# Using Modeling to Select the Type of Microwave Field Emitter for Dense-Layer Grain Dryers
## 2 Materials and Methods
### Features of Electromagnetic Field Transmission by Rectangular Waveguides  
The outlay of the waveguide subject to the electromagnetic field distribution studies is shown in Figure 3. In these studies, a magnetron with an operating frequency of 2.45 GHz was selected as the source of microwave energy. The generator wavelength is equal to [34]:  
\[\lambda=\frac{c}{f}, \tag{8}\]  
where \(c=3\cdot 10^{8}\) m/s is speed of light.  
For a frequency value of 2.45 GHz, wavelength is  
\[\lambda=\frac{3\cdot 10^{8}}{2.45\cdot 10^{9}}.\]  
\(\lambda=0.122\) m = 122 mm.  
In microwave communication devices, the selection of particular wave types such as, \(H_{10}\), \(H_{01}\) and \(E_{11}\), is essentially important [35]. Contrariwise, the wave type selection is of no importance when the microwave electromagnetic field is used for heating purposes. It is more critical to ensure loss-free transfer of the radiation to the load. That is why the focus was made on multi-wave guides. Additionally, the dielectric strength of the waveguide can be increased, and the energy loss can be reduced by increasing the dimensions of the waveguide in relation to its length [34]. We will consider wave types capable of transferring along rectangular waveguides. In this regard, let us draw a diagram of critical wavelengths for magnetic and electric-type oscillations.  
\[a=2b, \tag{9}\]  
Assuming that a and b are dimensions of the larger and the smaller walls of the rectangular waveguide, respectively.  
Critical lengths for the magnetic- and electric-type waves are defined by the following relationship [35]:  
\[\lambda_{\text{cr}}=\frac{2}{\sqrt{\left(\frac{m}{a}\right)^{2}+\left(\frac{n }{b}\right)^{2}}}, \tag{10}\]  
where m and n are oscillation-type indexes \(H_{mn}\) (\(E_{mn}\)). For \(E\) wave, \(m\geq 1\), \(n\geq 1\). For \(H\)-wave, one of the two indexes may be equal to zero [20].  
Calculating critical waves for various oscillation types was performed with the use of MATLAB software R2020b [36; 37; 38]. In calculations, it was assumed that \(a=1\). When drawing the diagram shown in Figure 8, calculated data were multiplied by the value of \(a\).  
Figure 8: Diagram for oscillation types transferred in the waveguide.  
To ensure the possibility of propagation of all modes in waveguides, the following conditions must be observed [39; 40]:  
\[\lambda<\lambda_{\text{cr}}. \tag{11}\]  
For waves of \(H_{10}\) type, Equation (7) can be written in the following form:  
\[122<2\cdot a.\]  
Dimensions of rectangular waveguides stipulated in GOST 51914-2002, for frequencies close to those discussed in this article, are as follows:  
Cross-section shall be 110.00 \(\times\) 55.00 mm and 90.00 \(\times\) 45.00, respectively, for the frequency ranges from 1.72 GHz to 2.59 GHz and from 2.14 GHz to 3.2 GHz.  
Taking into account that, in the processing plant, the microwave field has to be distributed as homogeneously as possible in the grain layer, we assume that the waveguide cross section of 110 \(\times\) 55 corresponds to this requirement to a greater extent. Therefore, the critical wavelength for this waveguide is \(\lambda_{\text{cr}}=2\times 110=220\) mm. It means that the selected waveguide dimensions comply with Requirement (11).