Field Enhancement at a Triple Junction in Arrangements Consisting of Three Media

The field singularity occurs at an edge point where wedge-like interfaces of dielectrics meet. This phenomenon is well known as "Takagi-effect" or "triple-junction effect" in the cases of two dielectrics. Its significance is twofold: (1) the negative phenomena of possible discharge or breakdown inception; and (2) the positive application of the field enhancement to field emission or electron beam generation in vacuum. This paper describes the analytical expression which gives the exponent of the field singularity in three dielectric media, and applications of this expression in various simple conditions. The analytical expression is also compared with the value given from the numerical field calculation