## 2 Research Method  
To assess the thermal state of the experimental device and determine the conditions for the experiment, a computer simulation of induction heating of the loaded burden at a stationary level of the inductor power was performed. The purpose of the simulation was to confirm the feasibility of testing with the considered device design and the volume of burden's materials. A value equal to 2500 K was taken as the achieved temperature of the cerium, based on previous experiments in the Lava-B facility with a similar burden composition [9; 10]. Computational studies were conducted using the ANSYS software package, based on the finite element method [11]. Based on the design of the MR's melt trap, a two-dimensional axisymmetric model was developed, which allows calculating the thermophysical parameters at control points. Figure 3 shows a diagram of such an experimental device. The melt trap is a cylindrical concrete structure inserted in the MR's inductor. A composition of materials for producing the cerium with a total weight of 30.0 kg was loaded into the concrete trap. The number of materials loaded into the trap:  
* Uranium dioxide (UO\({}_{2}\)), kg.. Therefore, the heat release in the melt was set depending on the characteristics of induction heating--the surface effect of penetration into the depths of materials of the conductive medium during induction heating, or the skin effect (in this calculation, 70% of the total heat release occurred on the surface layer). At the same time, the depth of this surface is determined by the theory of induction installations [14]. The prototype of the cerium is a burden consisting of several components. Considering the complexity of induction heating, it is impossible to fully take into account its effect on each of the burden components when computer modeling. Hence, a significant simplification is made. The trap load or the future cerium is presented as a single-structured material. Some properties of the cerium were used in computer modeling based on their sources [15; 16]. It should be noted that its value was assumed to be a constant in the calculations due to the lack of information on the dependence of the cerium thermal conductivity on temperature. In this case, the value of the thermal conductivity coefficient was set similarly to the earlier calculations of cerium heating within the framework of the ISTC Project No. K-1265 using the INVECOR program [17; 18]. The described method of decay heat simulation in the cerium prototype was validated earlier and, therefore, it can be applied for a non-stationary calculation of temperature changes in the trap components [19; 20]. The thermophysical properties of the trap components were used according to the literature source [21]. When simulating, the following control points were selected: c.p.1, c.p.2, c.p.3. Their layout corresponds to the layout of the thermocouples 1-04, 1-07, and 1-08 in the melt trap, (Figure 3) based on the symmetry condition. Based on the presented results of the computer simulation, the conditions for conducting physical modeling of cerium production in the MR's melt trap were determined. In order to provide conditions for a controlled environment during the experiment, the measured temperature and power of the induction heater were chosen as the main control parameters. The components were heated by raising the voltage on the MR's inductor  
Figure 3: Diagram of the experimental device. 1: concrete trap; 2: chamotte side blocks; 3: zirconium rod; 4: steel rod; 5: Zr + SS + ZrO\({}_{2}\) mixture; 6: chamotte bottom blocks; 7: thermocouples; 8: UO\({}_{2}\) pellets. to 900 V (rate: 100 V/min, N \(\approx\) 120 kW), while the integral amount of energy supplied to the burden in the concrete trap, the average value of the maximum power supplied by the constant speed drive (CSD), and the values of the melt temperature during the experiment should correlate with the results of the computer simulation.