## 5 Scientific Novelty and Scientific and Practical Significance of the Research Results
### The Main Areas of Practical Application of the Results
#### 5.2.2 Development of Microwave (MW) Technology and Electronic Control Systems  
The importance of microwave (MW) frequency radio wave diagnostic systems for modern science and technology is significant. Microwave communication systems are used in the development and operation of relay radio towers necessary for the transmission of electromagnetic signals of the microwave radiation type over long distances, both on land and for intercontinental communications. In the latter case, it is necessary to use artificial satellite communication devices, which, when launched into the Earth's geostationary orbit, can perform the functions of microwave communication relay stations [139, 140]. Special electrovacuum devices (magnetron and klystron) are capable of generating large amounts of microwave energy. A generator based on a conventional vacuum triode, used at low frequencies, is quite ineffective in the microwave range. Since classical wave theory is applicable to microwave frequencies, microwave frequencies can be used as a means of radar and communication (based on the same principles of radio wave theory). However, due to the high frequencies of the waves, the high-order polarization modes, and the nonlinear radio wave effects they generate, microwave frequency devices provide great opportunities for transmitting information and increasing the efficiency of communication [141, 142, 143, 144]. The theoretical application of the methods of nonlinear kinetic theory of relaxation polarization to optical processes, considered in Section 5.1 of this section, can also be transferred to radio wave processes in the microwave range in crystalline structures. A nonlinear problem appears in theoretical estimates of optical and dielectric permittivities when crystals are exposed to radio waves in the microwave (MW) frequency range (3000 MHz-300 GHz), corresponding to wavelengths from 0.1 to 0.001 m [145]. When a crystal interacts with microwaves with a high energy flux density, nonlinear effects arise, which are associated with the generation of frequency polarization harmonics that are multiples of the third power of the radio wave field (generation of the second frequency harmonic). Modern MW devices and communication and radar systems operate, as a rule, on this effect, which, in the terminology of the nonlinear polarization theory we are developing, corresponds to the third order of perturbation theory (k = 3) in a small dimensionless parameter and the order \(r\) = 3 in the field frequency. When moving to the study of MW devices, including the development of high-density MW generators themselves, the degree of influence of the parameters (amplitude and frequency) of the electric field of the wave on the processes in functional elements (receivers, sensors, signal converters, etc.) becomes so significant that polarization harmonics begin to appear in the equations of the models at frequencies that are multiples of fifth and higher degrees of the field. The effects of generating frequency harmonics of orders \(r\) = 5, 7,... etc. in microwave systems are similar, in a formal relationship, to the effects of generating frequency harmonics of high and ultra-high orders (r >> 1) in optical systems based on laser radiation, with a difference in the frequency range and signal intensity. The mathematical model of nonlinear polarization remains in effect and is applicable to both optical and radio wave devices and microwave frequency systems. Under such conditions, the formulas and equations of the nonlinear quasi-classical theory of relaxation polarization (proposed in this work) remain applicable to issues of mathematical modeling and forecasting the properties and parameters of elements and devices of microwave signal generation and control systems, which additionally emphasizes both the physical and technological universality of the models we are developing.