Four-factor formula

Thus our model replaces the actual neutron distribution by a slowing-down distribution plus a thermal group. The thermal group consists of neutrons of one speed, this speed to be defined by the effective neutron temperature Tn- The actual thermal distribution, which was approximated by the Maxwell-Boltzmann relation (4.200), is replaced then by a spike or group at E = (see Fig. 4.32). The selection of this thermal energy E i, is discussed shortly. 

32 Distribution of thermal neutrons (a) actual distribution (h) model. 

2 = absorption cross section of thermal group = th ih = thermal neutron flux n h = number of thermal neutrons per unit volume = speed of thermal neutrons 

The absorption cross section for the thermal group is computed by means of Eq. (4.238). As already demonstrated, in the event that the absorber has a 1/y cross section, the integral yields an especially simple form this result is given in Eqs. (4.245) and (4.246). The absorption cross section 

An appropriate definition of the thermal flux which is consistent with the thermal-cross section formula is given by [cf. (4.204)] 

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A key parameter in determining the possibiUty of a self-sustained chain reaction is the value of k for an infinite medium, k. In the four-factor formula,... 

This relation is known as the four factor formula. In our case = 1.12. 

Papers 29 and 30 served as the basis for the earhest calculations of the multiplication constant in an infinite heterogeneous reactor. By early 1942, the significance of fast fission was recognized, and all later calculations included estimates of e, the fast effect. This gave the four-factor formula, k = rjepf rj being the number of neutrons released per neutron absorbed in U. The quantity actually calculated in the following reports was rj = (1/ep/), k = r /rj ... 

Since Fermi s early work on exponential experiments the design of reactors has depended heavily on the experimental determination of nuclear properties of multiplying assemblies in subcritical Or critical experiments. In thermal assemblies the nuclear properties studied have included macroscopic flux traverses, from which the material buckling can be obtained, and ratios related to quantities which enter into the four-factor formula for k. One ratio measured in uranium fueled assemblies is ... 

School Four- Factor Formula Other Approach Year Instruction Starts ... 

School Four-Factor Formula Ocher Approach Number of Courses Instructional ilqpp roach Experimental Technique HuSber of Requrats for Criticality Specialists Per Year... 

The relation between the 2200 m/s parameters and the measured atomic concentrations for a critical system wiir be related using a simple four-factor formula for criticality for the large critical system under consideration. 

OSie xieutron spectrum in N Reactor is less thermal than in the older Hanford reactors. A question thus arises in the use of the classical Fermi picture of the neutron cycle In spite of thls> the familiar Fermi four-factor formula for the multiplication factor of an Infinite lattice is assumed valid for N Reactor and appropriate modifications are made in the definitions to Insure that all neu-tronlc processes are properly accounted for The Fermi formula is... 

This equation is referred to as the four-factor formula and is the extension of (3.22) to the muUivelodty reactor. Again it must be mentioned that (4.275) is useful only if e can be easily estimated in general (4.273) or (4.266) is to be applied. To summarize, then, we use the relation... 

The four-factor formula (4.275) may be given a simple physical interpretation. First we note that in the case of a critical system ly so that... 

Reference (NRC97) UWNR OTM, Reactor Physics I, Four Factor Formula ... 

The changes in concentration of the uranium and plutonium isotopes naturally lead to a change in the reactivity of the reactor as burn-up proceeds. In the four-factor formula for the infinite multiplication factor, = rjepf, the parameters s and p do not change significantly with bura-up for a natural uranium reactor, since both are functions of the concentration of which remains approximately constant. The reactivity change therefore depends on the variation of the product rjf The overall reactivity for a natural uranium system as a function of irradiation, and the main components giving rise to the total, are illustrated in Fig. 4.4. 

The threshold reaction contributions to the total fission rate can be assumed small for the AGN-201 reactor, since its moderator-to-uranium volume ratio is appreciable and its fuel is enriched with the isotope. Very fast fission is normally accounted for in the four-factor formula by the factor e, the number of neutrons produced by all fissions divided by the number produced by thermal fission. In the AGN-201, nonthermal fission is predominately resonance fission, since has finite fission cross sections at all energies. The amount of epithermal fission can be determined by a simple cadmium-ratio measurement of AGN-201-type fuel. The fission product activity of a bare and cadmium-covered fuel sample can be counted on a proportional counter after two similar irradiations in the reactor core. Their ratio will yield the amount of nonthermal fission to total fission after proper corrections for differences of sample weight, irradiation times, and, power level have been made. The final expression for power level then becomes, . . f... 

Qualitatively discuss the effect of temperature changes (in the region of room temperature) on the factors of the four-factor formula. 

Which factor in the four-factor formulas is changed when an absorber is placed in a critical reactor, and why ... 

On the average, in a critical reactor, one of the neutrons born in a fission event must cause another fission. From a consideration of this fission chain or cycle, the following important reactor (four-factor) formula is readily developed ... 

As the fuel enrichment is increased, it becomes more difficult to fit the four-factor-formula analysis to the evaluation of k g, because the separation of neutron events into the characteristic energy groups is not clear. 

The nonfission capture of is the significant contribution to one of the four factors of the four-factor formula. Which one, and what is the nature of the contribution ... 

In the exponential experiment the material buckling for a critical reactor of the same composition and structure was measured. Calculations can now be made to determine L, L, , or k if any two of these parameters are known. The infinite reproduction, koo, is a function of the material of which the reactor is made and equals "nepf, as given by the "four-factor formula." Here,... 

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