In order to develop a high gradient S-band electron accelerating structure, an optimized travelling wave (TW) single-cell cavity operating at the frequency of 3 GHz with 2π/3 phase advance, is proposed. Starting from the well-known accelerating cells design developed by the Laboratoire de l'Accélérateur Linéaire (LAL) and the Stanford Linear Accelerator Centre (SLAC), for linear accelerators; it is possible to improve the main RF parameters, such as quality factor, shunt impedance, enhancement factor and group velocity, by choosing a suitable shape of the inner surface. Even though surface electric field is being considered as the only main quantity limiting the accelerating gradient; the importance of power flow and the modified Poynting vector*, has been highlighted from high-gradient experimental data. In this context, the new field quantity (Sc) is derived from a model describing the RF breakdown trigger phenomenon wherein field emission currents from potential breakdown sites produce local pulsed heating. In particular, the modified Poynting vector takes into account both active and reactive power flow travelling along the structure. The main results presented in this paper have been carried out with the 3D electromagnetic simulation codes: High Frequency Structural Simulator solver (HFSS) and CST MICROWAVE STUDIO (CST MWS).