Improved transfer function for predicting the output voltage of vector inversion generators

High voltage pulses are useful in several engineering applications, such as food sterilization or rock fracturing. In this context, vector inversion generators, also called spiral generators, are a family of compact and lightweight pulse generators. These devices convert a DC voltage U0, typically in the range of hundreds of volts to a few kilovolts, into an oscillatory output pulse whose peak amplitudes strongly exceed U0, typically ranging in the order of tens to hundreds of kilovolts. This kind of generator consists of 4 alternative layers of conducting and dielectric tapes wound into a spiral of N turns and a switch, connected at the input. The generator is DC loaded with voltage U0 at the input terminals of the spiral. Once it reaches full charge, the switch closes, resulting in a transient over-voltage at the output. This over-voltage is the pulse of interest.
Ideally, the maximum peak amplitude of the output voltage is 2xNxU0. In practice, because of nonidealities, the actual amplitude is significantly lower, and a coefficient β<1 is introduced such that the peak amplitude of the output voltage is βx2xNxU0. Several researchers have tried to find models to predict the time evolution of the output voltage of vector inversion generators. In this work, the results of Rühl and Herziger (1980) and of Bichenkov et al. (2007) are used as a starting point to obtain an improved transfer function of the normalized output voltage in the Laplace domain B(p). This new model includes the interactions of the waveguide currents at the location of the switch as well as resistive losses. Using a numerical inverse Laplace transform, it is possible to obtain the evolution of the normalized output voltage over time β(t) = Uout/(2xNxU0).
This new model is validated experimentally, by comparing the predicted output voltages with measured output voltages. The experiments include two different tests: first, several switch inductances were connected at the input and second, the spiral generator was placed at both room and cryogenic temperatures. Experimenting with cryogenic temperatures makes it possible to change the resistivity of the copper tapes while keeping all the other parameters almost unchanged. In other words, it can be used to validate how resistive losses are taken into account in the proposed model.