Average neutron density

Since, from equation (21.33), the neutron flux is proportional to the neutron density, it follows that the radially averaged neutron density at any height, n fz), will bear the same relationship to the average neutron... 

Since the neutronics equations (21.24) and (21.28) will produce a value for average neutron density over the core as a whole rather than the maximum, centreline density, we need to convert equation (21.42) into an equivalent expression involving the average neutron density, n. This may be found by averaging over the whole height of the reactor ... 

This distribution equation, which allows us to calculate the axial distribution of neutron density from the core-average neutron density, n, is assumed to hold transiently as well as in the steady state. 

It is possible to estimate the average neutron density within the ith segment simply as half the sum of the radial-average neutron densities at heights iL/N and (i- )L/N ... 

The assumption inherent in equation (21.47) is that the variation in neutron density over the segment is linear. In fact, we know that its shape within the segment will actually be determined by the cosine function given by equation (21.45). We may use this fact to improve the estimate of the segment s average neutron density, which should follow an averaging equation similar to equation (21.43) ... 

Substituting from equation (21.44) into (21.48) and rearranging gives the average neutron density over... 

Table 21.3 Ratio of neutron density in segment to average neutron density over reactor core...

Hence for a typical core-average neutron density, n = 1.6 X 10, the core-average power density is f =... 

Using the average neutron densities of Fig. 19 for the n, we find = 1.116 this may be compared with 1.100 in the two region comparison system. 

The lattice spacing is not a critical quantity in the second arrangement. Of course, the total amounts of heavy water, beryllium, and solvent must be kept in such limits as can be obtained from Table I. In addition, one will not want the neutron density in the moderator to exceed substantially the neutron density in the solution. If zero < 1, the neutron density at the tube wall will be less than 10% higher than the average neutron density in the tube. Since K =. 2 for both the Bi and the fluorocarbon solution of Table I, this only gives ro < 5 cm. The ratio of the neutron density difference between surface of cell and surface of tube, divided by the density at the tube is... 

Herein d = ni/no is called the overall disadvantage factor it is the ratio of the average neutron densities in moderator and U. Similarly, ds = ni/us is the disadvantage factor of the surface of the lump. Mq is the total mass of the lump, and... 

Relay coil 206 then operates to cause armature 210 to connect with contact 215, thus reversing the motor 221 to drive the control rod into the reactor to a point where the neutron density starts to decay. The control rod 90, gg will thereafter hunt between a point above the balance position where the neutron density rises, and a point below the balance position where the neutron density decays, thus providing an average neutron density within the reactor as determined by the setting of slider 203 on resistor 205. As the mass of the reactor causes any temperature change to lag behind any neutron density change, the temperature of the reactor is maintained substantially constant. If desired, any of the well-known anti-hunting circuits may be utilized, as will be apparent to those... 

Then using the expressions for the averaged (n, 7) and (7, n) processes one sees that the most abundant isotopes in different isotopic chains have approximately the same separation energy of about 2-3 MeV for r-process conditions. Later network calculations get the equilibrium at neutron density greater than 1020cto 3. 

The neutron flux is the product of the neutron density and the neutron speed. Assuming that all the neutrons are travelling at the same speed, equal to the average speed, c , the reactor flux averaged over the complete core, Xavf> neutrons/mVs will be the product ... 

Hence at a moderator temperature of 310°C/S83K, = 128 X V583 = 3091 m/s. Substituting into equation (21.33) gives the relationship between neutron density, n, and average power density, at the start of core life as... 

For a typical neutron density of n = 1.6 x 10 neu-trons/m, the average power density emerges as =... 

Since the speed of the thermalized neutrons depends only on moderator temperature, the same average speed of 3091 m/s holds. Thus the relationship between neutron density and power density at the end of life is... 

This expression assumes equal distributions for protons and neutrons, or alternatively an averaged nucleon density. The nucleon density, nuc( )> generally representable for every nucleus a as... 

This figure illustrates immediately one of the disadvantages of batch fuel management. The power density, which is proportional to the product of the neutron flux and the fissile material concentration, is just as nonuniform as the neutron flux. If the local power density must be kept below some safe upper limit, to keep from overheating the fuel or cladding, only the fuel at the center of the reactor can be allowed to reach this power density, and fuel at all other points wiU be operating at much lower output. In a typical uniformly fueled and poisoned water-moderated reactor, the ratio of peak to average power density is over 3, so that the reactor puts out only one-third as much heat as it could if the power density were uniform. 

Equation 14.3 shows that the reaction is proportional to the total neutron density. BFj counters are most frequently used for the detection of thermal neutrons, for which one can calculate an average neutron speed v given by... 

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