, of fuel pellets, arranged in a hexagonal array and surrounded with a hexagonal SiC wrapper (3-5). Recently, two reactor thermal powers, namely 600 Megawatts thermal (MWt) and 2400 MWt, are being considered as appropriate operating powers of GCFR concept (2). Motivated by its many attractive features, CEA proposed a 2400 MW GCFR design which was called the GFR2400 academic core. It is considered a reference design for a commercial size GCFR (6). The design of this concept has been under development using computational codes mainly developed within the European Union initiatives. The aim of this study is to employ the powerful stochastic tool, MCNPX transport code to study and analyze the neutronic behavior of the GFR2400 concept and its isotopic transmutations as a function of burn-up time. 2. GFR2400 DESIGN DETAILS The main design parameters of the GFR2400 core are given in Table (1). It is utilizing pin fuel element and uses helium coolant at a high pressure of 7MPa to ensure adequate heat transfer (5). Figure (1) shows a layout of the GFR2400 core model. The active fuel region of this core consists of 516 fuel assemblies (FAs) loaded into two core zones namely, the inner core (IC) with 264 fuel assemblies, and the outer core (OC) with 252 fuel assemblies. For the safety and control of the reactor during operation, there are 13 diverse shut down (DSDs) and 18 controls shut down devices (CSDs) placed within the active fuel zone of the core. Both assemblies are constructed in the same manner with the absorber material in both sets is made up by boron carbide (B 4C, with 90% 10 B). The radial reflector region of the core consists of 480 assemblies composed volumetrically of 80 % Zr 3Si 2 and 20 % He while structural elements are composed of a special steel alloy (AIM1). Table (1): Design characteristics of GFR2400 core Reactor Parameter Value Thermal power [MW] 2400 Primary pressure [MPa] 7 Primary coolant Core inlet temp. [ C] 400 Core outlet temp.[ C] 780 Total No. of fuel assemblies (FAs) 516 No. of inner/outer core FAs 264/252 No. of safety/regulating rods 13/18 No. of radial reflector assemblies 480 He 178

3 Amr Ibrahim, et al. Arab J. Nucl. Sci. Appl, Vol 51, 1, (2018) Fig. (1): Layout of the GFR2400 core 2.1 Fuel assembly design The fuel assemblies of both the IC and OC are consisting of 217 fuel pins arranged in a hexagonal array, surrounded with a hexagonal SiC wrapper, the fuel in each pin is composed of mixed-carbide (PuC/UC) fuel pellets and extends for a length of 165 cm. The two cores have different fissile plutonium contents namely, 14.12% for the IC and 17.65% for OC, where the percentages represent the volume fraction of fissile plutonium material present within the fuel, the isotopic composition of the fissile plutonium vector is 2.7% Pu-238, 56% Pu-239, 25.9% Pu-240, 7.4% Pu- 241, 7.3% Pu-242 and 0.7% Am-241 (weight fractions). This composition is corresponding to the Pu scenario study of CEA, which is estimated as the one expected from a twice recycled mixed oxide (MOX) fuel (4). All uranium present within the fuel is considered to be natural uranium (99.28 w% U-238, 0.72 w% U-235). The density of the fuel is considered to be 80 % of the theoretical density (13.63 gm/cm 3 ) of ( Pu,U)C fuel, accounting for 20% porosity of ceramic fuel. Below and above the fuel region of pin, an empty plenum region is reserved for confinement of fission gases as well as axial thermal expansion of fuel and reflector materials. The empty plenum region extends for 85 cm above and 50 cm below the length of the active fuel region until the reflector region of the fuel pin is encountered. The fuel pin reflector region extends for 1.0 m beyond both the upper and lower empty plenum regions. The reflector material is made of zirconium silicide (Zr 3Si 2), which is proved to withstand high temperatures. Design details of GFR2400 fuel assembly are given in Table (2). Using MCNPX code, 3D heterogeneous models of the GFR2400 fuel assemblies (inner and outer) have been designed. Figure (2) shows a cross sectional view (at fuel level) of a fuel assembly as well as a fuel pin lattice configuration. 179

4 Amr Ibrahim, et al. Arab J. Nucl. Sci. Appl, Vol 51, 1, (2018) Table (2): Design dimensions of the GFR2400 fuel assembly and fuel pin Parameter Value Fuel assembly: Assembly geometry Hexagonal Number of pins in FA 217 pin Fuel pin lattice pitch cm Wrapper pitch (inside) cm Wrapper pitch (outside) cm Coolant pitch (outside FA) cm Active fuel height 165 cm Fuel Pin: Fuel pellets radius cm He Gap thickness cm W14Re liner thickness cm Re liner thickness cm Clad thickness 0.1 cm SiC liner thickness cm (a) (b) Fig. (2): Cross sectional view of: (a) GFR2400 Fuel assembly configuration with 217 fuel pins, and (b) fuel pin lattice 3. DESIGN AND SIMULATION TOOLS MCNPX 2.6 (7) computational code has been used to design 3D model of GFR2400 core to simulate the neutronics behavior and to trace fuel burn-up as a function of operation time. MCNPX is a general purpose Monte Carlo radiation transport code designed to track many particle types over a broad range of energies. It is capable of tracking 34 particle types including neutrons, protons, nucleons and light ions. It uses standard evaluated data libraries combined with physics models where experimental data are not available. MCNPX new physics subroutines and packages allow it to model complex geometries, such as the GFR2400 concept. Using an up to date continuous energy neutron data libraries, it is capable of predicting fuel isotopic transmutation and depletion as a function of burn-up and time. To simulate the neutronic behavior inside the reactor core and accumulate the 180

5 Amr Ibrahim, et al. Arab J. Nucl. Sci. Appl, Vol 51, 1, (2018) reactor tallies, source histories per cycle are used in the MCNPX simulations, and the number of cycles to be skipped is 50 and the total number of cycle is 250. MCNPX s Burn-up card is used to advance through time steps and calculate fuel burn-up transmutation. For this analysis study, ENDF/B-VI.2 cross sections library was used; it contains cross sections data for nuclides such as those used in constructing the reactor core given at different temperatures and neutron energies. 4. RESULTS AND DISCUSSIONS The two-zone core of the reactor is designed for a 3 batch cycle operation with total 1443 EFPD (effective full power day) fuel residence in the core (5). This section provides a discussion of the neutronic behavior and isotopic transformations of GFR2400 fuel at core level assuming one batch approximation (no fuel shuffle is being considered) with total burn-up time of 1443 Equivalent full power day (EFPD). MCNPX 2.6 code is used to simulate the neutronic behavior as well as the isotopic transformations of the fuel as a function of core operation time. For all simulations, operation conditions were considered with all control and safety rods being at their parking positions (above the fuel region) and temperatures of 1263, 913, 913 and 913 K were considered for fuel, coolant, clad and reflector materials, respectively. 4.1 Model validation To validate the designed model, its effective multiplication factor (k-eff) was calculated at cold and hot conditions, (i.e. at room temperature, 293 K, and at operating temperature, 1263 K) and the calculated results are compared with results obtained by Perko et al., (2015) (5) in which Scale code was used. In order to simulate hot conditions (operation conditions), the designed core was expanded in axial and radial directions using the same approach as in the Scale model, using a radial and an axial thermal expansion factor ( R=0.687% and H=1.163% respectively), and to preserve masses the densities of the core materials were decreased. The obtained results are compared with the results of Scale code as shown in Table (3) at BOL (time=0.0 EFPD). It is clear that MCNP heterogeneous model shows good agreement with the Scale model results which gives high confidence to the designed models. Table (3): Validation results of the designed GFR2400 core model Parameter Present study Previous study Study Code MCNPX Scale (5) k-eff (cold conditions) T = 293 K ±2.8E ±2.6E-4 k-eff (hot conditions) T = 1263 K ±2.9E ±3.7E Core flux and power distributions The neutron flux and power distributions at thebeginning of core life have been calculated using F4 and FM tallies in MCNPX (7). For the power distribution, the Energy tally (En) has been employed to divide the total power into three energy groups, with boundaries ev (thermal), ev MeV (intermediate) and > 0.1 MeV (fast), in order to quantify the contribution of neutrons belonging to each neutron energy group to the total power. Figure (3) shows the radial neutron flux distribution of the core, calculated using MCNPX code, along with that obtained by Perko et al., (2015) (5) using ERANOS diffusion code. It can be observed that there is a good agreement between the two distributions. As shown in Fig. 3 the radial flux profile is very flat across the core, and the peak does not occur in the middle of the core indicating that the enrichments of the two core zones were estimated efficiently. 181

6 Power Peaking Flux (n/cm²-s) Amr Ibrahim, et al. Arab J. Nucl. Sci. Appl, Vol 51, 1, (2018) Measured Flux (MCNPX) Reference Flux (ERANOS) 2.5E E E E E E Radial distance from core center (cm) Fig. 3: Radial neutron flux distribution of GFR2400 core Figure (4) shows the radial power peaking (distribution) across the core at BOL, measured at the center of the axial active core. As shown in that figure the core total power distribution is flat and the peak does not occur at the middle of the core, rather at the interface of the two fuel zones due to enrichment zoning. Moreover, the thermal neutrons have no contribution to the total power, and only neutrons in intermediate and fast energy ranges contribute to the power. Moreover, MCNPX calculations show that the percentage contribution of neutrons in the thermal, intermediate, and fast neutron ranges to the fission reaction are equal to 0.11 %, % and 56.1 %, respectively. Thermal Intermediate Fast Total power Radial distance from core center (cm) Fig. (4): Radial power peaking of GFR2400 core Figure (5) illustrates the power peaking (distribution) along the axial active core. As shown in this figure the axial power peaking occurs at the center of the axial fuel region and is similar to the radial power distribution. The thermal neutrons have no contribution to the power, and only neutrons in intermediate and fast energy ranges contribute to the axial power. 182

7 Axial power peaking Amr Ibrahim, et al. Arab J. Nucl. Sci. Appl, Vol 51, 1, (2018) Themal Intermediate Fast Total axial power Axial Fuel length (cm) 4.3 Core safety parameters Fig. (5): Axial power peaking of GFR2400 core This section discusses the main operating parameters that strongly affect the safety of the core, namely, the effective delayed neutron fraction, Doppler constant and depressurization coefficient (void coefficient). The obtained results are given in Table (4) along with their variances. The obtained values of β-eff (389 pcm), Doppler constant (-1038 pcm) and depressurization effect (314 pcm), are comparable to other values obtained by Perko et al., (2015) (5) (415 pcm, pcm, and 347 pcm) respectively. The effective delayed neutron fraction is determined in order to quantify the contribution of delayed neutrons to the fission since it is an important safety and control parameter. The effective delayed neutron fraction (β-eff) is calculated using Equation (1) (8), β eff = 1 ( k p k ) (1) Where k is the total effective eigen-value for both prompt and delayed neutrons and k p is the effective prompt eigen-value. Both eigen-values can be obtained from the straight calculation mode of MCNPX. The obtained values for k and k p are ±1.3E-4 and ±1.2E-4, respectively, which give a value of 389 pcm for the effective delayed neutron fraction with standard deviation within 2.2E- 4 (23 pcm). Doppler Effect is one of the basic inherent safety parameters to be considered. It is caused by the broadening resonances of nuclides with the increase in temperature. In fast reactors, not only the absorption rate but also the fission rate are affected by this broadening. The Doppler Effect strength can be estimated by the Doppler Constant (DC) which is defined by Equation (2) (5) : DC = ρ / ln(t per/t ref) (2) Where, ρ is a certain reactivity change due to an assumed variation of the fuel temperature from a perturbed value of T per= 300 K to a reference value of T ref=1200 K. Depressurization effect (void effect) is defined as the change in reactivity corresponding to a loss of coolant. In a GFR, the depressurized accidents present the most challenging situations due to the low thermal inertia of the core. The value of depressurization effect presented in Table (4) 183

8 Amr Ibrahim, et al. Arab J. Nucl. Sci. Appl, Vol 51, 1, (2018) corresponds to the most serious accidents, i.e. when the core suffers total depressurization and the coolant pressure decreases from nominal (7 MPa) to atmospheric (0.1 MPa) conditions. This situation is accounted in MCNPX input file by decreasing the coolant (He) density by 99%. The obtained value of the depressurization effect (314 pcm) is lower than the β-eff (389 pcm) which removes the risk of super-prompt-criticality due to loss of coolant accidents. 4.4 Control rod worth Table (4): GFR2400 safety parameters (measured at BOL) Safety parameters Value [pcm] Delayed neutron fraction 389±23 Doppler constant -1038±36 Depressurization effect 314±22 The reactivity of GFR2400 core is managed by the 19 control shutdown devices (CSDs) and the 12 diverse shutdown devices (DSDs) located within the active core. Therefore, it is essential to confirm the capability of both devices to introduce sufficient negative reactivity to shut down the reactor in case of accidents, the control rod worth (CRW) of these devices have been estimated using Equation. (3), CRW = k 2 k 1 k 2 k 1 (3) Where, k 1 and k 2 are the k-eff values of the core, being calculated without and with the insertion of control rods, respectively. Table (5) presents the results of control rod worth of each rods combination along with the corresponding k 2 value. The obtained results show that both DSD and CSD devices are able to insert sufficient negative reactivity to shutdown the reactor separately, i.e. without the need of the combined insertion of the other set. Moreover, the calculated CRWs of DSDs, CSDs and all control and safety rods (All CRs) are very comparable to the values obtained by Perko et al., (2015) (5) ( -4556, and pcm, respectively). Table (5): Reactivity worth of different control rods insertion combinations 4.5 Core reactivity analysis Control rods k 2 CRW [pcm] All DSDs All CSDs All CRs Figure (6) shows the effective neutron multiplication factor (k-eff) of the core as a function of core operation time. The k-eff value at begin of irradiation time is and it gradually decreased to by the end of irradiation time (1443 EFPD) due to fuel depletion and fission products accumulation. The discharged fuel burn-up has reached 50 GWD/T at the end of irradiation cycle. Furthermore, MCNPX burn-up calculations indicate that the percentage contribution of IC zone to total power during irradiation time is higher than the OC zone namely, 54% of inner core vs. 46% of the outer core. This is mainly due to the harder neutron flux and relatively larger number of fuel assemblies in inner core compared to the outer one. 184

9 Concentration (a/b-cm) k-eff Amr Ibrahim, et al. Arab J. Nucl. Sci. Appl, Vol 51, 1, (2018) Operation time (EFPD) Fig. (6): The effective multiplication factor (k-eff) as a function of operation time of the core 4.6 Isotopic transformations Figure (7) shows both the total fissile and total Pu concentration of the core in a/b-cm as a function of operation time in EFPD. As shown in Fig. 7 the core total Pu concentration is almost constant during burn-up time, mainly due to the breeding of 239 Pu from fertile 238 U. This figure also indicates that, the core fissile content shows a negligible change during burn-up time. Dividing the total fissile content of the core at EOC (2.54E-03 a/b-cm), by that at BOC (2.62E-03 a/b-cm), gives a breeding ratio (BR) value of 97%. This indicates that the core can achieve sustainability whereas the conversion of 238 U into 239 Pu during burn-up enhances the concentration of the fissile nuclides in the core as indicated by Figure (8). 4.4E-3 3.9E-3 3.5E-3 3.1E-3 2.6E-3 2.2E-3 1.7E-3 1.3E-3 8.7E-4 4.4E-4 0.0E+0 Total Fissile Total Pu Operation time (EFPD) Fig. (7): Total fissile and total Pu concentrations as a function of burn-up time 185

10 Concentration (a/b-cm) Amr Ibrahim, et al. Arab J. Nucl. Sci. Appl, Vol 51, 1, (2018) Figure (8) shows the concentrations of Pu isotopes (atom/barn-cm) as a function of core operation time (EFPD). The results indicate that 239 Pu concentration increases during irradiation time. The concentration of 239 Pu at BOL (t=0) is equal to 2.18E-03 a/b-cm and by the end of the irradiation time (t=1443 EFPD) this value is increased to 2.23E-03 a/b-cm, i.e. there is an increase by 2.2% in the 239 Pu concentration, mainly by breeding from 238 U. The concentration of 240 Pu is also increased by 6.0% due to neutrons absorption in the fuel during burn-up. Furthermore, due to fission as well as neutron capture, 238 Pu, 241 Pu and 242 Pu concentrations are decreased by 24.3%, 28.3% and 5.7%, respectively. 2.6E-3 Pu-238 Pu-239 Pu-240 Pu-241 Pu E-3 1.7E-3 1.3E-3 8.7E-4 4.4E-4 0.0E Operation time (EFPD) Fig. (8): Concentrations of Pu isotopes as a function of core operation time Figure (9) illustrates the variation in the concentrations of the main minor actinides isotopes (MAs: 237 Np, 241 Am, 243 Am, 242 Cm and 244 Cm) during operation time. It is clear that the buildup of minor actinides in the fuel is predominated by Am isotopes buildup, in particular 241 Am which is the only MA isotope present at BOL. 241 Am is transmuted into the shorter lived isotope 242 Am through neutron capture. 242m Am is in turn undergoing beta decays into 242 Cm. 242m Am decays also by electron capture into 242 Pu which through successive capture reactions followed by decay results in the production of 243 Am and eventually 244 Cm. The total MA content has increased from an average value of 75.1 kg (of 241 Am) at BOL (t=0 EFPD) to kg by the end of irradiation time (1443 EFPD), which gives an increase ( m) of only 182 kg in MA content during the entire burn-up duration. Furthermore, the minor actinide vector at the end of irradiation period is composed mainly from Np, Am and Cm with weight percentages of 11%, 81%, and 8%, respectively. 186

11 Concentration (a/b-cm) Amr Ibrahim, et al. Arab J. Nucl. Sci. Appl, Vol 51, 1, (2018) 6.0E-05 Np-237 Am-241 Am-243 Cm-242 Cm E E E E E E Operation time (EFPD) Fig. (9): Concentrations (atom/barn-cm) of main MAs isotopes as a function of core operation time 5. SUMMARY AND CONCLUSIONS An analysis of neutronic behavior and fuel isotopic transformations of GFR2400 concept has been carried out in the present work. For this purpose, a 3D heterogeneous model of the GFR2400 core has been designed using MCNPX computational code. The designed model was used to determine the important neutronic parameters characterizing the core at beginning of life (BOL) conditions as well as fuel isotopic transformations during burnup. An analysis of the core neutronic and safety related parameters showed that both the flux and power distributions are very flat across the core and both safety and regulating devices can separately shut down the reactor in case of accidents. Moreover, the core effective delayed neutron fraction was found to be higher than the depressurization reactivity effect which excludes super-prompt-criticality problems in case of a loss of coolant accident. On the other hand, the results of isotopic transmutation and burn-up within the reactor core showed that the core would still contain 97% of its initial fissile material at the end of the fuel cycle (1443 EFPD) which illustrates the capability of GFR2400 concept to achieve sustainability even without the use of fertile blankets. REFERENCES (1) Gen IV Technology Roadmap: Description of Candidate Gas-cooled Reactor Systems. Report GIF (2002). (2) Farmer, M. T., Hoffman, E. A., Pfeiffer, P. F., Therios, I. U., Wei, T. Y. C., Generation IV nuclear energy system initiative pin core subassembly design. Tech. Rep. ANL-GenIV-070, Argonne National Laboratory (2006). (3) Van Rooijen, W. F. G., Kloostermann, J. L., Van der Haagen T. H. J. J., Van Dam, H., Fuel Design and Core Layout for a Gas-Cooled Fast Reactor. Nuclear Technology, 151, (2005). (4) Van Gendt, G.J., Closing the nuclear fuel cycle, potential of the Gas Cooled Fast Reactor (GCFR). Master s thesis, Delft University of Technology, The Netherlands (2007). 187

12 Amr Ibrahim, et al. Arab J. Nucl. Sci. Appl, Vol 51, 1, (2018) (5) Perko, Z., Pelloni, S., Mikityuk, K., Krepel, J., Szieberth, M., Girardin, G., Vrban, B., Lüley, J., Cerba, S., Halasz, M., Feher, S., Reiss, T., Kloosterman, J. L., Stainsby, R., Poette, C., Core neutronics characterization of the GFR2400 Gas Cooled Fast Reactor. Progress in Nuclear Energy, 83, (2015). (6) Richard, P., Peneliau, Y., Zabi ego, M., Reference GFR 2400 MWth Core Definition at Start of GOFASTR. GoFastR Project Deliverable. CEA/DEN/CAD/DER/SESI/LC4G DO2 26/03/10 (2010). (7) Pelowitz, D.B., MCNPX User's Manual Version Los Alamos National Laboratory, U.S., April 2008, LA-CP (2008). (8) Bretscher, M.M., Evaluation of reactor kinetic parameters without the need for perturbation codes. International Meeting on Reduced Enrichment for Research and Test Reactors. Argonne National Laboratory, Illinois Jackson Hole, Wyoming, USA (1997). 188