Practical approach for the design of uniform-field electrodes in transversely excited CO₂ lasers

Uniform-field electrodes, which are commonly used in transversely excited CO₂ lasers, are essential to produce a uniform pulsed glow discharge. In this paper, a simple and novel approach associated with practical parameters is developed for the design of Chang and Ernst profiles. This approach not only provides a maximally flat distribution of the electrode surface field but also optimizes the geometric parameter k₀. The design procedure is investigated using this method based on approximate and exact solutions; for simplicity, an iterative method will also be suggested. Furthermore, a monolithic and composite profile is presented to calculate the 3D shape of realistic electrodes that brings desired values of field uniformity and aspect ratios. The obtained distribution of the electric field is discussed to explore more detail about the proposed approach. The approximate and exact methods are in good agreement, and the boundaries of the discharge region are determined by the field distribution across the discharge midplane. The results show that a square discharge also requires optimum applied voltage.