We present a new profile for the electrodes forming the radial transmission line of a switched oscillator (SWO). The profile is formed using a curvilinear orthogonal space based on a specific 2-D transformation called logarithmic-tangent. The proposed profile results in an optimal distribution of the electric field, with a peak amplitude occurring on the axis of symmetry of the SWO, and a smooth, monotonic decrease in amplitude, as we move away from the discharge point toward the coaxial transmission line. In addition, the proposed profile assures a smooth continuity at the junction of the radial transmission line-coaxial line. Numerical simulation results on the electrostatic field distribution in the SWO are presented and discussed.