Growing waves in drifting solid state plasmas

 Travelling Wave Tubes were widely used in generating and amplifying microwaves. Their operation relied on a slow electromagnetic wave (usually in the form of a helix) interacting with waves, namely the slow and the fast space charge waves, propagating on a drifting electron beam.

Amplification occurred when the slow space charge wave and the slow electromagnetic wave were in synchronism. The electrons drifted in vacuum hence there was no attenuation. If the electrons drifted in a collision dominated solid then, conventional wisdom said, no amplification was possible. The consensus was shattered with the discovery of the acoustic wave amplifier in which electrons drifting in a solid interacted with sound waves. Amplification occurred when the drift velocity exceeded the sound velocity. This idea, still in the '60s, was further developed by proposing a Solid State Travelling Wave Tube in which electrons drifting in a solid interact with an external slow wave structure. There were some realisations but very far from practical applications. The next step, still in the '60s, was torely on the optical branch of the acoustic wave in a III-V or II-VI material, and interact that wave with those on drifting electrons. Theory showed that amplification/generation was possible.

The subject did not die with the '60s. There were one or two papers each year ever since but no serious attempt at realisation. We have (a group in Erlangen and the Semiconductor group at Imperial College) decided to resurrect the subject. The main reasons are: (i) there is a need for a source in the THz region, (ii) we can now explore the relationships for a range of models and a range of parameters, and find optimum solutions thanks to the capabilities of modern day computers, (iii) the technology of producing small structures is now incomparably better than in the '60s.

In contrast to most of the solutions in the past which treated heuristically the coupling between the beam and the electromagnetic wave we have looked for self-consistent wave solutions for various configurations, e.g. the solid state plasma is surrounded by a dielectric and the whole structure is between perfectly conducting walls, and we solve the boundary conditions under steady state. We use the hydrodynamic model in which the drifting electrons are subject to collisions and diffusion. The electromagnetic wave is assumed to be slowed down either by a a dielectric of high dielectric constant or it is slow by nature because it is coupled to the waves on the optical branch.

The difficulties of identifying the growing waves will be discussed together with the concepts of absolute and convective instabilities. Various models will be presented and growing wave solutions shown.