Migration Area

The streaming correction to the age and dlflhslon area Cs can be estimated using Behren s formulas For example the effect of voids on the diffusion length of neutrons In the reactor may be calculated from the equation 

Q mean square chord length through the hole/square of the mean chord length  

The factor Q is dependent upon the shape of the hole and Is given in Reference l4. Modifications may be made to the equation to consider voids which are not uniformly oriented however, this is not necessazy for the N Reactor because of the symmetrical distribution of the axes of the voids. The above equation may be simplified to 

The calculated ratio of the squara of the diffusion length In a normal lattice to that of a condensed lattice (Ue without voids) Is 2 01 This magr compared with thesDqperloantaUy termlned ratio of mlgmtlon areas of 2 X. The calculated and measured values of l e diffusion length of the 

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  

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Normalize data to the original size of each spheroid recorded at f=0 (formula (migrated area at f = x/migrated area at f=0)xl00). 

The quantity + r is usually denoted by and is known as the migration area and M as the migration length ... 

A large homogeneous thermal reactor contains oidy dispersed in beryllium in the atomic ratio 1 3 X10. The migration area is 0.023 m. Assuming p — t = I, calculate the size of a cylindrical reactor with height equal to diameter. 

Among these C is undesirable because the radius of the pile would amount to about 60 cm, assuming a multiplication constant of 2.37 and a migration area corresponding to the age alone (i.e. assuming zero diffusion length for the thermals). Such a pile would contain far too much 23. Water is undesirable because the size of the pile would become too small so that one would run into... 

Wigner effect will be less pronounced. In the reactor actor, and M c is the migration area for neutrons in the... 

The subcadmium activation distributions were used in conjunction with cross sections computed by Westcott to calculate values of the thermal utilization f and the thermal migration area L in the usual way. A base value of V was calculated from Westcott values, assuming the neutron flux spectrum in the moderator to be Maxwellian at 2(PC. This value was then modified for flux hardening effects >y comparing the ratios of the 1/v activations (Cu and Mn) and the U-235 activations at various locations. Values of the fast fission factor < were obtained by comparing the fission product activities of natural and depleted uranium foils according to the technique described by Futch . The neutron age r was measured to indium resonance from isolated fuel assemblies in DjO. Corrections were calculated for the age to thermal energy and for lattice effects. 

Either ratio, Ra or pa, can be related to the resonance escape probability or the conversion ratio. Microscopic (intracellular) flux distributions can be measured, and values of disadvantage factors and thermal utilisation can be obtained from them, b lattices of slightly enriched uranium rods in ordinary water it has also been possible to determine, indirectly, the migration area or age, and thus to obtain an experimental link between the macroscopic and microscopic properties of such lattices. 

TABLE m. Comparison of Migration Areas (One Group Leakage Probability) with 0.387-in. Rods of 1.3% Enrichment... 

In the case of some measurements, it is possible to interpret the data in several different ways. For instance, measurements of migration area may be interpreted by age-diffusion, age, one group, or multigroup theory. Numerical values of M as computed by the different methods will vary coMiderably, although each will form a con-slstent set of reactor parameters in its own critical equation, hi addition, there appears to be agreement in values of M as measured by subcritical and by critical. methods. Thus, it is necessary to make any comparison between critical and subcritical experiments with a common theoretical interpretation. 

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

The measurements of k -l in the PCTR and those of from the mmonential piles have been compareif > by use of a calculated migration area M. The use of standard formulae for gave values of k -l from exponential bucklings which appeared to be systematically htyh by... 

Migration Area in Siightly-Enriched-UOj Light-Water-Moderated Lattices, M.Imai, T. Kami, and H. Kobayashi (Hitachi)... 

Using a one-group critical equation (with constant reflector savings assumed) migration areas of 44.6 cm in radial (M ) and 46.0 cm in axial direction (h were determined. Theoretical value for migration area for this lattice is 42.29 cm using Mercury code in which Deutsch s Method is used. ... 

The fundamental problem in nuclear criticality is the computation of neutron reaction rates in a multiplying assembly. The balance between reaction rates determines the behavior of the assembly. Simple formulas can be derived to illustrate this balance and the concepts of effective multiplication, migration area, and buckling.. ... 

Table I summarizes the results of these subcritical experiments. The systematic differences between static and pulsed determinations of k ff are probably due to the use of a calculated infinite-lattice migration area in k ff (static) and the presence of harmonic distortions in k f (pulsed). These differences decrease as the true critical condition is approached.

Then using one-group constants from ANL-5800, a value of Koo is calculated. From ANL-S800 a value of the extrapolation distance is obtained. This is used with the values of Em and sphere radius. obtained above to calculate an effective migration area. These constants are then used to calculate a value of Keff for the fuel plate holder. 

The local control strengths of the control rods Included in the table are defined as the change in buckling of a region with a cross sectional area of II90 In. (32 in. x 36 ln.) The migration areas listed gre those used to derive. the reactivity effect by the relationship k/k The full-... 

Refleoted core, one-veloeity (using migration area)... 

The strictly one-velocity calculations, methods 1 and 4, are seen to give much smaller critical radii than the others this indicates that the fast leakage is quite important in this system. Calculations 2 and 3 give identical results because of the large size of the bare core. It is interesting to note the comparative accuracy of the migration-area calculation, 5, which predicts, in this case, very nearly the same result as the two-group method. 

Once these factors have been determined, the remaining problem is to compute L and r since these quantities establish the neutron-leakage rates for the finite system. A first approximation to L has already been given, and a few remarks have been made about corrections for directional effects. Some methods have been developed for including anisotropic effects in the computation of the migration area, and these are reported in a subsequent section. 

Effects of Cavities and Fuel Lumps on Migration Area... 

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