Neutron Inventory

Of the fast neutrons produced in fission, some of them will be moderated to thermal energies and will induce other fission reactions while others will be lost. The ratio of the number of neutrons in the next generation to that in the previous generation is called the multiplication factor k. If the value of k is less than 1, then the reactor is subcritical and the fission process is not self-sustaining. If the value of k is greater than 1, then the number of fissions will accelerate with time and the reactor is supercritical. The goal of reactor operation is to maintain the system in a critical state with k exactly equal to 1. The extreme upper limit for the multiplication factor would correspond to the mean number of neutrons per fission ( 2.5 for 235U(n,f)) if each neutron produces a secondary fission. 

This scenario is impossible to attain and, in fact, the neutron inventory must be carefully monitored in order to maintain a critical reactor. 

Given that the number of neutrons emitted per fission event v = 2.5 for the fission of 235U, one would think that designing a system with k = 1 would be easy however, there are many ways in which neutrons can be lost. Fust of all, the core of the reactor that contains the fuel must be finite in size. Therefore, there will be a limit or edge of the core from which some neutrons can escape. Neutrons can be reflected back into the core by a layer of material such as graphite (low-absorption cross section and higher mass) that surrounds the core, but the reflection is not complete. 

The multiplication factor for an infinite sized reactor core is given by the four-factor formula  

For safe operation of the reactor, k must be exactly unity. That is difficult to achieve in practice. In fact, if the mean time between generations of neutrons is t, 

---

Tritium is also produced in ternary fission and by neutron-induced reactions with 6Li and 10B. Tritium is a very low energy (3 emitter with a half-life of 12.33 y. The global inventory of naturally produced tritium is 9.6 x 1017 Bq. Tritium is readily incorporated in water and is removed from the atmosphere by rain or snow. Its residence time in the stratosphere is 2-3 y after reaching the troposphere it is removed in 1-2 months. The natural concentration of 3H in streams and freshwater is 10 pCi/L. 

The inventory of this stable nuclide is based on its atmospheric inventory, which includes an appreciable contribution from crustal degassing of He. Based on atmospheric Kr/Kr ratio of (5.2 0.4) X 10. Based on atmospheric Ar/Ar ratio of (0.107 0.004) dpm 1 Ar (STP). Includes a rough estimate of C1 produced by the capture of neutrons at the Earth s surface. 

Calcium-41 Ca-41 is produced by neutron activation of natural Ca-40. It has been found to exceed the GQ by a factor of 2 in both graphite fuel struts and desiccant from HNA (3 streams). The reported desiccant value is an upper limit probably based on trace contamination by graphite dust. In decommissioning wastes, activation of the concrete bioshield would also be expected to produce Ca-41 but these wastes streams are regarded as low level wastes in the NIREX inventory and hence GQ values do not apply. Measurements of Ca-41 can be obtained after chemical separation of Ca, which is done routinely for Ca-45 measurements. After any Ca-45 (t 14 =163 days) has decayed away, it can be measured by liquid scintillation counting. Procurement of direct standards from NPL would be required. In fresh samples, if the Ca-45 has been measured, then the Ca-41 could be estimated by comparison of activation... 

Actinides in the environment can be classified into two groups (i) the uranium and thorium series of radionuclides in the natural environment and (ii) neptunium, plutonium, americium and curium which are formed in a nuclear reactor during the neutron bombardment of uranium through a series of neutron capture and radioactive decay reactions. Transuranics thus produced have been spread widely in the atmosphere, geosphere and aquatic environment on the earth, as a result of nuclear bomb tests in the atmosphere, and accidental release from nuclear facilities (Sakanoue, 1987). Most of these radionuclide inventories have deposited in the northern hemisphere following the tests conducted by the United States and the Soviet Union. 

To illustrate, we shall consider a 1000-MWe PWR with the same core composition and power density as the reactor described in Chap. 3. The in-core inventory of water is approximately 13,400 kg. The tritium produced by H(n, y) during one calendar year in an average thermal-neutron flux of 3.5 X 10 n/(cm -s) with an effective H(n, y) cross section of 3.35 X 10- b is... 

Inventory of D2O moderator in reactor core = 7.72 X 10 g Average thermal-neutron flux in moderator = 1.01 X 10 n/(cm -s)... 

Criticality. The process plant is designed on the principle of safe geometry under all conditions (e.g., the use of HARP tanks). Continuous monitoring is provided by an approved criticality detection and alarm system. Where additional operational control is required to maintain safe conditions, this is specified in the appropriate nuclear safety assessments and Criticality Clearance Certificate. The latter specifies limits and conditions that need to be complied with during operations for example, in respect of limited tap density, moisture content, isotopic inventory and mass. It identifies any systems or instrumentation that demonstrate that compliance is maintained during operation. In addition key points of the plant are monitored by neutron monitors to give early warning of the unanticipated build-up of solid plutonium which could lead to the development of unsafe conditions. 

---