The purpose of this paper is to investigate a metamaterial-based planar resistive wall amplifier and to demonstrate the applicability of simplified models for preliminary evaluations.

Methods. Two two-dimensional models are considered. The first model constitutes of an infinitely wide sheet beam immersed in a strong longitudinal magnetic field propagating between two identical layers of metamaterial, with the symmetry plane placed along the beam center; the layers of metamaterial and an envelope of parallel metal plates are separated by vacuum gaps. The second model is a periodic structure of thin sheet beams immersed in a strong longitudinal magnetic field propagating through drift channels in an infinite slab of metamaterial. In both cases, the frequency
properties of the metamaterial are accounted by the Drude model. The dispersion equations for these models are derived. The transition to one-dimensional linear theory is demonstrated and discussed. The results of linear theory and numerical simulations in CST Particle Studio for each model are compared and analyzed. In numerical simulation, the initial beam density modulation is utilized. In the linear regime, the gain is evaluated by the ratio of the maximum amplitudes of the Fourier transform of the collector current to the emission current.

Results and conclusion. The obtained theoretical results show the sensitivity of the metamaterial-based planar resistive wall amplifier performance to geometrical dimensions and properties of the medium. It is shown that by using metamaterial it is possible to obtain a significant increase of the initial beam modulation. A qualitative correspondence between the results of planar linear theory and numerical simulation for both models is shown. The hierarchy of models is formulated.