Effective neutron multiplication factor

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. 

If no credit for soluble boron in the SFP water is taken, the effective neutron multiplication factor (fceff) of the spent fuel storage racks loaded with fuel of the maximum fuel assembly reactivity must not exceed 0.95, at a 95% probability, 95% confidence level, if flooded with unborated water. If credit is taken for soluble boron in the SFP water, then the of the spent fuel storage racks loaded with fuel of the maximum fuel assembly reactivity must not exceed 0.95, at a 95% probability, 95% confidence level, if flooded with borated water. The /teff must also remain below 1.0 (i.e., subcritical) at a 95% probability, 95% confidence level under the assumed loss of soluble boron in the pool water, that is, assuming unborated water in the SFP (CFR, Title 10, Part 50). Finally, reactivity effects of abnormal and accident conditions are also evaluated to assure that under these conditions the reactivity will be maintained less than 0.95. 

FIG XXV-3. Effective neutron multiplication factor versus fuel burn-up with Pb and... 

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

The possibility of operating nuclear fission in the form of a chain reaction is governed by the effective multiplication factor keir, the ratio of the munber of neutrons in the second generation to that in the first generation ... 

Figure 11.1. Effective multiplication factor fceff for neutrons (schematically).

Therefore, the problems which faced the would-be designers of chain reactors early in 1941 were (1) the choice of the proper moderator to uranium ratio, and (2) the size and shape of the uranium lumps which would most likely lead to a self-sustaining chain reaction, i.e., give the highest multiplication factor. In order to solve these problems, one had to understand the behavior of the fast, of the resonance, and of the thermal neutrons. We were concerned with the second problem which itself consisted of two parts. The first was the measurement of the characteristics of the resonance lines of isolated uranium atoms, the second, the composite effect of this absorption on the neutron spectrum and total resulting absorption. One can liken the first task to the measurement of atomic constants, such as molecular diameter, the second one, to the task of kinetic gas theory which obtains the viscosity and other properties of the gas from the properties of the molecules. The first task was largely accomplished by Anderson and was fully available to us when we did our work. Anderson s and Fermi s work on the absorption of uranium, and on neutron absorption in general, also acquainted us with a number of technics which will be mentioned in the third and fourth of the reports of this series. Finally, Fermi, Anderson, and Zinn carried out, in collaboration with us in Princeton, one measurement of the resonance absorption. This will be discussed in the third article of this series. 

Calibration is necessary in all quantitative NDA measurements to relate measured responses (e.g., neutron coincidence rate or specific gamma intensity) to nuclear material characteristics. An accurate measurement depends crucially on the effective calibration of measurement instrumentation. This calibration is based on similar items whose nuclear material content is very accurately known. The resulting calibration functions including all necessary correction factors (such as those relating to neutron multiplication or gamma-ray... 

Values of the Effective Multiplication Factor, keff, and Neutron Age to Thermal Energy, r, for Uranyl Nitrate Assemblies... 

The response of foe array multiplication factor to changes in the radius of the units was explored and furnishes an internally consistent relationship allowing prescribed minimum reactivity adjustments to be made for environmental conditions Jn this way margins of safety arc e iq)resslble in terms of foe array reactivity. For example, the effects of. concrete as a reflector of an array and its Influence on neutron coupled arrays were investigated for several thicknesses of concrete. Also,... 

Fig. 2. Comparison among experimental and calculational effective multiplication factors keff. Closed circles, open circles, and triangles represent KENO IV, exponential, and pulsed-neutron source results, respectively. N is of n X n square lattices.

An essential part of the crihcality safety analysis is to ensme that the computer code accurately predicts the effective multiplication factor. Therefore, the computer code is benchmarked against experimental data, using critical experiments that encompass the pertinent design parameters of the canister basket. The most important parameters are (1) the enrichment, (2) the geometrical spacing between fuel assemblies, (3) the boron loading of the fixed neutron absorbing panels, and (4) the soluble boron concentration in the water. 

The appropriate cross sections for the nuclear reactions tahlng place In a reactor are dependent on the particular neutron accounting procedure employed In the reactor physics calculations. The usual Banford procedure Is to calculate the effective multiplication factor of the reactor via the veU-knoiin Fenal four factor foxtnula. (Section 2.2)... 

The neutron leakage In a reactor is a function of the reactor else and the neutron migration area it is strongly influenced by the presence of a reflector of pure moderator material surrounding the active core. For a uniform homogeneous loading the effective and Infinite lattice multiplication factors are related by the equation ... 

Answer If the delayed neutron effect sets the effective neutron lifetime as 0.1 seconds, it follows that for a reaction that is just barely critical (keff = l.OOO), the rate of neutron population increase or decrease will be determined by the average neutron emission time of 0.1 second. Since the delayed neutron effect is 0.75 per cent, or a fraction 0.0075 of the total, prompt critical can be avoided provided the multiplication factor is kept between 1.0000 and.1.0075-In other words, the control rods should be withdrawn in steps so that at criticality, the keff is less than 1.0075i but greater than 1.0000. If criticality can be attained with keff sli tly in excess of 1.0000, the neutron population can increase only throu the additional contribution from the delayed neutrons. 

Multiplication Factor - The ratio of the number of neutrons present in a reactor at a given time to the number present one finite lifetime earlier. Sometimes called the effective multiplication constant (Xeff) For a homogeneous medium the infinite multiplication constant ( qq) refers to the multiplication constants in an infinite mecium. The multiplication constant minus one is called the excess multiplication constant (kex) ... 

QUESTION 31. (1.0) Effective multiplication factor is defined as the number of neutrons in one generation by the number of neutrons in the previous generation and is represented by ... 

Describe the chain reaction, a neutron generation, the core multiplication factor, and primary operating factors that affect neutron multiplication and their effects. 

Neutronic characteristics of MSRs have been explored in the literature. Flow effects were considered when calculating the effective multiplication factor and fast neutron, thermal neutron, and delayed neutron precursor distribution of the liquid-fuel MSR based on the multigroup neutron diffusion equation and delayed neutron precursor conversation equation (Zhang et ah, 2009b Cheng and Dai, 2014 Zhou et ah, 2014). Spatial kinetic models were developed for better neutronic analysis of the MSRs (Zhang et ah, 2015 Zhuang et ah, 2014). 

The effective multiplication factor is the ratio of the number of neutrons of a given generation to the number of neutrons of the immediately preceding generation. It can be expressed as... 

The infinite multiplication factor koo is a basic reactor constant it is the ratio of the average number of neutrons in one generation to that of the preceding generation in an infinite reactor core. For a finite reactor core an effective multiplication factor keff is given in terms of koo as follows ... 

One of the most serious difficulties for experimentally accessing the dynamics in the low Q plateau is the presence of multiple scattering [210]. In order to assess this effect, NSE spectra were taken above and below the multiple scattering threshold. For neutron wavelengths A 14 A the first structure factor peak cannot be seen with neutrons and therefore multiple scattering contributions... 

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