## 2 Materials and Methods
### Studying the Effect of Moisture Content in Grain on the Microwave-Active Zone's Q-Factor  
In microwave energy transmission systems, the so-called resonators are normally applied to reduce power losses. These are cavities fully enclosed within a metal shell [15]. Once an electromagnetic wave oscillation has been excited in such a cavity, it will exist there continuously.  
In technological processes employing microwave field energy, such cavities are used to be filled with various materials subject to processing. In our case, resonators are applied to treat grain. We call a resonator chamber a'microwave-active zone'. Convective-microwave units for grain processing are composed of a certain number of microwave-active zones (resonator chambers) installed one upon another. Therefore, their specific feature is their open design. A microwave-active zone has no barriers either on the top nor on the bottom, and grain moves downwards, in a natural flow, from the upper microwave-active zone towards the discharge unit. Only the bottom active zone is bounded from beneath by a discharge tank casing.  
The value of a resonator's \(Q\)-factor shall be as high as possible to ensure an effective use of the radiation energy source for heating materials under processing.  
When a resonator is filled with a conductive medium (such as wet grain), its \(Q\)-factor will depend on the energy loss in this medium [22]:  
\[N=\int_{V}\frac{\sigma E^{2}}{2}dV, \tag{3}\]  
where  
\(N\) represents energy loss in Watt-hours (Wh),  
\(V\) stands for the volume of the resonator (m\({}^{3}\)),  
\(E\) denotes electromagnetic field density (V/m),  
\(\sigma\) represents electric conductivity (S/m).  
The total energy dissipated in the resonator can be defined from the following equation [23]:  
\[\Sigma N=\int_{V}\frac{\varepsilon E^{2}}{2}dV, \tag{4}\]  
where \(\varepsilon\) represents dielectric permeability (F/m).  
The \(Q\)-factor is defined by the following relationship:  
\[Q=f\frac{\Sigma N}{N}, \tag{5}\]  
where \(f\) represents the magnetron's frequency (Hz).  
Taking into account (3) and (4), we have:  
\[Q=f\frac{\varepsilon}{\sigma}, \tag{6}\]  
It is impossible to avoid power loss in the resonator's walls and directly in the medium that fills the resonator. Therefore, the overall \(Q\)-factor of the microwave-active zone takes the following form [23]:  
\[\frac{1}{Q}=\frac{1}{Q_{m}}+\frac{1}{Q_{st}} \tag{7}\]  
where \(Q_{m}\) is the \(Q\)-factor of the medium under processing, and \(Q_{st}\) is the \(Q\)-factor of the microwave-active chamber (resonator) structure made of steel.  
Equation (6) makes it clear that the \(Q\)-factor of a material under processing depends on its dielectric properties and its electric conductivity. These two parameters change in a rather wide range during grain processing in microwave fields [24; 25; 26]. It has to be noted that these changes involve not only the reduction in moisture content and the increase in grain temperature but also the polarization of seeds in the electromagnetic field.  
Furthermore, it is necessary to consider the fact that conventional calculation methods for the \(Q\)-factor of resonators do not take into account any structures inside them. However, when dealing with microwave field applications in technological processes designed for processing agricultural products, it is necessary to consider auxiliary equipment (such as agitators, tanks, reflectors, etc.) installed inside a resonator chamber [27; 28]. In our case, these are radiating waveguides mounted directly in the resonator chamber, which renders conventional calculation methods for the \(Q\)-factor of resonator chambers inapplicable.