# An ECCD--Electronic Charge Compensation Device--As a Quantum Dissipative System
## 3 Simulation Study of the Electromagnetic Radiofrequency Field in an ECCD
### Resonant Modes
The background attribution can be justified within a simplified form in the one-dimensional geometry of the DINTECO DDCE 100 model, with superior orders of non-axial resonant modes, specifically with orders 2 and 3 respectively. The closing Equation (1) used for the main modes was used for order 1. This seems correct for two reasons: the Qeq quality factor assigned is very low--which is compatible with separations between oblique electrodes--and because it is supported by simulation distributions of the electric and magnetic fields of the different modes analyzed; this will be used by us later. In any case, the geometrical dimensional correspondence coincides with the mean deviation value \(<\)10%. Finally, the propagation time--commonly referred as \"pulse duration\", of the radio frequency fields in ECCD, can be estimated from the profiles of the modes, where their base frequency behaves as a radiofrequency wave carrier, and the rest of the profile as a radio frequency pulse shaper, which is how these radio frequency electromagnetic fields behave in practice. Without entering into a formal analysis, an estimate of the temporal duration of the pulse can be obtained by using the Fourier transform of the spectral power distribution that facilitates a propagation time [8], which in our case originates from a product of convolution of the base profile with a Gaussian error function, specified as  
\[\mathrm{T}\approx 0.7/\Delta\overline{v}, \tag{2}\]  
where \(\Delta\overline{v}\) stands for the bandwidth. With Equation (2), two propagation time ranges were obtained: 0.25 \(\mathrm{\SIUnitSymbolMicro s}\) for the main modes and 2 \(\mathrm{ns}\) for the continuous background of modes for the DINNTECO DDCE 100 model. The important point here is that in the ECCD, there are two propagation time ranges for radiofrequency electromagnetic fields. Distributions of Electric and Magnetic Radiofrequency Fields, and Surface Current Density in an ECCD  
In most cases, the simulation results carried correspond to timed records (videos: simulated image records) relating to spatial distributions in 2 Ds and 3 Ds with different spatial orientations of electric and magnetic fields (scalar intensity values and vector orientations), Poyting vector, and surface current density obtained in different chosen frequencies of the large spectral resonance of the ECCD in the DINNTECO DDCE 100 model (SM 1). As a representative and significant example, we selected results of the radiofrequency field in the upper cap of a DINNTECO DDCE 100 model: electric and magnetic fields and surface current density at the resonant frequency 1.70 GHz for moments of temporal change characterized by the value of the phase in a semi-period. Five instances were selected at a phase step of 40\({}^{\circ}\) (see Table 3). \begin{table}
\begin{tabular}{c c c c c} \hline
**EM FIELD** & **Main Mode** & **Mode Background** & **Factor Q in Main Mode** & **Factor Qeq Background** \\ \hline Attenuation time & \(1.4\ \mathrm{\SIUnitSymbolMicro s}\) & \(5.5\ \mathrm{\SIUnitSymbolMicro s}\) & \(\approx\)650 & \(4.6\) \\ \hline Bandwidth & \(\approx\)2.8 MHz & \(330\) MHz & & \(350\) MHz \\ \hline \end{tabular}
\end{table} 
Table 2: General characteristics. A confinement in 2D and cylindrical revolution symmetry--very much in line with the designs of ECCD--is a situation analogous to the flat resonator case in 1D. However, the functions that represent the behavior of the electromagnetic field are somewhat more complicated. The mathematical expressions incorporate Bessel functions for the description of the confined resonant electromagnetic field. Additionally, the external part adjacent to the confined electromagnetic field (i.e., the evanescent electromagnetic field) continues to respond to a dampened exponential dependence, but is wider in scope regarding the volume. This situation is considered a 3D confinement that will exhibit cylindrical symmetry.