Delayed neutrons fraction

Since the total number of neutrons in the next generation will be proportional to k and the number of next-generation prompt neutrons will be proportional to kp, it follows that the fraction of prompt neutrons in the next generation will be kp/k. Similarly the fraction of next-generation delayed neutrons will be kdi/k, for I = 1 to 6. The delayed neutron fraction for group i is given the symbol ft, so that... 

Reactivity, p, is a dimensionless quantity, but sometimes it is assigned the dimensionless unit of Niles , where 1 Nile = 0.01. (The word Nile originates from the terminology Ak = k— I, and is a pun on the River Nile s well-known delta downstream of Cairo.) Alternatively, reactivity may also be referred to in dollars, the ratio of the reactivity to the delayed neutron fraction ... 

P delayed neutron fraction elD relative roughness of the pipe ... 

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 core delayed neutron fraction () ) varies from 0.0065 at beginning of cycle in the Initial core to 0.005 at the end of an equilibrium cycle. This average delayed neutron fraction was obtained by weighting the P s of each of the three major core fission Isotopes, U-235, Pu-239, and U-233, by their relative contribution to the neutron production rate. For example, the relative production rate contribution from U-235 varies from 100% at the beginning of the initial cycle to 57% at the end of an equilibrium cycle. The relative production rates of these three nuclides are given In Table 4.2-13a. 

Q = peak energy density in the core (joules/gm) f = total delayed neutron fraction / = neutron lifetime (sec)... 

Pi = delayed neutron fraction of /th precursor Cl = concentration of ith precursor (joules/gm-sec)... 

A parametric study carried out in order to establish the design orientations of burner cores taught us first that a considerable reduction of the fuel inventory (or dilution ) is always necessary to be able to operate a large core with a high plutonium content and therefore with an attractive plutonium burning performance. This dilution results in a decrease in in-pile fuel residence time as well as in a reduction (favourable) of the sodium void reactivity, whereas a decrease of the uranium content of the fuel brings about a reduction of the Doppler effect, a decrease of the conversion ratio which causes a daily reactivity loss ttiat makes it difficult to achieve long irradiation cycles, as well as a reduction of tiie delayed neutron fraction. 

The goal of this programme was to reduce uncertaincies as to the effective delayed neutron fraction, peff, from 10 % ((2 o) to 5 % (2 a) in order to obtain better prediction of the reactivity scale. 

Table n gives a comparison of the measured and calculated temperature coefficients and eigenvalues between 74 and 464 F. The temperature defect between 74° and 464 F was estimated from integrated rod worths to be about 3%. Rod worths and temperature coefficients were b d on a calci ted effective delayed neutron fraction fi of 0.0074 (i.e., p/p = 1.16). In addition to having a small absolute bias (all calculated eigenvalues are within + 0.5 and - 0.9% of measured values), the model describes the temperature effects quite accurately. 

G. A.. Price,"Migration Areas and Effective Delayed Neutron Fractions by Critical Exq[>eriments, J. Nuclear Energy, fO. Ill (1959). 

Core Effective delayed neutron fraction, Plqrsical coresize (in.) Gd septum (w/o) Measured keff Variational treatment keff Normalized iterative treatment keff... 

The ratio of the effective delayed neutron fraction (3eff) to the effective prompt-neutron generation time (f ) was measured for several unpoisoned configurations, employing both pulsed neutron and nOise analysis methods. The two methods were in satisfactory agreement, giving a best value of 4.76 x 10 sec". The correspon ng value for the beryllium-reflected reactor has been measured as 1.38 X lO sec". The much greater f for the water-reflected assembly is attributable to reflector delayed neutrons. 

A si rles of experiments with unreflected and unmoderated cylinders of enriched-uranium metal (93.15% U-23S) has been performed at the ORNL Critical Experiments Facility to determine the dependence of the prompt-neutron lifcitime on the cylinder dimensions. Five cylinders ranging in diameter from 17.77 to 38.09 cm and in height-to-diameter ratio from about 0.2 to 0.7 were assembled and their prompt-neutron decay crnistants measured at delayed critical by the Rossi-a technique. Prompt-neu-tnm lifetimes were obtained from the measured decay constants and effective delayed-neutron fractions calculated by transport theory. The average uranium density for each assembly was greater tium 18.7 g/cm. . 

A computational study has been carried out on several plutonium-fueled and mixed-lueled critical assemblies of small to medium size to verify the plutonium cross sec-tlons of the twenty-six groiq> set recently produced at Argonne National Laboratory. Plutonium worths in some larger uranium-fueled reactors have been computed to ascertain the effect of softer spectra on the comparisons. Other reactor parameters included in the study were detector-response ratios and U-235,U-238 and B-10 central clanger coefficients, as well as effective delayed-neutron fraction and prompt-neutron lifetime. 

Central reactivity worths were calculated in spherical. geometry by void replacement. Effective delayed-neutron fractions were determined both by subtraction of delayed-group spectra from the fission-source distribution and by the standard diffusion-theory perturbation method. Prompt-neutron lifetimes were calculated by 1/v poison and by perturbation methods. 

The fast fission factor e, the material buckling B, the quantity Ap/AB were measured in critical assemblies of each fuel mixture. The thermal-neutron diffusion area L wa.8 calculated from thermal-neutron cross sections. The delayed-neutron fraction was determined from the delayed-neutron fractions for U and measured by Keepin and the "U-to- U fission ratio measured in the critical assemblies. 

Values of the absorption rate, v 2 == 14798 sec , and diffusion area, L 6.214 cm, were taken from a GAMTEC-II calculation made for the same material in another study in which koo - 1.0294 was also measured. If the delayed-neutron fraction is assumed to be 0 =... 

T. MIHALCZO, The Effective Delayed Neutron Fraction from Firakm in an Unreflected Ur um Sphere from tirne Correlation Measurements with Californiuro-252, iVrici Set ng., 60.262 (1976). 

Because DUPIC fuel has a faster dynamic response than UO2 due to the lower delayed neutron fraction and lower prompt neutron lifetime for plutonium isotopes, the same positive reactivity insertion will result in a faster response than for UO2. To compensate for this in a postulated large LOCA, void reactivity for the DUPIC fuel was reduced by adding a small amount of neutron absorber to the center element (26 g of natural dysprosium). This is an embodiment of the LVRF concept and reduces void reactivity sufficiently so that the power pulse with the DUPIC fuel is lower than that with natural uranium. The downside, of course, is reduced bumup without the neutron poison the bmnup of the DUPIC fuel is 18.8 MW d/kg HE with the burnable poison, the bumup drops to 15 MW d/kg HE, which is still double that of NUE fuel (Table 15.8). 

After the plant is brought to the nominal parameters, the reactor changes over to the power self-control mode when the compensation group absorber elements are all located in the upper part of the core they create an operating reactivity margin within the limits of one effective delayed neutron fraction (Peff), which does not threaten reactor safety under an erroneous or even malevolent personnel action. 

For the ELENA-NTEP, the basic option is a once-through fuel cycle with uranium dioxide fuel. It is possible to use MOX fuel. A lower value of the delayed neutron fraction typical of MOX-fuelled reactors might not pose a problem for the ELENA-NTEP because it is designed to operate at a constant power level, resulting in essentially no transients. 

The delayed neutron fraction of U is lower than that of U and half of the delayed neutrons are generated outside the core therefore, the effective delayed neutron fraction in the FUJI-233Um is relatively small. However, safe control of the reactor is possible because of a large negative reactivity coefficient on fuel salt temperature and small overall reactivity margin ... 

In the design basis reactivity insertion accident (RIA) [XXX-25], the maximum reactivity insertion in the MSR corresponds to the drop of one graphite control rod into the core. Since the worth of a single graphite rod is only 0.06 %5K/K and less than one effective delayed neutron fraction, such initiating event does not result in any prompt criticality of the FUJI. 

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