Uniform-field Electrodes with Minimum Width

In order to obtain high output powers from transversely excited pulsed lasers it is important to have a very uniform energy loading of the active gas medium That is why there is a need for specially contoured electrodes that produce a very uniform field-strength distribution over a certain amount of surface. A number of authors tried to solve this problem. Rogowski’s [ 1 ] and Chang’s [2] profiles are most commonly used up to now. For some applications, however, a smaller electrode width is required for a given discharge width than will be obtained by e.g. Chang’s formulas. This, for instance, is the case for large-aperture CO, and CO lasers, where the distance of the UV source from the electrode centre is an important measure, or for large-aperture UV lasers, where the electrode inductance contributes significantly to the total circuit inductance. Recently [3] Chang profiles have been improved by modification of the conformal transformation. Although those profiles are excellent as for their specifications, the analytic expressions are rather complicated, which limits their use. We present here a family of analytic profiles for uniform-field electrodes that have minimum width and can produce almost any degree of field-strength uniformity at the electrode surface, and have analytic expressions as simple as Chang’s. We start with the following conformal transformation: