Transcript anderskorsback_breakdownmeeting_141118 - Indico

Breakdown statistics in Fixed Gap
System (revisited)
Anders Korsbäck
Overview of experiment
 Fixed Gap System was run at constant conditions for 24 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:

35 819 breakdowns happened over 158 474 876 pulses, aggregate BDR of 4.569e-4

Mean number of pulses before breakdown: 21 888

Median number of pulses before breakdown: 1 160

Largest number of pulses before breakdown: 44 791 343
Anders Korsbäck, University of Helsinki / CERN , BE-RF-LRF
18.11.2014
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4
x 10
4
Cumulative nr of breakdowns vs pulses
3
2.5
44
xx 10
10
3.6
12000
2.67
2
3.5
10000
Cumulative nr
nr of
of breakdowns
breakdowns
Cumulative
Cumulative nr of breakdowns
Cumulative nr of breakdowns
3.5
2.665
3.4
1.5
8000
3.3
2.66
6000
3.2
1
3.1
4000
2.655
0.5
0
3
2000
2.65
2.9
2
0
1
2
3
6.8
26.9 2.5
7
4
4 7.1 3
7.2
3.5
6 7.3
Cumulative nr of pulses
Anders Korsbäck, University of Helsinki / CERN , BE-RF-LRF
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7.4 8 7.5
Cumulative
5 nrnr
6
Cumulative
nrofof
ofpulses
pulses
Cumulative
pulses
4.5
7.6 10 7.7
7
7.88 12
7
x 10
108
xx 10
x 10
8
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18.11.2014
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Breakdown rate vs cumulative nr of pulses
10
Breakdown rate
10
10
10
10
-3
Overall BDR
5 Mpulse window
25 Mpulse window
100 Mpulse window
-4
-5
-6
-7
0
1
2
3
4
5
Cumulative number of pulses
6
7
8
x 10
8
 An estimate of change of breakdown rate over the course of the experiment is shown here, by
counting the number of breakdowns in a fixed-size, sliding window of number of pulses, shown
with different window sizes
Anders Korsbäck, University of Helsinki / CERN , BE-RF-LRF
18.11.2014
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Probability density of nr of pulses before BD
10
Probability density
10
10
10
10
10
10
10
-5
-6
-7
-8
-9
-10
-11
-12
0.5
1
1.5
Nr of pulses before breakdown
2
x 10
6
 Probability density function of number of pulses before breakdown. Datapoints were obtained by
smoothing out histogram of pulses before breakdown, bundling together histogram bins so that
each PDF datapoint was determined from at least 50 histogram counts. PDF y-axis shown as
logarithmic, as then a straight downward slope corresponds to Poisson statistics.
Anders Korsbäck, University of Helsinki / CERN , BE-RF.LRF
18.11.2014
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Probability of breakdown on next pulse
BD probability vs nr of pulses without BD
10
10
10
10
-3
-4
-5
-6
10
4
10
5
10
6
Nr of pulses without breakdown
 Because the slope of the PDF on a log-y plot is equal to BDR, BD probability on the next pulse
as a function of nr of pulses without BD can be extracted by fitting lines locally to the PDF
 Doing so showed that breakdown probability on the next pulse keeps decreasing over the entire
range, rather than stabilizing in any Poissonian region. Change in overall BDR over the course of
the run might obfuscate this result somewhat though.
Anders Korsbäck, University of Helsinki / CERN , BE-RF.LRF
18.11.2014
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Two-BDR model for breakdown statistics
 92% of all breakdowns happened before 10000 pulses, thus
the early part of the PDF might be of particular interest
 Hypothesis: Each breakdown is either a ”primary”
breakdown, or a ”follow-up” breakdown caused by collateral
damage from an earlier one, thus the actual distribution is a
superposition of two Poissonians of different breakdown
rates
Anders Korsbäck, University of Helsinki / CERN , BE-RF.LRF
18.11.2014
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Two-BDR model for breakdown statistics
Probability density
10
10
10
Probability density
Two-exponential fit A + B
Short-term component A (BDR = 2.90e-3)
Long-term component B (BDR = 2.57e-4)
-5
-6
-7
2000
3000
4000
5000
6000
7000
8000
9000
10000
Nr of pulses before breakdown
 Fitting a superposition of two exponentials to the range 1500 to 10000 pulses
before breakdown yielded a remarkably good fit over the whole range. The ratio
between the two breakdown rates is about 11.
 Integrating both components gives a ratio of total breakdowns of I(A)/I(B) = 1.07.
Thus, with the current voltage ramp-up, each primary breakdown would on average
cause about one follow-up breakdown. Analysis is however obscured by exclusion
of breakdowns during the ramp-up, i.e. before 1500 pulses
Anders Korsbäck, University of Helsinki / CERN , BE-RF.LRF
18.11.2014
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Conclusions
 Even when run at constant input conditions, BDR
fluctuates over a few orders of magnitude over time,
fluctuations happen on several timescales simultaneously
 Breakdown statistics don’t seem to become Poissonian
after any amount of pulses without BD, though higher end
of distribution hard to interpret due to BDR fluctuations
mentioned above
 Two-BDR model decently explains breakdown statistics in
the lower end of the distribution, as well as matches
previous knowledge about breakdown clustering
Anders Korsbäck, University of Helsinki / CERN , BE-RF.LRF
18.11.2014
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