Neutron cycle

Neutron cycle is die average life history of a neutron m a nuclear reactor. The gain in the number of neutrons in a reactor during any individual neutron cycle ts given by n(k-1). where n is the number of neutrons in the reactor of the beginning of the cycle and k is the multiplication factor. 

Pu) of thermal absorption cross section a , and Ng atoms of fertile material ( U or Th) of thermal absorption cross section Og. For this model we shall develop expressions for the number of neutrons produced or absorbed at any point in the neutron cycle per unit volume per unit time. Assume that the fissionable material absorbs only thermal neutrons. The rate of... 

FIG. 19.6. The neutron cycle in a thennal reactor. The number of neutrons for 100 in first generation are given in circles (data from an old Belgian research reactor, BRl). 

The mean lifetime 6 for a neutron in a reactor is the time it takes on the average for the neutrons to complete one loop in the neutron cycle. In thermal reactors 6 is 10 — 10 s due to the comparatively low speed of thermalized neutrons and average distance in the moderator covered by random walk when travelling from and to a fuel pin. For each loop the number of neutrons is multiplied by a factor k f. Since one neutron is used for maintaining the chain reaction, the neutrons in the reactor change with time according to... 

The new fast neutrons resulting from the fissions in the isotope U pass through the same neutronic cycle as just described, there being a certain proportion that 55 will produce fast fission, some that will be lost to the chain reaction, and others that will reach thermal energy and be absorbed in the uranium. 

As a final comment, the importance interpretation of the adjoint function may be used to write the adjoint equation by similar physical reasoning as is used to write the equation for the neutron density n. Thus the importance of a particular neutron is the same as the total importance of the neutron distribution that results from the original neutron at any later stage in the neutron cycle. Stating this relation in mathematical form results in a correct equation for the adjoint function m. 

In order to maintain a chain reaction, k has to be at least one. A state of the reactor with fc > 1 is called supercritical. For every generation of neutrons the reactor power increases by the factor k. The duration of a generation is the average time span between the birth of a neutron and its capture. This time span in a thermal reactor is mainly determined by the time it takes the neutron to be moderated down to thermal energy (usually about 40 ps, see Sect. 57.3.2) and to diffuse to an absorption site. In a state of exactly fc = 1 the reactor is called critical. The reactor power is constant. A state with fc < 1 is called subcritical. This topic will be discussed further below (reactor dynamics). The neutron cycle includes a number of steps that have been partly studied already but that will be discussed here in the context of a full neutron cycle. 

The evolution of the generated power after a change in the reactivity is an important point for the control of nuclear reactors. For this purpose, the duration of a neutron generation, i.e., the average lifetime t of a neutron (from its formation in fission until its capture) is important. Values for these neutron cycles in different types of fission assemblies are given in Table 57.6. 

Average time of neutron cycle in different fission assemblies... 

The time of the neutron cycle in the thermal reactor is mainly determined by the time required to bring the neutrons to thermal energy. This requirement does not exist in the fast reactor and in nuclear weapons. Therefore the cycle times are shorter in these two latter cases. 

At every pass of the neutron cycle the number of neutrons (and so the power of the reactor) changes by the factor k. Hence, the change in the absolute number of neutrons per unit of time (dMdt) is... 

The quantity t/(fc — 1) is usually called the reactor period. It is given by the time of the neutron cycle (t), which is a constant for a given reactor and is determined mainly by the properties of the moderator. It is also determined by the criticality value k that varies, e.g., as a function of the position of the control rods. 

A nuclear weapon is a fission assembly with a very short neutron cycle time t = 10 s. The criticality factor in a fission weapon is near k=2. From these parameters and Eq. (57.34) it can be easily estimated that the fission reaction in a bomb is over in less than 10 s. 

Evolution of the reactor power with time (in units of the time span r of the neutron cycle)... 

A fission bomb is a homogeneous reactor of metallic or Pu that can reach a very high reactivity (criticality factor k= 1.5 to 2 see O Sect. 57.3.5) and possesses a very short neutron cycle time (t = 10 to 10 s, seeO Sect. 57.3.6). 

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... 

Ansver When acre than one neutron becones sivailable to continue the fission in each neutron cycle o The reaction viU accelerate at a rate which depends on how many spare neutrons are created each generation In addition to those needed to continue the chain reaction. 

During the neutron cycle from one generation to the next, several processes occur that may increase or decrease the available number of neutrons. Which ONE of the following factors describes an INCREASE in the number of neutrons during the cycle ... 

A. Estimated Conversion Ratio 1 This method is derived from an analysis of the neutron cycle starting with a neutron entering the resonance region, although one could start anywhere in the cycle. The situation is described in Fig. 14.9. 

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