Open planar sheath slow-wave structure

Summary form only given. Recent demands on power and frequency lead to consideration of sheet electron beams with large aspect ratios¹. New SWSs need to be developed to interact with these sheet electron beams^2,3. In this paper, we consider a planar sheath-like structure with metal conductors on the surface of two surrounding dielectric layers. The structure can be easily microfabricated with current technology, resulting in excellent reliability and repeatability³. The motivation for the sheath nature of the structure is to allow the period of the structure to be shortened without changing the pitch of the conductors. The shortened period raises the frequency of backward wave modes thus suppressing them. The multiple conductors in the sheath open the possibility of transverse modes which can interact with the beam. These, however, will have transverse components in their group velocity and will propagate out of the structure. We assume the sheath approximation and fields having propagation constant k_z and k_y in the longitudinal and transverse direction respectively. Matching analytically the fields at the conducting sheaths boundaries, we obtain a transcendental dispersion relation. Three solutions propagate to zero frequency, one having even parity in axial electric field and the other two having odd parity. The even parity solution interacts strongly with the electron beam, hence is the operating mode. The transverse propagation modes have neither even nor odd parity, and some of them intersect what would be the beam line. However, their group velocities are essentially parallel to the conductors on either the upper or lower sheaths at those intersecting points. Thus they will be heavily damped in a structure with finite lateral extent. The Pierce parameter is analyzed and calculated for a beam with voltage at 19.5kV, current at 3.5A, wave frequency at 35GHz, and tunnel width equal to 0.6452cm while tunnel h- ight is 0.07cm. This gives an expected gain rate of 11.8dB/cm.