Statistics of vacuum breakdown in the high-gradient and low-rate regime

In an increasing number of high-gradient linear accelerator applications, accelerating structures must operate with both high surface electric fields and low breakdown rates. Understanding the statistical properties of breakdown occurrence in such a regime is of practical importance for optimizing accelerator conditioning and operation algorithms, as well as of interest for efforts to understand the physical processes which underlie the breakdown phenomenon. Experimental data of breakdown has been collected in two distinct high-gradient experimental set-ups: A prototype linear accelerating structure operated in the Compact Linear Collider Xbox 12 GHz test stands, and a parallel plate electrode system operated with pulsed DC in the kV range. Collected data is presented, analyzed and compared. The two systems show similar, distinctive, two-part distributions of number of pulses between breakdowns, with each part corresponding to a specific, constant event rate. The correlation between distance and number of pulses between breakdown indicates that the two parts of the distribution, and their corresponding event rates, represent independent primary and induced follow-up breakdowns. The similarity of results from pulsed DC to 12 GHz rf indicates a similar vacuum arc triggering mechanism over the range of conditions covered by the experiments.

Figure 1

Operation history of the TD26CC, cumulative number of breakdowns as a function of cumulative number of rf power pulses. Insets of zoom-ins show how the curve is self-similar over different time scales.

Figure 2

Left to right: A regular TD26CC cell [2] and simulations of the electric field and modified Poynting vector inside the cell. The peak surface fields are located on the iris. Simulations courtesy of Alexej Grudiev.

Figure 3

Signal propagation through a traveling wave structure. Conceptual drawing of signal propagation with and without breakdown (above), example timeseries of recorded rf signals (below). In the absence of breakdown, rf power propagates through, reaching the output coupler after the filling time ($t_{\text{fill}}$). If a breakdown happens, rf power is reflected back and reaches the input coupler after the return trip time ($t_{\mathrm{RT}}$), roughly proportional to longitudinal breakdown position. A graph shows incident power at the input coupler (blue), transmitted power at the output coupler (green), and power reflected back to the input coupler (red). Solid lines are for a breakdown, dashed lines for a preceding nonbreakdown pulse. Breakdowns are characterized by the rise of the reflected power and the simultaneous premature fall of transmitted power. Higher-order reflections between the vacuum arc and the rf network cause oscillations in the tail ends of the signals.

Figure 4

One of a pair of electrodes used for pulsed DC experiments (above), and example time series of gap voltage and current when a breakdown occurs (below). Vacuum gap is formed between the top surface of the electrode, and the same surface on an identical top electrode facing it symmetrically. The outer rim of the electrode supports the ceramic spacer that holds the electrodes apart and determines the vacuum gap distance. Electrode edges are gently rounded (rounding radius $\gg$ gap distance) to prevent breakdown through the ceramic, and to prevent field enhancement from sharp edges. When the switch is closed, gap voltage (blue) rises to its top value, and gap current (red) briefly spikes as the gap capacitance is charged. During the pulse, gap voltage ripples due to reflections in the PFL. When a breakdown happens ($t=0$), gap voltage rapidly drops as the breakdown plasma short-circuits the gap, while gap current rises to a value determined by the circuit resistance in series with the gap. Upon depletion of charge in the PFL, gap current drops and the plasma burns out.

Figure 5

Distribution of number of pulses between breakdowns and two-exponential fit, data set A. Inset shows a zoom-in of the start of the distribution.

Figure 6

Distribution of number of pulses between breakdowns and two-exponential fit, data set B. Inset shows a zoom-in of the start of the distribution.

Figure 7

Distribution of number of pulses between breakdowns and two-exponential fit, data set C. Inset shows a zoom-in of the start of the distribution.

Figure 8

Distribution of number of pulses between breakdowns and two-exponential fit, data set D. Inset shows a zoom-in of the start of the distribution.

Figure 9

Distribution of number of pulses between breakdowns for five subsets (in order: pink, red, black, blue, green) of data set B, and a two-exponential fit for each. Inset shows a zoom-in of the start of the distribution.

Figure 10

Data set A, comparison of spatio-temporal correlation (above) and distribution of number of pulses between breakdowns (below), plotted on a common x-axis. Top graph shows longitudinal distance (in units of signal travel time) between each pair of successive breakdowns, as a function of number of pulses between them. Dashed, dotted, and dash-dot lines show, respectively, the intervals containing the middle 25%, 50%, and 75% of the data. Bottom graph is the distribution of number of pulses between breakdowns, i.e., the same as Fig. 5, but drawn with a logarithmic x-axis. The black circle marks the value of number of pulses between breakdowns for which there is, according to the two-exponential fit, a 95% probability that a breakdown is a primary breakdown rather than a follow-up of the preceding one. This value of number of pulses between breakdowns is marked as a vertical red line in the upper graph.