Linear voltage recovery after a breakdown in a pulsed dc system

Breakdowns (BDs) may occur in high-voltage applications even in ultrahigh vacuum conditions. Previously, we showed that it is important to pay attention to the post-BD voltage recovery in order to limit the appearance of secondary BDs associated with the primary ones. This can improve the overall efficiency of the high-voltage device. In this study, we focus on the optimization of the linear post-BD voltage recovery, with the principle aim of alleviating the problem of the secondary BDs. We investigate voltage recovery scenarios with different starting voltages and slopes of linear voltage increase by using a pulsed dc system. We find that a higher number of pulses during the voltage recovery produces fewer secondary BDs and a lower overall BD rate. Lowering the number of pulses led to more dramatic voltage recovery resulting in higher BD rates. A steeper voltage increase rate led to a more localized occurrence of the secondary BDs near the end of the voltage recovery period. It was also found that the peak BD probability is regularly observed around 1 s after the end of the ramping period and that its value decreases exponentially with the amount of energy put into the system during the ramping. The value also decays exponentially with a half-life of ($1.4\pm 0.3$) ms if the voltage only increased between the voltage recovery steps.

Figure 1

Theoretical voltage increase in each of the ramping scenario in the first set of measurements as a function of time and the number of pulses. With the repetition rate of 2000 Hz, one second equals 2000 pulses. The figure also contains a 20 step ramping scenario used in Refs. [24, 28] for comparison.

Figure 2

Actual measured voltage increase in each of the ramping scenario as a function of time and the number of pulses. The measurement was performed by using the power supply to increase the voltage to 1000 V over a circuit with a capacitance of 650 pF.

Figure 3

Probability density function for a BD to occur at a number of pulses after the previous BD event for the different voltage recovery scenarios. The number in the legend after each scenario shows the full width at half maximum value for the peak (in pulses).

Figure 4

Location of the maximum value of each PDF in 3 as a function of the number of pulses in the voltage recovery scenario.

Figure 5

Peak BD probability during linear voltage recovery as a function of the ramping energy. Also a fit describing an exponential decay is shown.

Figure 6

Decay of BD probability as a function of pulses (or time) since the beginning of the ramping step. The red line shows an exponential fit on the data. The inset shows the relationship between the peak BD probability during a ramping step and the increase of voltage since the previous step.