Delayed-neutron groups

The nuclear reactor kinetics was modelled using simple point kinetics. The point kinetics model utilised in the calculation was developed as an analogue to the point kinetics module of the RELAP5 code. The number of delayed neutron groups considered was six. A Doppler feedback coefficient of -0.0095 was used. Xenon feedback was also modelled, although due to the time scales considered in this document the xenon feedback is not relevant and has almost no impact on the results. 

To give another example, the number of delayed neutron groups for thermal fission of uranium-235 could be reduced from six to three by combining groups 3, 4, 5 and 6 = 0.005247 and X3 = 0.2463,... 

The problem is separable for a bare homogeneous reactor. However, only the case of a step input of reactivity, i.e., the case of a constant value of p, is easily solved. In this case, the kinetic equations are readily reduced to a second order (for the case of one delayed neutron group) homogeneous linear differential equation with constant coefficients. For an input of positive reactivity two solutions arise, of the form and where o>i > 0 and 0)2 < 0. The first solution controls the persisting exponential rise of the flux, where it is recalled that T = l/o>i is the reactor period, and the second solution which rapidly becomes small is called the transient solution. 

In the case of a ramp insertion of reactivity and one delayed neutron group the mathematical problem reduces to the consideration of an equation of the form... 

Cylindrical reactor with source. An attempt is made here to describe the kinetics of a homogeneous cylindrical reactor with a point source of fast neutrons located at an arbitrary interior point on the axis of the reactor. The theory developed is quite general, at least to the extent that five delayed neutron groups are taken into consideration and appropriate ages are assigned to the source neutrons, the prompt fission neutrons, and each of five groups of delayed fission neutrons. Application of the theory is made to the problem of the determination of the power level in a so-called zero power critical assembly. 

Measurement of reactor period with correlation to one and six delayed neutron groups. 

Power decay and delayed neutron group measurements. 

The kinetics problems of the second category are concerned with the influence of the reactor temperature on the time-dependent behavior of the neutron flux and on the power generation. The phenomena of interest here are again short-term effects, and the importance of the delayed-neutron groups in establishing dynamically stable systems is discussed. The analytical models used in these treatments draw principally from the so-called Stein model. ... 

TWINKLE is a multidimensional spatial neutron kinetics code, whieh is patterned after steady-state codes currently used for reactor core design. The code uses an implicit finite-difference method to solve the two-group transient neutron diffusion equations in one, two, and three dimensions. The code uses six delayed neutron groups and contains a detailed multi-region fuel-clad-coolant heat transfer model for calculating point-wise Doppler and moderator feedback effects. The code handles up to 2000 spatial points and performs its own steady-state initialisation. Aside from basic cross-section data and thermal-hydraulic parameters, the code accepts as input basic driving functions, such as inlet temperature, pressure, flow, boron concentration, control rod motion, and others. Various edits are provided (for example, channel-wise power, axial offset, enthalpy, volumetric surge, point-wise power, and fuel temperatures). 

In-Hour - (ih or IK) - A measure of reactivity. If zero reactivity is defined as that reactivity which causes the reactor to operate with constant power (infinite period) a reactivity of one inhour will result in a stable period of one hour. For a reactor which is very nearly critical (long period), the reactivity in inhours is the reciprocal of the period in hours. For wider departures from critical (shorter periods) the Inverse period does not hold because of the delayed neutron groups. Since the delayed neutron makeup of a production reactor is exposure dependent, the "inhour" is a somewhat elastic unit. 

As explained in Chapter 2, the delayed neutrons are not emitted from the direct products of the fission, but from nuclei which are formed by subsequent jS decay of these products. While many of the delayed neutron precursors have been identified, it is more convenient in practice to analyze the time behavior of the delayed neutrons by an empirical division into a number of groups, each characterized by a single decay constant, or half-life. It is found that the characteristics of the delayed neutrons from all the fissionable isotopes of interest can be adequately described by the use of six groups. The half-lives and yields of the delayed neutron groups for the fissile isotopes and Pu, and for the fertile isotope are sum-... 

In specifying the source term here, separate account has to be taken of the contributions of prompt and delayed neutrons. For accurate analysis of the time variance of the flux, the fractional yields and half-lives of the six delayed neutron groups have to be fed into the source term. The method of solution is given in many reactor physics texts, and will not be repeated here. To illustrate the time behavior predicted by the solution, we may consider a reactor where, starting from an initially critical condition, the reactivity is suddenly increased from zero to a small positive value, such as p = 0.001. Assuming six delayed neutron groups, the time dependence of the flux after the reactivity increase is given by an expression of the form... 

Fissile Elements. Reactor activation of fissile elements and counting of the delayed neutrons emitted in the decay of short-lived fission products provides a very specific method of analysis. Unfortunately, in order to provide discrimination between the different fissile isotopes (or elements) it is necessary to irradiate the samples in two different flux spectra thus utilizing the differing rates of reaction of fast and thermal fission. Decay curve analysis is impractical because of the similarity of the half-lives of delayed neutron groups from all the fissile isotopes. 

The most common use of delayed neutron counting is the simultaneous determination of U and Th in rocks which, apart from the irradiation facility, requires little electronic equipment a 4—6 BFs detector array embedded in paraffin wax and a multiscaler system or a simple scaler are adequate. Brownlee has described the use of a sophisticated 40 BF3 detector array embedded in a 1.5 m diameter by 1.8 m long cylindrical graphite moderator stack. The system was used for the measurement of binary mixtures of fissile isotopes. Discrimination between isotopes was accomplished by analysis of decay curves in order to estimate delayed neutron group yields. The method appears to have no advantages over the more conventional methods, although the potential for the analysis of more complex mixtures is perhaps greater. 

The condition (10) is hardly any restriction from a physical viewpoint, but on the other hand, (11) requires the kernel to be of a fairly special type. Theorem 4 has not so far been extended to an arbitrary number of delayed neutron groups. The following result, obtained by Smets (II), does however allow for several delayed neutron groups. 

A small sample of the fissile material is irradiated in a neutron flux9 to saturation of the delayed-neutron groups (which takes 6 min). Then the sample is suddenly ejected to a remote, well-shielded neutroncounting system, and the delayed-neutron emission as a function of time is determined. 

The neutron counts versus time are analyzed to obtain the delayed-neutron groups (periods and relative abundances) as follows The neutron counts less background are plotted as a function of time on semilog paper. A typical curve is shown in Fig. 15.2. The period of the longest group is apparent from the straight-line portion of the graph. 

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