Transcript Breakdown statistics in Fixed Gap System

Breakdown statistics in Fixed Gap
System
Anders Korsbäck
Description of experiment
 Fixed Gap System was run at constant conditions for 10 days, with experimental
parameters of

Gap voltage 2300 V

Pulse length 6 µs

Pulse repetition rate of 1 kHz
 Series of identical pulses were sent until a breakdown happened. At the start of
each series, voltage was ramped up towards the final value by using the charging
of the PFL, max voltage reached at about 1500 pulses
 Overall statistics of collected data:

22 079 breakdowns happened over 158 474 876 pulses, aggregate BDR of 1.393e-4

Mean number of pulses before breakdown: 7 178

Standard deviation of nr of pulses before breakdown: 129 880 (!)

Largest number of pulses before breakdown: 16 776 936
Anders Korsbäck, University of Helsinki
04.11.2014
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Probability density of nr of pulses before BD
 The probability densities of nr of pulses before BD were
calculated from histogram data
Probability density (not normalized)
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Probability density of distribution of nr of
pulses to breakdown, estimated from
histogram. Each datapoint was calculated
from a group of adjacent histogram bins
containing at least 25 counts in total,
y-value being average bin height and x-value
the average of bin positions, weighted by bin
heights.
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Nr of pulses to breakdown
Anders Korsbäck, University of Helsinki
04.11.2014
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Probability density of nr of pulses before BD
 Poisson statistics and constant BDR lead to exponentially decaying PD

On a log-y, linear x plot, constant BDR would show as PD going down in a
straight line

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Probability density (not normalized)
Probability density (not normalized)
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Change in slope on such a plot shows change in BDR over the distribution
Probability density of
distribution of nr of pulses to
breakdown, shown with a
logarithmic y-axis, x-values up
to 10000 pulses
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7000
Nr of pulses to breakdown
Anders Korsbäck, University of Helsinki
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Probability density of
distribution of nr of pulses to
breakdown, shown with a
logarithmic y-axis, x-values
10000 pulses and above
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Nr of pulses to breakdown
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BDR vs nr of consecutive pulses without BD
 By fitting exponential functions to parts of the PD, the breakdown rate at
that part of the distribution can be obtained:
Breakdown rate
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Breakdown rate as a function of number of consecutive
pulses without breakdown, obtained via exponential fits to
parts of the probability density of nr of pulses without
breakdown. Fits done with window sizes of 11, 21 and 31
points shown for comparison.
11 point fit
21 point fit
31 point fit
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Number of pulses without breakdown
Anders Korsbäck, University of Helsinki
04.11.2014
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Change in breakdown rate over time
 Changes in breakdown rate over time was calculated by bundling
together 100 consecutive pulse series, discarding the top and bottom 5
values for nr of pulses before BD (to keep outliers from obscuring the
results). Fluctuations in this ”middle 90%” BDR clearly visible
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x 10
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Breakdown rate
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Cumulative nr of breakdowns
Anders Korsbäck, University of Helsinki
04.11.2014
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Autocorrelation of nr of pulses before BD
 An autocorrelation plot was made of an array of consecutive values of nr
of pulses to breakdown. It seems like there is weak but significant
autocorrelation up until about 400 pulse series, corresponding about to
the scale at which breakdown rate was found to fluctuate
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x 10
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Autocorrelation function
Moving average, 11 points
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Autocorrelation
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Autocorrelation function of nr of pulses before
breakdown, between pulse
series. Autocorrelation function scaled so that
for lag = 0, autocorrelation = 1 (perfect correlation)
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Lag (nr of pulse series)
Anders Korsbäck, University of Helsinki
04.11.2014
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Conclusions
 Breakdown statistics are definitely not Poissonian, and
don’t seem to become so even after a hundred thousand
consecutive pulses without breakdown. Does BDR ever
stabilize? How many orders of magnitude can it go below
its initial value?
 A sample has an intrinsic breakdown rate that fluctuates
over extended pulsing (comparable to ”hot cells” in RF?)
Anders Korsbäck, University of Helsinki
04.11.2014
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