17.4.1 Sensitivity to Infinite-Dilution Cross Section

Core characteristics such as keff, power distribution, and control rod worth are calculated by using effective cross section in deterministic methods. Sensitivities are usually calculated by using sensitivity calculation codes such as SAGEP [9], SAGEP-T [10], and SAINT [11]. However, the sensitivities are for relative changes of effective cross sections. Here we derive a calculation method of sensitivities relative to infinite-dilution cross sections for fast reactor analysis. Usually the effective cross sections are calculated by using the Bondarenko self-shielding factor method, the subgroup method. In that method the effective cross sections are expressed by the infinite-dilution cross section and the self-shielding factors f

e = f • о (17.10)

The self-shielding factors depend on the background cross section and temperature. The background cross section for nuclide i’ in a homogeneous medium is calculated by the formula

where Nk is the atomic number density of light nuclide к and ф is the microscopic total cross section. The sensitivity coefficient is defined by the relative changes of the core characteristics caused by the relative changes of the cross sections. Here we
consider the following two sensitivities, the sensitivity S, which results from the relative change of the infinite-dilution cross sections, and the approximate sensi­tivity S, which is the result of the relative change of the effective cross sections. From Eq. (17.10), the change of the effective cross section can be expressed by

ds df da

s f + a

Therefore, the improved sensitivity is expressed by using the approximate sensi­tivity as follows:

S ^ dR/R = dR/R / + df /f do/a ds/s da/a

Sensitivities and cross sections are dependent on nuclides, reaction types (such as fission, capture, and scattering), and energy groups. Here we consider the case where there is a perturbation in a of nuclide i, reaction type j, in energy group g. This perturbation causes a change in the self-shielding factorf of nuclide i’, reaction j’, in energy group g’. The second term of the right-hand side of Eq. (17.14) has to cover the contributions for all nuclides i’, reaction types j’, in energy groups g’; therefore, we have to take the summation over i‘, j’, and g’. The sensitivity for the nuclide i, reaction type j, in energy group g is given by

The first term is the direct contribution to S; it can be calculated using the conventional tools evaluating sensitivity coefficients such as SAGEP, SAGEP-T, and SAINT. The second term represents the indirect contribution through the change of self-shielding factor. These coefficients can be calculated as follows: here we apply the resonance approximation for heavy nuclides, which is suitable for treating fast reactors with hard neutron spectra rather than light water reactors. The self-shielding effect depends on the neutron spectrum; where the neutron spectrum for the heavy nuclide i0 is written as

Equation (17.15) indicates that when alt (E) and a‘b change by the same factor, the neutron spectrum remains the same; this shows that the ratio h has an effect on the neutron spectrum, and also on the self-shielding factor. Following a similar method [12], the coefficient in the second term of the right-hand side of Eq. (17.14) is called TERM and can be written as
where the derivative of f to a is calculated by

f (hi:) fj’ (ab + ДО!) — fi’ (ab0)

3a(

Utilization of borated water may not be feasible if the water issue cannot be remedied. An alternative may be subcriticality monitoring. It is necessary to detect the signs of approach to the critical condition across the defense line set in the subcritical region in Fig. 21.4, and an intervention measure must be deployed quickly before the critical condition is reached. Detection may be possible by setting neutron counters near the fuel debris.

There are key natures of the intervention measure to be understood. The injec­tion of neutron poison is the only way, and it will be realistic only if the actual condition of fuel debris is far from critical condition. It will be, however, difficult to make the defense line effective if the buffer zone is small. To retain the effect of intervention even after the event, the neutron poison concentration must be maintained in the coolant water.

Large

voume

Dry process

Boration

(235U/U enrichment., bum-up, density, water content, temperature, etc.)

Fig. 21.3 Prevention of criticality by boration or dry process

Thus, this option does not differ, essentially, from the first option, which is prevention of criticality by poison. Monitoring still makes sense if we integrate it with the first option and use it as an implementation of the “double contingency principle.”

The results of the “Fundamental literacy for members of society” questionnaire are summarized in this section. Responses were obtained from a total of 42 students (Enshu I): responses from 10 of the 12 students registered for the course; Introduc­tion to Debate (first semester): 26 of the 27 students; Introduction to Debate (second semester): 6 of the 8 students. The composition of the classes was as follows: Enshu 1: third — and fourth-year female students; Introduction to Debate (first semester) and Introduction to Debate (second semester): second — and third-year female and male students. Because the sample was small, no comparison of data based on gender and year of study was made; instead, the results of the group as a whole is shown (see Fig. 25.1 and Table 25.1).

To gain a firm understanding of the disposal of high-level radioactive waste, and to be able to consider the issues, requires specialist knowledge as well as critical and logical thinking skills. In this respect, the overall results of the questionnaire were positive, but the scores were particularly high for items

30

25

С0 CD CO

20

CO

CD

15

CD

_Q

10

z

5

15, 16, and 17 (that is, Specialist knowledge and Skills, Logical thinking Ability, and Critical thinking ability). The results overall indicated that debate can be an effective activity for shedding light into, and for examining, social issues that require specific background knowledge and judgment.

In this section we define the effective transmutation rate and transmutation half-life that represent performance of a transmuter in the case of a phase-out scenario. A transmutation amount after an in-core period of Tin years is

Here, the effective transmutation rate, Л^, is transmuted amount divided by initial amount and time needed for transmutation including out-core period.

where,

Because a can be regarded as constant for Pu-transmuters, Лц. is determined by operation efficiency, eo, cycle efficiency, ec, and specific heat, h. A time evolution of amount of heavy metal after introducing transmuters is expressed as

dW Ull 2

— = — AtrW, w = W0e ^ , Ttr = —

dt Atr

where TtI is a transmutation half-life. In the phase-out scenario, there is heavy metal of w0t when transmuters are employed in full scale. Ttr means a period needed to transmute half of w0 in the case that the maximum number of transmuters are introduced. Another fact is that Atr and Ttr depend on two parameters relating to operation time efficiency and one fundamental core parameter, h. The thermal output of core affects a number of transmuters, but not transmutation behavior in the mass-flow analysis.

To prepare for further increase of the demand for primary energy and to stop global warming by reducing CO2 emissions into the air, we need to develop renewable energy as well as nuclear energy.

others

34%Warming of the climate system is unequivocal, and since the 1950s, many of the observed changes are unprecedented over decades to millennia. The atmosphere and ocean have warmed, the amounts of snow and ice have diminished, sea level has risen, and the concentrations of greenhouse gases have increased.

Professor Akimasa Sumi and his collaborators have carried out computer simulations using climate models for many years.

According to their results, it seems very very clear that the anthropological emission of greenhouse gases (mainly CO2) is a main contributor to global warming.

We must stop the emission of CO2 to avoid global warming.

A known amount of I_ or IO3~ was added to 1 g pine bark, representative of tree samples taken at the establishment of the Japan Atomic Energy Agency, and the bark was put in a wet oxygen gas line set in an electric furnace. Because smoking was observed with noncontrolled temperature increase, especially around 240 °C, the rate of temperature increase in the range from 100 °C to 300 °C was controlled by steps and slow. The vaporized I was trapped in three steps of 20 ml 2 % TMAH solution. Because insoluble organic material was deposited in the gas line and the trap, an oxidant (8.2 g hopcalite II) was set between the sample and traps to decompose it (Fig. 27.2). The temperature of the oxidant was set to 500 °C before the temperature increase of the pine bark sample. The temperature of the sample was kept at 500 °C for 1 h and then increased to 900 °C for 1 h to vaporize iodine species in the sample. The extracted I in the traps was measured by DRC-ICP-MS.

This chapter describes specifications for selection of a uranium-free TRU metallic core and performance of the uranium-free TRU metallic core. Then, the core and fuel are developed on the basis of those results and the feasibility of the developed core is evaluated.

15.4.1 Specification Selected for Uranium-Free TRU Metallic Core

On the basis of the results of the parametric surveys, the uranium-free TRU burning core was specified as shown in Table 15.3 and Fig. 15.5. TRU-Zr alloy fuel pins and BeO pins were employed to enhance the Doppler coefficient. The reason for adopting the TRU-Zr alloy fuel is to use a simpler fuel fabrication method, that is, injection casting, in contrast to a TRU-Zr particle fuel in a zirconium metal matrix. Then, the zirconium content in TRU-Zr alloy was assumed to be limited below 35 wt% to keep the melting point of the TRU-Zr alloy below 1,200 °C to prevent Am vaporization during injection casting [19]. The fuel pins and the BeO pins were separately located in the fuel subassemblies (Fig. 15.6). The diameter of fuel pins was reduced from 0.65 to 0.48 cm to compensate for the increase of the average linear heat rate caused by employment of the BeO pins. Core height is 65 cm to reduce burn-up reactivity swing, whereas the core diameter was increased from 180 to 250 cm to keep the linear heat rate of the fuel pin similar to the 93-cm- height core. The operation cycle length is 150 days, which can be controlled by conventional control rods and fixed neutron absorbers.

О Neutron shield 294

A sensitivity coefficient is defined as the ratio of the variation in concentration of the target activation product to the variation in the initial composition or cross section. The sensitivity coefficient of the initial composition and cross section is expressed by the following equations, respectively:

W0: Concentration of the target activation product under normal condition AW(=W0 — W0): Variation in concentration of the target activation product X0: Initial concentration of the element in the material under normal condition AX(=X’ — X0): Variation in initial concentration of the element in the material o0: Cross section under normal condition Aff(=ff’ — o0): Variation in cross section

For the calculation of concentration of activation products, ORIGEN2.2 was used with ORLIBJ40 [2], which is a set of the one-group cross-section libraries based on JENDL-4.0 [3]. The sensitivity coefficients are evaluated by executing two different burn-up calculations under normal condition and under composition — changed or cross-section-changed condition. In the former, the ORIGEN2.2 input files are changed; in the latter, the cross-section library files are changed. Utility programs to evaluate the sensitivity coefficients were prepared and used in these analyses.

In September 2010 the Science Council of Japan (SCJ) received a deliberation request from the Chairman of the Japan Atomic Energy Commission, and SCJ formed a Review Committee for Disposal of High-Level Radioactive Waste. The author participated in the Review Committee as a member of SCJ. The Review

Committee made a Reply on Disposal of High-Level Radioactive Waste [3] in September 2012.

The Review Committee of SCJ pointed out the following six proposals to search for a path toward consensus formation: (1) fundamental reconsideration of policies related to disposal of HLW with extended definition, which includes spent nuclear fuels as well as vitrified HLW canisters; (2) awareness of the limits of scientific and technical abilities and securing scientific autonomy; (3) rebuilding a policy frame­work centered on temporal safe storage and management of the total amount of HLW; (4) necessity of persuasive policy decision procedures for fairness of bur­dens; (5) necessity of multiple-stage consensus formation by establishing opportu­nities for debate; and (6) awareness that long-term persistent undertakings are necessary for problem resolution.

Considering the SCJ report, the Japan Atomic Energy Commission, however, expressed its intention to maintain a policy of implementing the geological disposal on December 2012 with extension of the scope to include the direct disposal of spent nuclear fuel [4].

To calculate reliable MA transmutation rates, it is important to evaluate the uncertainty of calculated MA transmutation rates. The uncertainty can be calculated when the sensitivity of the MA transmutation rates to the cross sections called burn — up sensitivity is known. Therefore, we developed a calculation code of burn-up sensitivity based on the generalized perturbation theory [9]. The burn-up sensitivity S relative to effective cross sections is calculated by

In Eq. (17.18), the term containing |S is called the direct term; the second term is the number density term, which represents the effect of the change of nuclide number densities caused by cross-section changes; the third term shows the effect of the change of flux from to cross-section changes; the fourth term shows the effect of the change of adjoint flux caused by cross-section changes, and the last term shows the effect of constant power production even when there are cross-section changes. The adjoint number density N* is calculated from the end of a burn-up period to the beginning of the period, and the generalized flux and generalized adjoint flux are calculated at each burn-up step. The adjoint number density N* is not continuous but has a discontinuity at each burn-up step. To calculate true burn-up sensitivities S relative to infinite-dilution cross sections, we introduce S to Eq. (17.14) to obtain S.