Wave processes in the electron beam in crossed static electric and magnetic fields as it moves in a medium with a complex conductivity

Resistive wall amplifier is vacuum microwave device. The gain is due to the phase shift between a.c. of electron beam and the alternating field components. The absorbing device walls influence on the alternating field components is considered. It is interesting that there is no need for a slowing system that is important to learn the submillimeter range. Furthermore the feedback is completely absent between the output and the input. Recently, attention has been paid to resistive wall amplifier in connection with the possibility of using metamaterials that significantly increases the gain. It is worked out (developed) two-dimensional linear adiabatic theory of a device with an electron beam moving in crossed static electric and magnetic fields (magnetron-type flux). The electron beam of finite thickness is inserted between two flat surfaces with complex conductivity. In this paper, a consistent theory for an M-type absorption amplifier with a beam of finite thickness, and for the motion of an electron beam of a magnetron type in a medium with complex conductivity is present for the first time. The cases, when both surfaces are metallic, and when one of the surfaces is metallic, and the other has active, capacitive or inductive conductivity, are considered. The cases of a thin and thick beam are investigated. It is shown that the complex conductivity of surfaces increases the instability region, and with capacitive conductivity, an instability of thick beams is created, which is impossible only because of the diocotron instability. An increase in the gain as the flow approaches the flat surfaces with complex conductivity is shown.