Neutron speed

A more advanced design is the plutonium-fuelled fast reactor, where the higher neutron speed permitted by avoiding thermalization means that slightly more neutrons are produced at each fission event. 

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 ... 

The neutron flux is the product of the number of neutrons per unit volume and the neutron speed. It has the physical significance of being the total distance traveled in unit time by all the neutrons present in unit volume. It seems reasonable that the rate of reaction of neutrons should be proportional to the distance they travel in unit time. The flux has the dimensions of neutrons pet square centimeter per second. Typical values of the flux in nuclear reactors range from around lO" to 10 n/(cm -s). 

The neutron kinetic energy E is related to the neutron speed by... 

Dimensionless flux distributions may be obtained by multiplying the neutron density distributions by the neutron speed ratio v/vo ... 

If the cross section is one that varies inversely with the neutron speed, as in the case with many of the absorption cross sections, then... 

The factor g is called the non-1 /u correction factor. It becomes greater than unity for a cross section that decreases with increasing neutron speed less rapidly then 1 /u, and it becomes less than unity when the cross section decreases more rapidly than 1 /v. 

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... 

Thus, if V is known, the reaction rate is proportional to the total neutron flux (f>. For example, for the commonly encountered Maxwell-Boltzmann distribution of thermal neutrons, v = Iv / fir, where Vp is the most probable neutron speed. 

If the moderator temperature is now raised, changes in overall reaction rate can be expected because the neutron speeds are changed and resonances do not preserve the overall reaction rate. The high RBMK graphite temperature is imposed to secure favourable resonance effects. 

The term p in the operator (r contributes the term —pn to the neutron equation. This term is the same as (—p/v) nv where v is the neutron speed, and is equivalent to an absorption of neutrons by a l/v absorber. It has been called the time absorption term. 

These devices make the wavelength-band selection by taking advantage of measuring the neutron flight time selectors and choppers are usually chosen if the desired band is fairly wide. A typical thermal neutron speed is about 2,000 m/s, which means that it takes about 5 X 10 s for a neutron to travel 1 m this, in turn, makes it possible to determine the time-of-flight very accurately over just a few meters. 

For thermal neutrons, the absorption cross section is usually inversely proportional to the neutron speed ( 1/v law), andO Eq. (30.1) is reduced to the simple product ... 

Carbon fiber can prevent atom radiation and reduce neutron speed ... 

This is not strictly true because the nuclei themselves are in motion, but in many problems the neutron speeds are very great, and nuclear motion can be neglected in comparison. 

Note that we have retained the specification of the neutron speed in defining the microscopic cross section a(v). This is in keeping with our recognition of the fact that the neutron cross sections are in general a function of the neutron speed (cf. Sec. 2.4a). 

A statement of the neutron-balance condition involves the collision densities of the various possible neutron-nucleus reactions. The collision densities, in turn, may be described in terms of the neutron densities and the appropriate cross sections [cf. Eq. (3.5)]. Although the neutron density n is the fundamental quantity which describes the neutron population, it is frequently more convenient in reactor calculations to work with another function, called the neutron flux. The neutron flux 0 is related to the neutron density through the definition (y = neutron speed)... 

We conclude the present chapter with a few remarks on the units of measure for neutron flux and collision density. It is customary to specify neutron densities in neutrons/cm thus, if the neutron speed is given in cm/sec, the flux has the units neutrons/cm /sec. Likewise if, as is the custom, the neutron microscopic cross sections are given in square centimeters and the nuclear densities in nuclei/cm , then the macroscopic cross sections Z are given in cm" and the collision densities in collisions/cmVs We can obtain some idea of the magnitudes of... 

The slowing-down density may also be defined in terms of the neutron speed or lethargy. As in the case of the neutron cross sections [cf. Eq. (4.59)],... 

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