Impact of Parasitic Elements in Low-Energy Marx Generators

This investigation attempts to analyze and optimize the number of stages of low-energy Marx generators. Fast-discharging low-energy Marx generators are composed of stage capacitors of lower capacitance values, which are often comparable with various stray capacitances formed within the Marx system. In this article, analytical expressions for equivalent erected capacitance and open-circuit terminal voltage of the Marx generator are estimated considering the significant presence of stray capacitances. Mathematical observations consistently demonstrate an asymptotic decay in voltage multiplication efficacy with increasing stage count, ultimately reaching a regime of diminishing returns where incremental stages contribute insignificantly to the output potential. The erection dynamics are modeled as a discrete-time process, with comprehensive circuit analysis incorporating distributed stray capacitance elements. Acorrelation function relating three basic parameters: 1) stage count; 2) stage capacitance; and 3) parasitic capacitive coupling between elevated-potential nodes and the grounded containment structure is established. Two innovative design factors, namely stray capacitance loading factor ($\boldsymbol {\beta }$) and effective voltage multiplication factor ($\boldsymbol {\Gamma }$), are introduced to accurately estimate and optimize the number of stages. It is also established that the relating equation of these factors under certain conditions omits two fundamental polynomials. One of them is a depressed cubic, whose only real solution is the inverse plastic ratio, and the other is a quadratic whose root is the golden ratio. The inverse plastic ratio solution is opted as the most optimal solution, which is a balance between voltage amplification and energy efficiency, while the golden ratio solution could be the point of relatively higher voltage amplification at the cost of reduced energy efficiency. Amathematical analysis regarding the surge impedance of Marx discovers a condition that indicates the coexistence of Marx and PFN behavior at the same time. On the basis of these analyses and simulations, a 500-kV, 5-kA, 60-ns FWHM Marx generator is developed. Experiments are carried out using a resistive load and validate the analytical findings within 5%–7% accuracy. Details of analysis, optimization, and experiments are narrated in this article.