Modern vacuum tube devices dominate the field of high power and high frequency electronics. Among them, the Traveling Wave Tube Amplifier (TWTA) has broad bandwidth and consequently a wide range of applications. In this thesis, a planar sheath-like slow wave structure with rectangular geometry is studied and considered for use in a TWTA driven by a sheet electron beam. Although use of a wide sheet beam promises high power, the large transverse dimension of the structure risks interaction of the beam with multiple backward wave modes. Both the operating mode and the parasitic modes are analyzed using field theories with the planar sheath approximation. These solutions are then compared with finite element computations. Suppression of backward waves is then considered by designing the structure to preferentially absorb these waves. The results show good control of mode competition and high primary mode gain.