Basic theoretical formulations of plasma microwave electronics. I. A fluid model analysis of electron beam-wave interactions

This two-part paper presents the first complete, generalized basic theoretical formulation for electron beam-wave interactions in a plasma-filled (corrugated or smooth-walled) waveguide immersed in a finite magnetic field. The general interaction and dispersion equations of the longitudinal and transverse interactions in both smooth and corrugated magnetized plasma-filled waveguides (MPWs) are formulated. Our approach differs from that of previous investigators in that we begin by first deriving the dispersion relation of an MPW and then using the resulting electromagnetic fields, which embody the plasma effects, as the basis field vectors. We then investigate the underlying interactions with a superimposed electron-beam in a variety of microwave device configurations. For example, we examine plasma Cherenkov radiation, the plasma-filled travelling-wave-tube/backward-wave-oscillator (TWT/BWO), the plasma-filled electron cyclotron resonance maser (ECRM), and other beam-wave interactions including those involving ion-channels. Some possible new interactions in a magnetized plasma-filled waveguide (MPW) are proposed. A detailed discussion and analysis of the important physical role of the plasma background are given. Many interesting features of beam-wave interactions in an MPW are pointed out, three of them being most essential. One is that transverse interactions are always accompanied by longitudinal interactions. The second is that the magnetized plasma itself is strongly involved in the interaction mechanisms via an additional component of the field. The third interesting feature is that the plasma-filled ECRM prefers to operate at high cyclotron harmonics. The first part of this two-part paper presents formulations using a fluid model for both the plasma and the beam. It also includes a detailed treatment of the physical effects of the ion channel that is formed in the plasma by an intense electron beam. Part II extends the analyzes by retaining a fluid treatment for the plasma-fill but substituting a kinetic theory treatment for the electron beam. This kinetic theory model should be used when the velocity spread of the beam's electrons must be taken into account. The theory presented in both parts of this paper is based upon the "given field" approach that has been widely used successfully in science and technology, in particular in microwave electronics. In both parts of the paper, sample numerical calculations are also presented in order to illustrate the physics.