An analytical solution for the secondary capacitor charging time of Tesla transformer with different optimal coupling coefficients

In the domain of high-voltage generation and pulsed power systems, Tesla transformers play a critical role, where the charging time of secondary capacitors fundamentally determines the design of system repetition frequency and control sequence optimization. To the best of our knowledge, this paper first presents an analytical solution for calculating the secondary capacitor charging time with different coupling coefficients. The analytical solution is applicable not only to Tesla transformers featuring open magnetic cores, where the coupling coefficient is close to 1, but also to air-core Tesla transformers with coupling coefficients of 0.6 or 0.385, which provides valuable guidance for designing high-voltage generation systems in related fields. Both numerical calculation experiments and circuit simulation experiments have confirmed the precision and broad applicability of the analytical solution derived in this paper.