Neutron multiplication factor

Transmutation. Recycling actinides to the LWRs will decrease the average material neutron multiplication factor by only 0.8 percent, provided that they are of high purity [C2], Recycling to LMFBRs, however, will be preferred. There will be less neutron capture in impurities, such as lanthanides, and the average fission-to-capture ratio of the actinides should be higher in a fast spectrum than in a thermal one. 

These 112 thermal neutrons constitute the second generation of neutrons which according to our definition of neutron multiplication factor is so that... 

This section will cover some simple calculations related to the reactor. The reactor had a cold, beginning of life, neutron multiplication factor of 1.037 0.001, which corresponds to an excess positive reactivity of 5.7 based on a delayed neutron fraction of 0.0065. The burnup for the reactor was determined using a fairly simple set of equations. The consumption over 10 years at a power level of 200 kWth was 0.8 kgs of and at 400 kWth, 1.6 kgs of would be consumed. Given that the fuel loading is 186 kgs of the burnup is -0.86% for the upper end of the uranium consumed. This burnup results in a loss of 1 reactivity. 

The primary goal of this study was to ensure that there was sufficient excess reactivity in the neutron multiplication factor to keep the reactor critical for the 10 year lifespan while ensuring that the reactor would be subcritical during major accident scenarios. The position of the reflector can be used to set the multiplication factor of the reactor. Burnup in the reactor causes a proliferation of additional materials to absorb neutrons and reduces the density of fissile materials, lowering the neutron multiplication of the reactor. This can be offset by closing the reflector, which decreases the neutron leakage of the system. This is shown in Figure 5-1. 

The change in neutron multiplication vs reflector position is nearly linear for an extended region. Beyond 22 cm it starts curving, asymptotically approaching the neutron multiplication factor of the core without reflectors. The combined worth of the moveable reflectors is roughly 26.5 from full open to full closed position. Figure 5-2 shows how the reflectors open up on the core and where the centerline of the reactor is. It also indicates the length of the reflectors. 

The neutron multiplication factor (k-effective) was 0.964 0.001, well below the desired value of 0.985. 

For a package containing fissile material in quantities not excepted by para. 672, the term maximum damage should be taken as the damaged condition that will result in the maximum neutron multiplication factor. 

As it was shown before, the condition for the establishment of a chain reaction is that at least one of the neutrons originating from fission is inducing a new fission reaction. This condition is expressed by the neutron multiplication factor k (also called criticality factor), k is defined as... 

The critical state is characterized by a neutron multiplication factor k = 1. With this condition O Eq. (57.30) becomes N = Nq. (The contribution of the constant neutron source JCused for starting purposes can be neglected since Kis six to seven orders of magnitude smaller than N in an operating reactor.)... 

Both et riments and KENO code calculations have shown that the neutron multiplication factor for the heterogeneous assemblies were no more than 1% greater than keff for homogenized materials. These experiments wUl be described more fully in an ORNL report. ... 

The neutron multiplication factor for a variety of uranium-metal annuli and cylinders surrounded with thick carbon reflectors has been measured and calculated by a Monte Carlo method. The material within the aimult was carbon or air. The thickness on the side, top, and bottom reflector was equal in any one assembly. The density of the indivklual pieces of Type-HLM graphite varied between 1.688 and 1.783 g/cm. The uranium metal was. enriched to 93.2% in U and has been described previously. ... 

Neutron multiplication factors have a standard deviathm of O.OOS. 

Neutron Age and Infinite-Medium Neutron Multiplication Factor for UF4-Paraffin Mixtures with Low Enrichment, S. J. Raffety, (ORNL), J. T. Mihalczo (UCC-Y12)... 

The infinite-medium neutron multiplication factor k , and the neutron age to thermal energy for UFt-paraffln mixtures have been inferred from critical experiments with 2 and 3% U-enriched uranium. The volume fraction of paraffin was varied so that the H U atomic ratio was between 195 and 972 for the 2% enrichment and was 133 and 277 for the 3% enrichment. 

Performance criteria established by regulatory statutes to ensure that the shipment is safely subcritical must also be met. Nuclear criticality in Irradiated fUel shipments can be successfully controlled through the use of l-in. boral plates to reduce the excess reactivity of the fuel element array such that kw, the infinite-medium neutron multiplication factor, is less than unity. This is a requisite for Fissile Class I shipments. 

Fig. 1. Neutron multiplication factor for arrays of U(93.2) metal units.as afunction of the moderating and reflecting water density.

TART Monte Carlo neutron transport calculattons are customarily processed with 160,000 neutron histories yielding a probable error M better than 0.2% in the ejq>ectation value of- the neutron multiplication factor. ANISN time-independent S calculations are carried out in parallel as needed in the P-3, S-16, 66-grcnip format with a convergence Criterion of 0.1%. Calculated results of TART and ANISN are stored by computer to make their correlation and interpretation easier. 

Monte Carlo Calculations of the Influence of Double-Batched Units on Storage Array Neutron Multiplication Factors... 

The Monte Carlo code KENO was used to calculate the required neutron multiplication factors (keff). mie keif values typically had a standard error of 0.008 and involved the tracking of between 10,000 and 15,000 neutrons. Hansen-Roach 16-group cross-section sets were used with the exception of magnesium, silicon, manganese, and cojqjer, which were obtained by iSDRN calculations, and calcium and zinc which were obtained by GAM-2 calculations. 

The solid-angle method has been used for nearly 20 years to specify safe spacings for subcritical components of fissile materials. This method is based on the concept that neutron interaction is directly proportional to the solid angle subtended among fissile units and can be related to the neutron multiplication factor of an individual unit. 

Using results ol criticality calculations, which were submitted to the NRC by the licensees, a aphlc method has been developed which appears to provide neutron multiplication factors, k , in spent fuel pools within accuracy limits of about one-half of one percent. 

Fig 1. Infinite neutron multiplication factor, k. , for 0.635-cm Type 304 st nless-steel storage rack for PWR fuel assemblies with... 

Calculated criticality results show that all closely packed configurations of packages which were modeled are subcrltical. The highest calculated effective neutron multiplication factor is 0.37, which was obtained for an array of 1000 closely packed hypothetically damaged and burned-out packages. 

The neutron multiplication factor (Keff) of each benchmark core was calculated using the Monte Carlo criticality code KENO IV. The 123-group XSDRN cross-section set was used. Resonance self-shielding was accounted for in the U isotope only. Self-shielding corrections were made with the NIT AWL code from the AMPX package. ... 

An important advanta of the method is that only known or measured properties of the fts e system at the subcritical state of interest are required to interpret the measured quantities. Alternative methods fix inferring reactivity Usually require calibration at the delayed critical condition, which may not be possible or desirable in many situations. In addition to the neutron multiplication factor k, the -driven method inherently yields additional useful properties of the fissile system, such as the prompt neiutron decay constant and the inverse neutron count rate, which is related to the source neutron multiplication. 

The solid angle model relates the neutron multiplication factor of a uniform array of units to the multiplication factor of the units and the total solid angle subtended at a unit by all other units of the array. The solid angle method in application is an empirical procedure. The use of such is permitted by the American National Standard for Nuclear Criticality Safety, N16.1-1975, provided the procedure has been validated. The American National Standard N16.9-197S outlines the requirements for establishing the validity and area(s) of applicability of such a calculational method. This standard on solid angle will permit use of the solid angle technique in compliance with the requirements of N16. l and N 16.9. ... 

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