Several codes were combined for ADS design (Fig. 19.1) containing proton transport, neutron transport, cross-section preparation, and depletion. The PHITS code  was used for transportation of protons and neutrons above the energy boundary of 20 MeV. Transportation of neutrons slowing down less than 20 MeV is interrupted, and position, direction, and energy are stored in a cutoff file. This file is processed as to be readable by the PARTISN code , which is a neutron transport code with multi-group theory. A 73-group cross section is prepared by SLAROM  code with the JENDL4.0  nuclear data library. A 1-group micro-cross section is calculated by multiplying the 73-group cross section to the 73-group flux from PARTISN. One-group micro-cross section and total flux is used in the ORIGEN2
Fig. 19.1 Calculation codes
code  to obtain material change after depletion. The material composition from ORIGEN2 is processed by a fuel control program that simulates reprocessing and fuel fabrication with adjustment of MA content ratio.
The NMB code  was employed for the scenario analysis. The code calculates material balance of 26 actinides (through Th to Cm, T1/2 > several days) in spent fuels with an accuracy comparable to the ORIGEN2 code. LWR, CANDU, gas-cooled reactor, several sodium-cooled FRs, and lead-bismuth-cooled ADS are available. Each reactor can be coupled with appropriate fuel such as UO2, MOX, ROX, Pu-nitride (PuN), and MA-nitride (MAN). Fission products are estimated by dividing them into several groups (iodine, rare gas, technetium and platinum group metals, strontium, cesium, and others). The number of waste packages and repository size are determined by temperature analysis based on several repository layouts. Potential radiotoxicity that is defined as dose by direct ingestion can be also estimated.
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
210 K. Nishihara et al.
PTin • 3600 • 24 • 365 • εo • A
wtr ¼ Efiss NA : ð19:1Þ
Here, the effective transmutation rate, λtr, is transmuted amount divided by initial amount and time needed for transmutation including out-core period.
tr wi 1
Ti þ To ¼ aεoεch, ð19:2Þ
3600 • 24 • 365 • A 4
Efiss NA ﬃ 3:8 • 10 : ðt=MW=yearÞ ð19:3Þ
Because a can be regarded as constant for Pu-transmuters, λtr is determined by operation efficiency, εo, cycle efficiency, εc, and specific heat, h. A time evolution of amount of heavy metal after introducing transmuters is expressed as
dt ¼ -λtrw, w ¼ w0e- λtr t , Ttr ¼ ln ð 2 Þ
λtr , ð19:4Þ
where Ttr is a transmutation half-life. In the phase-out scenario, there is heavy metal of w0 t 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 λtr 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.