K effective factor in the ADSR using liquid lead target and (Th233U)O2, (Th235UO)2, (Th238U)O2 fuel mixture

The study of using liquid lead target for the accelerator driven subcritical reactor (ADSR) has been proposed by Nguyen Mong Giao, Vu Thi Diem Hang, Tran Minh Tien (International Journal of Modern Physics and Application. Vol. 2, No. 3, 2015). The calculations about neutron distribution, neutron fluxwith thorium fuel and thorium mixturehas been showed by Tran Minh Tien (Distribution of Neutrons from The Reaction (p, n) on the Liquid Lead Target in The Accelerator Driven System Reactor, J. Phys.: Conf. Ser. 1172 012066, 2019; Distributions of neutron flux from (p, n) reaction on the liquid lead target for accelerator driven subcritical reactor (ADSR), J. Phys.: Conf. Ser. 1324 012061, 2019). In this paper, the k effective factor is calculated with(Th233U)O2, (Th235U)O2and(Th238U)O2fuel mixture.


Introduction
The accelerator driven subcritical reactor (ADSR) is being developed for safety, along with the ability to transmute radioactive wastes and the potential to use thorium as a fuel. Since ADSR was proposed by C. Rubbia [1],there have been many different studies around this. Many authors have studied the (p, n) reaction on the solid target [2][3] [4]. We had proposed using liquid lead as a target and coolant [5], calculated neutron distribution, neutron flux distribution with different types of fuel mixture [6] [7]. To further assess the stability of ADSR when using liquid lead target, thorium fuel mixure, we have calculated k effective multiply factor in the ADSR, with Th 233 UO 2 , Th 235 UO 2 and Th 238 UO 2 fuel mixture.

Calculation and results
In this calculation, ADSR is simulated by MCNP5 program [8].ADSR is simulated with 90 thorium fuel rods, and 10 reflectors made of graphite; all fuel rods and reflectors are placed in the liquid lead [7]. Details are described in figure 1.  Figure 1: The position of fuel rods, reflectors inside ADSR is simulated by MCNP5 [7] Details are described in table 1 [7]. K code calculation technique is used to calculate k eff for each fuel case with different ratios of thorium, uranium and oxygen.

(Th 233 U)O 2 fuel mixture
The fuel is (Th 233 U)O 2 mixture. The thorium ratio in the mixture is 0; 0.2; 0.4; 0.6; 0.8 and 1. This results is shown on figure 2, 3.  These results show that when thorium ratio is 0%, k eff changes from 0.92 to 0.98. This ratio increases to 20%, range of k eff is from 0.76 to 0.84; and this range is from 0.62 to 0.65 for 40%. When thorium ratio increases to 60%, k eff changes from 0.42 to 0.44; ranges are 0.16 to 0.18, 0.02 to 0.05 for ratios 80% and 100%.
For U 233 fuel mixture, as thorium ratios increase, k eff will tend to decrease. Especially, when the thorium ratio is 100%, the k eff is close to zero, which shows that it is not advisable to just use thorium as a fuel but instead combine other fuels.  These results show that when thorium ratio is 0%, k eff changes from 0.65 to 0.68. This ratio increases to 20%, range of k eff is from 0.54 to 0.57; and this range is from 0.42 to 0.44 for 40%. When thorium ratio increases to 60%, k eff changes from 0.27 to 0.30; ranges are 0.12 to 0.14, 0.02 to 0.03 for ratios 80% and 100%.

(Th 235 U)O 2 fuel mixture
For U 235 fuel mixture, as thorium ratios increase, k eff will also tend to decrease. When the thorium ratio is 100%, the k eff is also close to zero. These results show that k eff is very low. When thorium ratio is 0%, k eff only changes from 0.07 to 0.08. This ratio increases to 20%, range of k eff is from 0.06 to 0.07; and this range is from 0.03 to 0.04 for 40%. When thorium ratio increases to 60%, k eff changes from 0.03 to 0.04; ranges are 0.02 to 0.03, 0.01 to 0.02 for ratios 80% and 100%.

(Th 238 U)O 2 fuel mixture
For U 235 fuel mixture, the k eff is also close to zero. We should not use the combination of thorium with U 238 as a fuel for ADSR.

Comparison of average k eff between (Th 233 U)O 2 , (Th 235 UO) 2 , (Th 238 U)O 2 fuel mixture
These results of average k eff are shown on the table 2 and figure 8. The results show that thorium should only be combined with U 233 , according to suitable ratios.

Conclusions
MCNP5 program was used to simulation an accelerator driven subcritical reactor with thorium mixture fuel. K eff effective multiply factor was calculated for cases of fuel. The results shown that thorium can be combined with uranium as fuel for ADSR. U 233 is the best choice in all cases. However, it is important to carefully calculate the ratio between thorium and uranium to suit each ADSR structure used.