Traveling-wave amplification and power flow in conducting solids

An RF power-density function is used to obtain some of the characteristics of small-signal traveling-wave amplification in solids. Criteria for determining instability conditions are developed, in terms of well-defined drift and phase velocities, for both electrostatic and electromagnetic wave systems. The results are useful, typically, at or below the microwave range. More exactly, we investigate cases where the operating frequency is much less than the carrier-lattice collision frequency and the wavelength λ is much greater than l, the mean-free path. Effects due to a transverse or longitudinal applied magnetic field and the presence of more than one carrier type are included; this leads to modification of the v
drift
> v
phase
amplification rule used in simpler systems. Diffusion effects are discussed. Helicon, acoustic-wave, and two-stream problems are used to illustrate some of the results. In considering the carrier-to-wave energy transfer, kinetic power is shown to be negligible in solids when kl > 1, where k =2π/λ. The important term is seen to be one neglected in earlier work. It represents power loss when no drift field is applied and negative loss under amplification conditions.