**Simulation and optimization of coaxial gyrotrons**

To optimize the design and to increase the efficiency of gyrotrons, being the promising energy sources for microwave technologies and controlled thermonuclear synthesis the following works are performed:

The mathematically rigorous scheme for calculations of electromagnetic fields in coaxial gyrotrons with taking into account the higher spatial harmonics is constructed. | ||

The methods of direct numerical solution of the singular integral equation being completely equivalent to the boundary value problem for the coaxial cavity with a rippled internal conductor are developed. | ||

The theory allows one to evaluate the gyrotron efficiency parameters such as the value of ohmic loss leading to the decrease in the efficiency of the device, and to heating of its walls and of a coaxial insert. | ||

The multiwave theory of microwave field attenuation in the rippled conductor of a coaxial gyrotron cavity was formulated. | ||

The accuracy of calculations within the framework of this theory is ~1%. | ||

It is shown that the field attenuation calculations basing on the standard impedance model are incorrect and overestimate the attenuation approximately by two times. | ||

In the model of the cold collisionless plasma with immobile ions the influence of the background low-density plasma on the resonance frequencies and HF field distribution in the cavity of a finite-size gyrotron are studied theoretically. | ||

The finite geometry of the plasma cavity is thoroughly considered. | ||

It is shown that the plasma in the cavity leads to the gyrotron operating frequency decrease and the frequency shift value does not depend on the plasma density. |