## 3 Implementation of Proposed Models in Open-Source FEM-Oriented Software  
In the microwave field, there are a few specialized programs that provide FEM solutions for models. However, development tool chains are usually highly expensive, which can be an obstacle for researchers and smaller companies to utilize them. The alternative is open-source software, which also has the benefit of freely available code for calculation verification purposes. Implementation of the proposed model was carried out exclusively with the use of an open-source microwave modelling tool chain, operated under LINUX MINT [37], covering OCTAVE (free equivalent of MATLAB) [38], NETGEN mesh generator [39; 40; 41], ELMER FEM microwave FEM solver [42] and PARAVIEW [43; 44] software for visualization of results. The tool chain block diagram is presented in Figure 3. The whole process was controlled by scripts in Octave, which generated a series of NETGEN batch.geo files describing the geometry of the model. NETGEN discredited the model with the Delaunay triangulation algorithm [45] and converted the mesh into ELMER mesh files. ELMER FEM software was used for solving Maxwell equations and introducing the module for wave equations [46]. After each model computation, the results were saved both into Octave (.mat) and PARAVIEW (.vtu) format for further analysis. The software was used under a GNU GPL license; thus, the cost of possible commercialization will not be a barrier to the use of the results presented in this paper. In the case of tetrahedral meshes generated during the Delaunay triangulation process being implemented in NETGEN, the mesh granularity is determined by the maximal height of tetrahedral element \(h_{max}\). In order to check mesh influence on the resonant state, a number of simulations were carried out prior to the commencement of the planned experiment. The first series made it possible to find the radius for which there is the strongest resonance (as mentioned in the previous section; as a result of the calculations we only get an approximate value). It was identified that the best resonance occurs for \(R=171\) mm. In the next series of calculations, a series of models with radius ranging from 168-174 mm in intervals of 1 mm and for five mesh granularities with the maximum element height of the mesh (\(h_{max}\)) set to 8, 10, 12, 15, 20 mm, respectively, was carried  
Figure 3: Schematic block diagram of data flow in the modelling. out. Only the results for the coarsest mesh (for \(h_{max}=20\) mm) show a different extreme field strength for the model with 170 mm radius, whereas for all of the others, the best resonance parameters were gained for a chamber of 171 mm radius. The obtained results were used in the main part of the experiment. Finally, seven models of radiuses \(R\) range from 169.25-171.75 mm with an interval of 0.25 mm were implemented. The maximum element height of the mesh (\(h_{max}\)) was the same as in the preliminary experiment: 8, 10, 12, 15, and 20 mm, which gave 35 models in total. The specific range of radiuses \(R\) depended on the maximum element height for the mesh: \(R\) was in the range of 169.25-171.75 mm for \(h_{max}\) equal to 20 mm and R was in the range of 170.25-171.25 mm for all the other \(h_{max}\) values, which were equal to 8, 10, 12, 15 mm. The example of meshes used for modelling is given in Figure 4.  
To perform the analysis, the electromagnetic field value was sampled along the line shown in Figure 5. The line was parallel to the chamber's axis of symmetry and placed 40 mm away from it in the \(YZ\) plane. The position of the line was selected based on 3D data from PARAVIEW so that it passes through the local maxima of the electromagnetic field strength, \(H\).