# An ECCD--Electronic Charge Compensation Device--As a Quantum Dissipative System
## 3 Simulation Study of the Electromagnetic Radiofrequency Field in an ECCD  
### Resonant Modes  
A simulation study has been carried out with the help of the Radiofrequency Department of INTA--Instituto Nacional de Tecnica Aeroespacial--using the Ansys HFSS software tool (SM 3), to evaluate the ECCDs' impacts on electromagnetic radiofrequency fields. The characterized devices correspond with the DDCE 100 and DDCE 50 models of ECCDs from DINNTECO; however, in this paper, we only present the results of the most general model--DDCE 100. In Ref. [4], the full report of both models is presented. For the ECCD with the material properties and structural dimensions of the DINNTECO model DDCE 100, the simulation study obtained 40 different modes in the frequency range from 0.59 to 2.42 GHz. Outside that interval, no resonance modes were found (See Appendix A). Figure 5 is a graphical representation to show in an intuitive way the ECCD resonance modes of DINNTECO DCCE 100, where the quality factor Q of each mode is represented against its frequency. However, the resonance modes with low quality factor Q modes, \(<\)240-250, can be considered overlap. That is because of the fact that the simulation analysis did not take into account manufacturing dimensional tolerances of the devices. It did not consider either assembly deviations and dimensional changes due to thermal variation (expansions and compressions) that may contribute to uncertainties \(>\)3%, which correspond to random errors that are specified in the product of the convolution of the spectral profile of each mode by a Gaussian error function [5,6]. The consequence is an increase in the bandwidth of all modes with lower values in Q by a factor of 3 to 5. It is, therefore, more representative to consider that the performance of the ECCD with respect to radio frequency resonances consist of a continuous background and of two generalized main resonant modes (which are multi-mode envelopes with high values in Q). Figure 6 shows these considerations, and we have shown two asymmetric profiles (Fano type [7]) as two corresponding resonances with a quasi-continuous background of modes. In general, this quasi-continuous background is associated to a dissipative process. Figure 4: One of the register measurements of electric potential done at four different points of the large dock crane in Tomihama quay: (**A**) without ECCD protection; (**B**) with ECCD protection. Table 2 presents a numerical summary of the general characteristics, in terms of modal behavior of the DDCE devices, in which the Qeq value (equivalent Q factor) is included as an estimate for the background of modes, together with the characteristic values of the main mode. In the case of the DINNTECO DDCE 100 model, a second main mode is to the left (at 1.153 GHz) with a lower quality factor. We considered it more convenient to include in Table 2, as the main mode, the highest value of Q factor (which the simulation grants, in fact, to two overlapping modes and others with lower quality factors). Figure 5: Resonance frequency modes of an ECCD corresponding to a DINNTECO DDCE 100 model. Figure 6: Functional behavior of resonant modes in an ECCD (DINNTECO DDCE 100 model). The values that the simulation gives to the frequency of the main modes are quite in agreement with the dimensional geometry of the DINNTECO DDCEn 100 model. Thus, this gives us an approximate solution: using a fundamental equation applicable to the case of flat resonators that respond to the closing equation  
\[\frac{\overline{v}}{c}2 nd=1, \tag{1}\]  
where \(d\) is the separation between electrodes (ideally: flat plates; real: caps), \(\overline{v}\) is the frequency of the mode considered, and \(c\) is the speed of light in a vacuum (\(2.9979\times 10^{8}\) m/s). Therefore, for the mode selected as the main one in the DINNTECO DDCE 100 model, the deviations from the above-mentioned closing equation are \(+/-6\%\).