High Flux Reactor

All analyses are performed in a high flux lead-bismuth reactor under design. It has a 90-day refueling cycle with the highest flux of 6.7×10¹⁵. The inlet temperature is 170℃, the outlet temperature is 536.5℃, and coolant velocity is 4.0 m/s. ²⁰⁸Pb-Bi is used as the coolant, and ²⁰⁸Pb is used as the reflector layer. Figure 4 shows the X-Y and X-Z sections of the reactor.

Fig. 4Full-screen View

　X-Y (a) and X-Z (b) sections of the reactor

The fuel rod is a simplified model consisting of fuel pellets, an air gap, and cladding, with a total length of 50 cm. The fuel assembly has a hexagonal design and contains 91 fuel rods. The geometry of the fuel rod and fuel assembly are shown in Figure 5. Detailed parameters of the high flux reactor are listed in Table 1.

Fig. 5Full-screen View

Geometry of the fuel rod (a) and fuel assembly (b)

The target for producing ²⁵²Cf is a mixture of plutonium, americium, and curium [9]. The nuclide composition of the target is shown in Table 2. The target is irradiated for five cycles of 25 d of irradiation each. This target irradiation is representative of typical operations during a californium production campaign.

Production Evaluation by Monte Carlo Burnup Calculation

The yields of transplutonium isotopes can be obtained by performing the Monte Carlo burnup calculation, a coupling of the Monte Carlo criticality calculation and the burnup calculation. Figure 6 shows the flowchart for evaluating transplutonium isotope production using the Monte Carlo burnup calculation.

Fig. 6Full-screen View

Flowchart for evaluating production by Monte Carlo burnup calculation.

The point burnup equation describes the transmutation of nuclides over time when the target is irradiated in a high flux reactor. For each nuclide in the burnup chain, the time-dependent point burnup equation can be written as $\frac{\text{d}{n}_i}{\text{d}t}={\displaystyle \sum _{i\ne j}{b}_{j,i}^{\text{eff}}}{\lambda }_j^{\text{eff}}{n}_j-{\lambda }_i^{\text{eff}}{n}_i,$ (1) where n_i is the density of the i^th nuclide, λ_i^eff is the effective decay constant of the i^th nuclide, and b_i,j^eff is the branching ratio of the transmutation of the i^th nuclide to the j^th nuclide. λ_i^eff and b_i,j^eff can be calculated using the following formula: $\{\begin{array}{l}{\lambda }_i^{\text{eff}}={\lambda }_i+\varphi {\displaystyle \sum _j{\sigma }_{i,j}}\\ b_{i,j}^{\text{eff}}=\left(b_{i,j}{\lambda }_i+{\sigma }_{i,j}\varphi \right)/{\lambda }_i^{\text{eff}}\end{array}$ (2) where λ_i is the decay constant of the i^th nuclide, ϕ is the neutron flux, and σ_i,j is the one-group cross-section where the i^th nuclide’s reaction generates the j^th nuclide.

During the burnup calculation, the one-group cross-section and neutron flux within each burnup step are assumed to be constant so that the point burnup equation can be treated as a first-order linear ordinary differential equation. We wrote this into a matrix form and obtained an expression more concise than the prior expression: $\frac{\text{d}\overrightarrow{n}}{\text{d}t}=A\overrightarrow{n},$ (3) where A represents the coefficient matrix of the N order point burnup equation, which is regarded as a constant matrix in a single burnup step.

Because of initial boundary conditions, the solution to Eq. (3) can be written in the form of an exponential matrix: $\overrightarrow{n}(t)=e^{At}{\overrightarrow{n}}_0,$ (4) where matrix At is referred to as the burnup matrix for the convenience of quotation.

Because of the extremely low yields of transplutonium isotopes and the complex nuclide composition of the target, the point burnup model usually adopts a complex nuclide system, which needs to cover more than 1,000 isotopes, including many short half-life nuclides. For example, the ORIGEN-S burnup database [43] contains approximately 1,500 nuclides. Some of these nuclides, such as ²¹²Po, have half-life of 10^-7s. Therefore, the point burnup equations for transplutonium isotope production are not only large in number but also rigid, which makes the solution difficult.

As shown in Eq. (2), the cross-section of the target is required for the Monte Carlo burnup equation; therefore, a criticality calculation should be performed. The k-eigenvalue neutron transport equation can be written as [44]: $\left(L+C-S\right)\varphi =\frac{1}{k\text{eff}}M\varphi ,$ (5) where L is the leakage operator, C is the collision operator, S is the scattering operator, M is the fission operator, k_eff is the effective multiplication factor, and ϕ is neutron flux.

The physical parameters around the target, such as the neutron flux, fission reaction rate, and absorption reaction rate, can be obtained by solving Eq. (5). The Monte Carlo method uses the following formula for calculating the reaction rates: ${\Sigma }_g{\varphi }_g=\frac{{\displaystyle {\int }_{E_g}^{E_{g-1}}\text{d}E}{\displaystyle {\int }_V\text{d}V{\displaystyle {\sum }_{i=1}^{N}W\cdot T{L}_V^i}(E)\cdot \Sigma (r,E)}}{V{\displaystyle {\sum }_{i=1}^N{W}_0^i}},$ (6) where ∑_g represents the macroscopic cross-section in the g^th energy interval, and ∑ represents the cross-section of nuclides related to position r and energy E.

Therefore, we have the following formula for calculating the cross-section required by the Monte Carlo burnup calculation: ${\Sigma }_g=\frac{{\displaystyle {\int }_{E_g}^{E_{g-1}}\text{d}E}{\displaystyle {\int }_V\text{d}V{\displaystyle {\sum }_{i=1}^{N}W\cdot T{L}_V^i(E)\cdot \Sigma (r,E)}}}{{\displaystyle {\int }_{E_g}^{E_{g-1}}\text{d}E}{\displaystyle {\int }_V\text{d}V{\displaystyle {\sum }_{i=1}^{N}W\cdot T{L}_V^i(E)}}}.$ (7)

The aforementioned formulas show that the Monte Carlo burnup calculation is complex and costly [45,46]. Testing in the high flux reactor (Fig. 4), with the calculation parameters of 1,000,000 neutrons per cycle, 100 inactive cycles, 300 active cycles, and 10 burnup steps, demonstrated that the duration to perform one Monte Carlo burnup calculation with 64 threads on the 2nd Gen AMD EPYC™ 7742 was 150 min. Even when only considering the production of ²⁵²Cf, ²⁴⁴Cm, ²⁴²Cm, and ²³⁸Pu, and only analyzing the five design parameters (shown in Figure 9), a total of 9720 calculations are necessary, with a computing time of 1458,000 min (1012.5 d). This amount of computation time is unacceptable.

Fig. 9Full-screen View

(Color online) Optional values for these five design parameters

Moreover, because the Monte Carlo burnup calculation only requires a one-group cross-section, the calculations only provide the influence of the entire neutron spectrum on the production efficiency, not a closer analysis of each single energy interval. Therefore, when optimizing the neutron spectrum, only the macroscopic design parameters can be obtained, leaving unknown which energy intervals are favorable or unfavorable to production; thus, more detailed guidance for the optimization cannot be provided.

Therefore, understanding the physical nature of the production process and finding a new rapid diagnostic method that can simplify the calculation and analyze the production process in more detail are necessary. Moreover, a rapid diagnostic method is helpful for evaluating, screening, and optimizing irradiation schemes.

Rapid Diagnostic Method Based on SEIV and ESTV

The root cause of the low production of transplutonium isotopes is fission loss [14]. When the target is irradiated in a high flux reactor, the target material changes from nuclides with a small mass number to nuclides with a large mass number through absorption reactions. In addition to the absorption reaction, fission reactions occur. Once the fission reaction occurs, the production of transplutonium isotopes stops, causing fission losses and leading to a low conversion rate. Therefore, the ratio of the absorption rate to the fission rate (A/F) is an important physical quantity affecting production efficiency. Production efficiency can be assessed by analyzing the A/Fs of nuclides in the nuclide chain. Moreover, A/F can be calculated in individual energy intervals, achieving a refined neutronics analysis. For example, regarding the production of ²⁵²Cf from the target described in Table 2, Figure 7 shows the A/Fs of intermediate nuclides ²⁴⁴Cm, ²⁴⁵Cm, ²⁴⁶Cm, ²⁴⁷Cm, ²⁴⁸Cm, ²⁴⁹Bk, ²⁵⁰Cf, and ²⁵¹Cf. Nuclear data were obtained from the JANIS database [47].

Fig. 7Full-screen View

(Color online) A/Fs of the intermediate nuclides for producing ²⁵²Cf

As shown in Fig. 7, the A/Fs of different nuclides vary greatly, as do the A/Fs of different energy intervals; thus, different nuclides and different energy intervals have significantly different effects on production efficiency. Analyzing only the entire energy spectrum will not yield an accurate result; thus, a detailed analysis of each energy interval is required.

In this study, a rapid diagnostic method based on the neutron spectrum around the target is proposed to realize a rapid, refined evaluation of different production schemes. The model only needs to obtain the neutron spectrum around the target by using the Monte Carlo criticality calculation [48-49] to evaluate the efficiency of different production schemes, avoid the burnup calculation, and greatly reduce the required computing resources. Therefore, the rapid diagnostic method can quickly screen out the optimal scheme for transplutonium isotope production and help provide a direction for optimizing the irradiation scheme.

The model is divided into four steps: 1) obtain the neutron spectrum around the target by using the Monte Carlo criticality calculation, which can be described by the 46-group neutron flux, the 46-group fission rate, and the 46-group absorption rate; 2) define the physical quantity “Single Energy Interval Value (SEIV)” and calculate the SEIV of these 46 energy intervals; 3) define the physical quantity “Energy Spectrum Total Value (ESTV)” and use the 46-group neutron flux and the 46-group SEIV to calculate the ESTV of the neutron spectrum; and 4) evaluate the efficiency of different schemes by comparing the ESTV. Those with a higher ESTV are considered to have higher production efficiency and yield. A schematic of this process is shown in Figure 8.

Fig. 8Full-screen View

Schematic of the rapid diagnostic method

The Single Energy Interval Value (SEIV) is calculated by ${\text{SEIV}}_i=\frac{R_{a,i}}{R_{f,i}}\times \frac{R_{a,i}}{{\varphi }_i},$ (8) where the subscript “i” represents the serial number of the energy intervals, R_a,i represents the absorption rate in the i^th energy interval, R_f,i represents the fission rate in the i^th energy interval, and ϕ_i represents the neutron flux in the i^th energy interval.

The SEIV is the product of the two expressions. The first expression is A/F, indicating whether it tends to undergo an absorption or fission reaction within this energy interval. The other expression is the ratio of the absorption rate to the neutron flux, which indicates the probability of an absorption reaction occurring in this energy interval. Therefore, a higher SEIV means that within this energy interval, absorption reactions tend to occur rather than fission reactions, and more absorption reactions occur. An energy interval with a high SEIV is considered important in the production process, and the neutron flux in this energy interval should be increased as much as possible.

The energy spectrum total value (ESTV) is calculated by $\text{ESTV}={\displaystyle \sum _{i=1}^{46}\left({\text{SEIV}}_i\times {\varphi }_i\right)}.$ (9)

The ESTV is the integral value of the SEIV along with the neutron spectrum, indicating the target nuclide’s overall trend of absorbing neutrons without fission. We posit that a production scheme with a higher ESTV produces transplutonium isotopes more efficiently. The ESTV is only related to the neutron spectrum around the target, and the burnup calculation is no longer required; therefore, the ESTV can be used for the rapid evaluation of the production scheme.

Numerical Verification

The rapid diagnostic method is verified by comparing the burnup calculation with ESTV. The production efficiency is optimized by adjusting five design parameters: 1) moderator selection, 2) moderator layout, 3) target position, 4) target size, and 5) target shape. The optional values for these five design parameters are shown in Figure 9.

A large hexagonal prism target with Position #1 as the initial scheme and zirconium hydride as the moderator is used. Different irradiation schemes are obtained by modifying the moderator layout. Criticality calculations are used to obtain the neutron spectrum around the target. The SEIV and ESTV are determined and used to evaluate the efficiency of the irradiation schemes.

²³⁸Pu, ²⁴²Cm, ²⁴⁴Cm, and ²⁵²Cf are examples. The target for producing ²³⁸Pu is ²³⁷Np. The target for producing ²⁴²Cm is ²⁴¹Am. The target for producing ²⁴⁴Cm is ²³⁹Pu. The nuclide composition of the target used for producing ²⁵²Cf is listed in Table 2. The SEIV and ESTV for the target without the moderator (bare target) and the six layouts of the moderator are calculated; thus, there are seven production schemes for each transplutonium isotope to be produced. The SEIV for the production of these four transplutonium isotopes is presented in Table 3. The ESTV for the production of these four transplutonium isotopes is presented in Table 4.

As shown in Table 3, the optimal neutron spectra for producing ²³⁸Pu, ²⁴²Cm, ²⁴⁴Cm, and ²⁵²Cf are not always softer. The energy interval [4.14×10^-7MeV, 8.76×10^-6 MeV] has the highest SEIV for producing ²³⁸Pu. The energy interval [1×10^-11 MeV, 1×10^-7 MeV] has the highest SEIV for producing ²⁴²Cm. The energy interval [1×10^-7 MeV, 4.14×10^-7 MeV] has the highest SEIV for producing ²⁴⁴Cm. The energy interval [8.76×10^-7MeV, 1.86×10^-6MeV] has the highest SEIV for producing ²⁵²Cf. Moreover, the SEIV varied significantly at different energy intervals. For example, the maximum deviation of the SEIV in different energy intervals can be up to 1.37×10⁹ times for producing ²⁵²Cf. Therefore, the efficiency of transplutonium isotopes can be improved by modifying the neutron spectrum around a target [50-51].

As shown in Table 4, the ESTV varies significantly for the different irradiation schemes. For example, the maximum deviation of the ESTV can be up to 21.3 times for producing ²⁵²Cf. Moreover, the bare target always has the lowest ESTV regardless of the isotope produced. Therefore, the production of transplutonium isotopes requires the placement of a moderator around the target. Layout #6 of the moderator has the highest ESTV for producing ²³⁸Pu, ²⁴²Cm, and ²⁴⁴Cm, and Layout #5 has the highest ESTV for producing ²⁵²Cf. Because the SEIV and ESTV can be used to analyze the production efficiency of each energy interval in detail, the SEIV and ESTV are helpful in providing direction for optimizing the irradiation scheme.

Comparing the different irradiation schemes using only SEIV and ESTV is not rigorous; therefore, this method needs to be verified. To verify the effectiveness of the rapid diagnostic method, burnup calculations are performed with RMC code [52] to calculate the yields of ²³⁸Pu, ²⁴²Cm, ²⁴⁴Cm, and ²⁵²Cf. Because the neutron spectrum changes during the burnup process, first, the one-second burnup process was stimulated to ensure that the neutron spectrum used to calculate the ESTV was consistent with the neutron spectrum used to calculate the yields. In the 1 s burnup process, the relationship between the ESTV and the yields with a fixed neutron spectrum is clarified. The yields at 1 s for ²³⁸Pu, ²⁴²Cm, ²⁴⁴Cm, and ²⁵²Cf are presented in Table 5.

As shown in Table 5, regardless of the isotope produced, the yield in 1 s increases as the ESTV increases. Therefore, ESTV can be used to evaluate the yield with the same neutron spectrum. However, the one-second burnup only describes the physical process at the early stage of irradiation and cannot describe the entire irradiation cycle. For the assessment of whether the ESTV can indicate the yield of the whole irradiation cycle, the burnup process of the target irradiation for 90 d is also simulated. The yields at 90 d for ²³⁸Pu, ²⁴²Cm, ²⁴⁴Cm, and ²⁵²Cf are given in Table 6.

As shown in Table 6, regardless of the isotope produced, the yield after 90 d increases as the ESTV increases. Therefore, the ESTV not only indicates the production efficiency at the early stage but also indicates the efficiency of the entire irradiation cycle. Therefore, a rapid diagnostic method based on SEIV and ESTV can be used to evaluate the efficiency of transplutonium isotope production.

Experimental Verification

Because the high flux reactor shown in Fig. 4 has not been built, experimental studies cannot be conducted with this reactor; thus, the experimental verification of the rapid diagnostic method was conducted using the HFIR [53]. The HFIR has been producing ²⁵²Cf since 1966 and currently accounts for 70% of the world’s supply; therefore, the HFIR has a large amount of measured data on transplutonium isotope production.

Rated at 100 MW and currently operating at 85 MW, HFIR has the world’s highest steady-state neutron heat flux (2.6×10¹⁵ cm^-2·s^-1). The HFIR is a light-water-cooled moderated flux trap reactor that uses highly enriched ²³⁵U. The reactor core consists of many concentric annular zones, each approximately 61 cm high (fuel height, 51 cm). At the center is a 12.70 cm cylindrical pore called a “neutron flux trap”, containing 37 vertical experimental holes. The neutron flux trap is surrounded by two concentric fuel assemblies. The reactor core and neutron flux trap are shown in Fig. 10 [54].

Fig. 10Full-screen View

(Color online) Reactor core (a) and neutron flux trap (b) of HFIR

Because the rapid diagnostic method uses the ESTV to evaluate the production efficiency of different irradiation schemes, Monte Carlo criticality calculation should be performed to calculate the ESTV. The RMC code is used to model the HFIR, and the input card of the HFIR is provided in the attachment. Figure 11 shows the core modeling and neutron flux trap modeling results.

Fig. 11Full-screen View

(Color online) Core modeling(a) and neutron flux trap(b) modeling of RMC code

For the verification of the correctness of the modeling, the radial distributions of the thermal neutron flux and total neutron flux were calculated and compared with the reference solutions (Fig. 12). This shows that the flux distributions calculated by the RMC are in good agreement with the reference solutions, which proves the correctness of the HRIR model.

Fig. 12Full-screen View

(Color online) Comparison of the radial flux distributions

Next, an experimental verification was conducted. The target design shown in Fig. 13 was irradiated with HFIR for 5 d. Four irradiation schemes were formed with two target nuclide compositions and two irradiated positions: ²⁴⁵Cm_A, ²⁴⁵Cm_C, Cf_A, and Cf_C. The yields of heavy nuclei (all nuclides heavier than the nuclides in the target) for the four irradiation schemes were measured [9], and the corresponding ESTV was calculated. The experimental results are listed in Table 7.

Fig. 13Full-screen View

Experimental target design

Because the target nuclide composition should be the same when comparing the ESTV of different irradiation schemes, we compared ²⁴⁵Cm_A with ²⁴⁵Cm_C and Cf_A with Cf_C. As shown in Table 7, the measured yield of heavy nuclei of ²⁴⁵Cm_A was lower than that of ²⁴⁵Cm_C, and the corresponding ESTV of ²⁴⁵Cm_A was also lower than that of ²⁴⁵Cm_C. Additionally, the measured yield of the heavy nuclei of Cf_A was lower than that of Cf_C, and the corresponding ESTV of Cf_A was also lower than that of Cf_C. The experimental results satisfy the law in the rapid diagnostic method that as the ESTV increases, production efficiency increases. Therefore, the experimental verification proved the correctness of the rapid diagnostic method.

In the next chapter, we use a rapid diagnostic method to realize rapid screening and determination of the optimal irradiation scheme.

Logic of Optimization

Five design parameters were optimized: 1) selection of the moderator, 2) layout of the moderator, 3) position of the target, 4) size of the target, and 5) shape of the target.

As shown in Table 3, regardless of the isotope produced, the energy interval with the highest SEIV is always in the thermal range; therefore, we had to arrange the moderator to soften the neutron spectrum around the target. We aimed to select the material with the strongest moderating power to achieve the best neutron spectrum by deploying the least amount of moderator. The moderating power of various materials is an inherent property of the material and not affected by other design parameters; therefore, the moderator material can be determined first. We used a large hexagonal prism target with Layout #1 and Position #1 as the initial scheme. Nine moderator materials were tested, and the neutron spectra around the target were tallied (Figure 14).

Fig. 14Full-screen View

(Color online) Neutron spectra with different moderators

As shown in Fig. 14, zirconium hydride has the best moderating power; thus, zirconium hydride was selected as the moderator, and the moderator selection was not considered in all subsequent analyses.

To determine an optimal production scheme, we had to determine the optimal design parameters for the layout of the moderator and the position, size, and shape of the target. We used a large hexagonal prism bare target with Position #1 as the initial scheme and then optimized the four design parameters. The optimization order of these four parameters is important. We determined the optimization order using a sensitivity analysis. The sensitivity coefficient of design parameter d to production efficiency is defined as ${\eta }_d=\frac{\partial P}{\partial d}\propto \frac{\partial \text{ESTV}}{\partial d}\propto \frac{\max {(\text{ESTV})}_d}{\min {(\text{ESTV})}_d},$ (10) where P represents the production efficiency, d represents a design parameter.

Therefore, the sensitivity coefficient is positively correlated with the maximum increase in ESTV, which can be obtained by adjusting a design parameter. The larger the maximum increase, the greater the importance of this design parameter to the optimization process; therefore, we optimized it first. After optimizing one of these design parameters, we used the optimized scheme as the starting scheme to optimize the remaining design parameters until all design parameters were optimized. A logical diagram of the optimization process is shown in Fig. 15. This paper uses ²⁵²Cf as an example to describe the optimization process of the irradiation scheme in detail. The optimal schemes for ²³⁸Pu, ²⁴²Cm, and ²⁴⁴Cm are presented in Sect. 3.6.

Fig. 15Full-screen View

(Color online) Diagram of optimization logic

First Round of Sensitivity Analysis and Optimization

The first round of sensitivity analysis and optimization had to consider four design parameters: the layout of the moderator and the position, size, and shape of the target. The optional values for the four design parameters are shown in Fig. 9. New irradiation schemes can be obtained by adjusting one of the four design parameters based on the initial scheme. The ESTVs for all new schemes are listed in Table 8, and the symbol “η” represents the sensitivity coefficient.

As shown in Table 8, the moderator layout can improve the ESTV the most; therefore, the moderator layout should be optimized first. Moreover, Layout #5 had the highest ESTV; therefore, the layout of the moderator was selected as Layout #5. After the first round of optimization, the scheme became a large hexagonal prism target with Positions #1 and #5.

Second Round of Sensitivity Analysis and Optimization

The second round of sensitivity analysis and optimization had to consider three design parameters: the position, size, and shape of the target. All new irradiation schemes were obtained based on the scheme after the first round of optimization. The ESTVs for the second round of optimization are listed in Table 9.

As shown in Table 9, the position of the target can improve the ESTV the most; therefore, the position of the target should be optimized in the second round of optimization. Moreover, Position #1 has the highest ESTV; therefore, the position of the target is selected as Position #1. After the second round of optimization, the scheme became a large hexagonal prism target with Positions #1 and #5.

Third Round of Sensitivity Analysis and Optimization

The third round of sensitivity analysis and optimization must consider two design parameters: the size and shape of the target. All new irradiation schemes were obtained based on the scheme after the second round of optimization. The ESTVs for the third round of optimization are listed in Table 10.

As shown in Table 10, the target’s shape and size had similar effects on improving the ESTV, with the target’s size being slightly larger; thus, target size should be optimized in the third round of optimization. Moreover, the small target had the highest ESTV; therefore, it was selected. After the third round of optimization, the scheme became a small hexagonal prism target with Positions #1 and #5.

Fourth Round of Sensitivity Analysis and Optimization

The fourth round of sensitivity analysis and optimization had to consider one design parameter, that is, the shape of the target. All new irradiation schemes were obtained based on the scheme after the third round of optimization. The ESTVs for the fourth round of optimization are listed in Table 11.

As shown in Table 11, the hexagonal prism had the highest ESTV; therefore, a hexagonal prism target was selected. After the fourth round of optimization, the scheme became a small hexagonal prism target with Positions #1 and #5.

Final Irradiation Scheme

The optimized scheme for producing ²⁵²Cf was a small hexagonal prism target with Positions #1 and #5. Similarly, we optimized the schemes for producing ²³⁸Pu, ²⁴²Cm, and ²⁴⁴Cm. The final optimized irradiation schemes for producing ²³⁸Pu, ²⁴²Cm, ²⁴⁴Cm, and ²⁵²Cf are listed in Table 12. A comparison of the production efficiency before and after optimization is shown in Fig. 16.

Fig. 16Full-screen View

Comparison of efficiency before and after optimization of ²³⁸Pu(a), ²⁴²Cm(b), ²⁴⁴Cm(c) and ²⁵²Cf(d)

After four rounds of sensitivity analysis and optimization, we quickly obtained the optimal scheme for transplutonium isotope production. As shown in Figure 16, the optimal scheme effectively improves production efficiency more than the initial scheme: efficiencies of ²³⁸Pu, 7.41 times; ²⁴²Cm, 11.98 times; ²⁴⁴Cm, 65.20 times; and ²⁵²Cf, 15.08 times. Therefore, an optimization strategy based on a rapid diagnostic method is helpful for transplutonium isotope production.