Effect of dc voltage pulsing on high-vacuum electrical breakdowns near Cu surfaces
Anton Saressalo, Iaroslava Profatilova, William L. Millar, Andreas Kyritsakis, Sergio Calatroni, Walter Wuensch, Flyura Djurabekova
EEffect of dc voltage pulsing on high-vacuum electrical breakdowns near Cu surfaces
Anton Saressalo, ∗ Iaroslava Profatilova, † William L. Millar,
2, 3
AndreasKyritsakis, Sergio Calatroni, Walter Wuensch, and Flyura Djurabekova Helsinki Institute of Physics and Department of Physics, University of Helsinki,PO Box 43 (Pietari Kalmin katu 2), 00014 Helsingin yliopisto, Finland CERN, European Organization for Nuclear Research, 1211 Geneva, Switzerland Cockcroft Institute, Lancaster University, Bailrigg, Lancaster LA1 4YW, United Kingdom (Dated: August 6, 2020)Vacuum electrical breakdowns, also known as vacuum arcs, are a limiting factor in many devicesthat are based on application of high electric fields near their component surfaces. Understandingof processes that lead to breakdown events may help mitigating their appearance and suggest waysfor improving operational efficiency of power-consuming devices. Stability of surface performance ata given value of the electric field is affected by the conditioning state, i.e. how long the surface wasexposed to this field. Hence, optimization of the surface conditioning procedure can significantlyspeed up the preparatory steps for high-voltage applications. In this article, we use pulsed dcsystems to optimize the surface conditioning procedure of copper electrodes, focusing on the effectsof voltage recovery after breakdowns, variable repetition rates as well as long waiting times betweenpulsing runs. Despite the differences in the experimental scales, ranging from 10 − s between pulses,up to pulsing breaks of 10 s, the experiments show that the longer the idle time between the pulses,the more probable it is that the next pulse produces a breakdown. We also notice that secondarybreakdowns, i.e. those which correlate with the previous ones, take place mainly during the voltagerecovery stage. We link these events with deposition of residual atoms from vacuum on the electrodesurfaces. Minimizing the number of pauses during the voltage recovery stage reduces power lossesdue to secondary breakdown events improving efficiency of the surface conditioning. I. INTRODUCTION
Electrical vacuum arcing is a phenomenon connectedto any device or component operating under high electricfields. If a device operates in air, it is not able to with-stand high electric fields, since the dielectric strength ofair does not exceed 3 . / m [1]. To improve this com-mon device-limiting factor the air can be replaced by aspecific gas with the higher dielectric strength – or sim-ply, by vacuum with the dielectric strength that is ul-timately high. However, even in vacuum, the arcing isnot avoidable. Its appearance limits the operation of di-verse applications, including vacuum interrupters, satel-lites, medical devices, miniature x-ray sources, free elec-tron lasers and particle accelerators, such as fusion reac-tor beam injectors or elementary particle colliders [2–7].Even though these vacuum devices have been used formore than a hundred years [8–15], the exact descriptionof the vacuum arcing process is still under investigation.The open questions revolve around how the arc is initi-ated, how its location on the electrode surface is deter-mined and where the neutral atoms required for plasmaconduction are taken from. Regardless of recent progressin answering these questions [16], linking the atomic scalemodels with experimental observations is still object ofexperimental and computational research [17–19].One of the major open questions is what triggers thevacuum arcing [20–23]. There are different hypotheses ∗ anton.saressalo@helsinki.fi † [email protected] proposed to explain the phenomenon. For instance, sur-face impurities, dust and other types of contaminationare believed to be main factors triggering vacuum arc-ing near the metal surface [24]. However, the extent ofthis effect is not yet fully clear, since surface condition-ing (exposure of the surface to pulsed electric field forlong time) is believed to clean the surface from impu-rities (by detaching the particles from the surface or byburning them away in localized vacuum arcs) and, hence,to reduce the effect of these extrinsic factors drastically.However, there are indications that after the surface hasbeen conditioned, the arcing susceptibility still exhibitsdependence on the electrode material, revealing an intrin-sic nature of conditioning [21, 25–30]. Understanding towhich extent both the extrinsic and intrinsic factors af-fect the vacuum arcing may help in focusing the effortsfor mitigating this phenomenon.The phenomenon of vacuum arcing, or a vacuum elec-trical breakdown (BD), is especially crucial for the Com-pact Linear Collider (CLIC), a linear electron–positroncollider proposed to be built at CERN, where high elec-tric fields are required to make the accelerating lengthas short as possible. In the first stage, the particles areaccelerated to energies up to 380 GeV over the course ofaround five kilometers, leading to accelerating voltagesof more than 75 MV / m. Copper has been selected as thematerial of the accelerating structures, which are essen-tially waveguides for electromagnetic radio-frequency (rf)pulses (11 . a r X i v : . [ phy s i c s . i n s - d e t ] A ug extensive facilities require large amount of resources todevelop and operate. To tackle the BD problem pur-posely, a more compact system for generating BDs withdirect-current (dc) voltage pulses has been designed andused at CERN and later also installed at the Universityof Helsinki.In experiments where metal surfaces are exposed tohigh electric fields, it is a common practice to performconditioning of the surface before the experiment toreach the highest conditioning state. Since numerous BDevents will take place during the conditioning, the systemneeds a recovery procedure to return back to the puls-ing mode after such an event. In a recent study [33], itwas shown that the voltage recovery procedure influencesthe BD probability distribution function (PDF) over thenumber of pulses between two consecutive BDs. It wasnoticed that the probability was significantly higher for aBD to occur during the first pulse right after a step-wisevoltage change during the recovery. It is not clear whatmay cause such an increase since there are, in fact, twofactors during the change of the ramping step: a changein the voltage and a 20 second pause needed to set a newvalue of the voltage.Since the dc pulsed system produces pulses with higherfrequency (up to 6 kHz) than the ones generated in the rftest stands at CERN (50 Hz to 400 Hz), for compatibilityof the conditioning results, it is also important to under-stand how the breakdown rate (BDR) may depend onthe pulsing frequency, also known as pulsing repetitionrate.In this study, we performed various breakdown rateexperiments on Cu electrodes. We compared the effectsof different voltage recovery algorithms, pulsing repeti-tion rates and pauses of varied lengths between pulsingruns in order to understand how the electrode surfacesare cleaned during electric pulses and breakdowns. II. EXPERIMENTAL APPARATUS ANDMEASUREMENT TYPES
The experiments were concluded with similar pulseddc systems installed at the University of Helsinki andat CERN. The systems contain a power supply, a Marxgenerator [34] and a Large Electrode System (LES) com-bined with data acquisition and measurement electron-ics [33, 35]. A schematic of the full system can be seenin Fig. 1.Two cylindrical electrodes made out of copper [36] areplaced inside the vacuum chamber of LES with a dis-tance of typically 40 or 60 µ m and vacuum pressure below1 × − mbar when pulsing. The Marx generator is usedfor generating square dc pulses with voltages up to 6 kV(150 MV / m with a 40 µ m gap and assuming E = V /d )and with pulse width typically 1 µ s. The Marx generatoralso monitors the current during pulsing. When a peak inthe current exceeds a threshold value, the device detectsa breakdown and stops pulsing. DC POWER SUPPLY
MARXGENERATOR
MEASUREMENT CONTROL& DATA ACQUISITIONVACUUM GAUGE & PUMPOSCILLOSCOPELARGE ELECTRODE SYSTEMHVPULSE
FIG. 1: A schematic of the pulsed dc system used inthe measurements.Another way of tracking the breakdowns is monitoringthe vacuum pressure with an ion gauge. The readingsshow a pressure spike every time a breakdown occurs.Combining different methods of breakdown-detection al-lows more accurate information on each event and makesit possible to find if some of the events either falsely de-tected as BDs or real BDs not detected by the generator.Other key parts of the measurement system includean oscilloscope for monitoring the voltage and currentwaveforms during pulsing and breakdowns as well as anion gauge for measuring the vacuum pressure.
A. Pulsing modes
A majority of the measurement runs were conductedusing either of the two pulsing modes discussed below –or a combination of both.In feedback mode, the target breakdown rate (BDR) is10 − BDs per pulses (bpp). This means that the pulsingis done in periods of typically 100 000 pulses (to matchthe target BDR). If a BD occurs during the period, thepulsing is immediately stopped and the voltage is eitherdecreased or kept constant, depending on the BD pulsenumber as explained in more detail in [35]. Otherwise thevoltage is increased. The maximum change after one pe-riod is typically set to ±
10 V, which equals ± .
16 MV / mwith a 60 µ m gap. A pulsing run is defined as a com-bination of pulsing periods and breakdown events thatoccurred during one continuous experiment without ad-ditional pauses.The feedback mode is used to condition the electrodesurfaces. After being exposed to air – especially withpristine electrodes – they need to be conditioned to beable to operate at the highest possible electric field witha reasonable BDR. The conditioning is typically startedwith a low electric field, such as 10 MV / m. The feed-back algorithm gradually increases the voltage over mil-lions of pulses until the number of breakdowns starts in-creasing and the voltage level saturates typically close to100 MV / m [33, 37, 38]. The value varies slightly depend-ing on the electrode type and the gap size.In the other pulsing mode, which we call flat mode, thevoltage is kept constant during the whole measurementrun, except for the voltage recovery after each BD. Usu-ally this mode is used only after the specimen has beenconditioned and the flat mode voltage level is chosen closeto the saturation value reached during the conditioning,so that the breakdown rate fluctuates close to the targetvalue. However, sometimes choosing the correct level isdifficult and some conditioning effect is seen in the formof BDR fluctuations also during the flat mode. B. Voltage ramping scenarios
To recover the voltage after a breakdown we applya voltage ramp procedure, i.e. we increase the voltagegradually, ramping it from an initially low value to thetargeted one ( ∼ V i = ( V target − V start ) (cid:20) − exp (cid:18) − P i F × P step (cid:19)(cid:21) + V start , (1)where V i and P i are the voltage and the pulse numberat the beginning of each ramping step i , respectively. P step is the number of pulses per each step and F de-termines the curvature. The shapes of different rampingmodes obtained with different F parameters can be seenin Fig. 2. As one can see, the F parameters between 1and 4 produce smooth curves asymptotically approach-ing the target value. With F <
1, the ramping voltagerises as a step function while with
F >
10, the voltage rises almost linearly. The starting voltage V start is deter-mined by the ramping factor, and is typically set to onefifth of the target voltage V target , i.e. the next voltagein the feedback mode or the set voltage of the flat mode.During the voltage ramp, there is always a pause of ∼ Number of pulses V o l t age [ V ]
20 stair steps, F=420 stair steps, F=10009 stair steps, F=15 stair steps, F=15 slopes, F=13 slopes, F=0.51 slope, F=100 (a)
Time [s] V o l t age [ V ]
20 stair steps, F=420 stair steps, F=10005 stair steps, F=15 slopes, F=11 slope, F=100 (b)
FIG. 2: a) Comparison of five different rampingscenarios with voltage against number of pulsesfollowing the Eq. 1 with V target = 5000 V and V start =1000 V (ramping factor ). Each markerrepresents the voltage at the beginning of each rampingstep or slope. A 20 seconds pause (idle time) in thesystem always precedes the pulse with the marker. b)Shows the selected scenarios with respect to elapsedtime after the previous breakdown. In the beginning ofeach step, there is a fraction of a second of pulsingfollowed by nearly 20 seconds of idle time during whichthe voltage change is performed. The voltage increasein the slope scenarios is not instant but takes placeduring this fraction of a second and thus the slope isnot really visible in the graph.Voltage ramp is applied only after a breakdown. Aftera pause due to other reasons, such as changing the pulsingperiod, the target voltage is applied directly without aramp.In our system the voltage can be ramped step-wiseor linearly. In the former case, the voltage is changedabruptly at the end of each step, during an unavoid-able pause. In the latter, the voltage is gradually in-creased according to a given slope without pauses duringthe pulsing. The linear voltage ramp scenarios with dif-ferent slopes were implemented to investigate whetherthe gradual increase in the voltage is more beneficial forthe optimal voltage ramp scenario. In order to mimicthe asymptotic behaviour of the ramping procedure with1 < F <
4, we applied linear voltage ramp scenarios withmultiple slopes. Changing the slope of the linear rampalso requires a 20 second pause, hence, we note that in allvoltage ramp scenarios, except for the single slope linearramp, there was always an additional idle time needed fora voltage parameter to be changed. In single slope sce-nario, an idle time is not required even after the voltageramp is complete.In our previous studies [33, 35, 38],where a voltageramp scenario with 20 steps with and curvature F = 4was applied, we noticed the increased an BD probabilityright after the change in the voltage value at the be-ginning of the step, especially between 200–1000 pulses,where both the absolute voltage and the relative voltagechange were significant.Currently, we focus on different voltage ramp param-eters to analyze the effect of this procedure on surfaceperformance at high electric fields to optimize the sur-face conditioning. We compare the total BDR, the frac-tion of sBDs and the average number of sBDs in a seriestriggered after a primary event, µ sBD .The sBDs were determined by fitting the BD proba-bility density function ( ρ BD ( n )) of the number of pulses n between the two consecutive BD events by a two-termexponential model ρ BD ( n ) = A exp( − αn ) + B exp( − βn ) (2)as introduced in [39]. The cross-point of the two-exponential curves was used as the dividing line so thatthe BDs that occurred at a smaller number of pulses weredefined as secondaries and the ones with a larger num-ber of pulses as primaries. The exponential coefficientscorrespond to the breakdown rate of each regime, α toBDR of primaries and β to that of secondaries. C. Repetition rates of pulsing
The nominal repetition frequency for CLIC energystages is 50 Hz [13]. Nevertheless, the latest klystron-based X-band rf test facilities at CERN can operate atrepetition rates of up to 400 Hz in order to reduce the time required to pre-condition the accelerating struc-tures [40]. However, the effect of repetition rate on condi-tioning is not well understood and breakdown rate mea-surements performed in the test stands typically requirelong time frames of the order of months and as a conse-quence there is currently little literature on the subject.High repetition rates available in the pulsed dc systemsoffers a unique opportunity to clarify this effect. Pre-viously a potential relationship between repetition rateand BDR was investigated experimentally in both the rf(25 Hz to 200 Hz) and dc (10 Hz to 1000 Hz) test stands.The results showed a small BDR increase at lower repe-tition rates, however, it was concluded that the observeddifference was statistically insignificant and, hence, wassuggested to be negligible [41]. Since a newly installedpulse source, such as a Marx generator, allows for widerrange of repetition rates in the pulsed dc system, thesensitivity of the BDs to the pulsing frequency can bemeasured with higher accuracy. The following steps weredesigned to perform the experiment:1. Choose several values of repetition rates in therange from 10 Hz to 6000 Hz in increasing order andapply high-voltage pulses using flat mode.2. Choose two values of repetition rates and to swapthem several times to prevent electrode condition-ing from masking the effect of the repetition ratechanges. Reference frequencies of 100 Hz and 2 kHzwere chosen and regularly compared between themeasurements with different repetition rates. Thisalso mitigated the effect of the BD clustering as thesBD series do not generally continue after a repeti-tion rate change.3. In the last step, so-called burst mode, the repeti-tion rate is different for odd- and even-numberedpulses. This also means that the idle times be-fore the odd-numbered pulses at 100 Hz are twoorders of magnitude longer than those before theeven-numbered pulses at 2 kHz. The pulse periodsare then 10 ms and 0 . .
05 %.
D. Pauses between pulsing runs
In many rf test stand and pulsed dc system break-down experiments, it has been qualitatively noticed thatthe breakdown probability is notably increased duringthe first pulses following a significant pause in opera-tion. This effect has been noticed in the experimentsFIG. 3: Schematic of burst mode, where pauses betweenodd and even-numbered pulses (red and blue) aredifferent. Note that the x-axis is not linear as the 1 µ spulse width has been exaggerated for visualization.even when vacuum integrity was maintained throughoutthe pause, typically in the ultra-high vacuum range. Todate however, this phenomenon has not been the subjectof a purpose study.In the present study, we analyzed this effect by car-rying out a number of experiments with pauses rangingfrom 15 s to 1 × s and 4 × s to 2 . × s betweenpulsing runs with the dc and rf systems, respectively.High or ultra high vacuum was maintained during thepause. We quantify the effect of these pauses in both thepulsed dc system and the rf test stands by recording thenumber of breakdowns triggered in the system right afterthe pause.In the dc case, the initial BDs after the random lengthpause were defined as the events that occur within thefirst second of pulsing (2000 pulses) with a constant volt-age. Each pause was preceded by 50 000 pulses with-out a BD to ensure that the system was always in thesame condition when the pause started. Hence, no volt-age ramping was used after the pause. In the rf case, thesystem was run continuously for 2 hours after the pauseand a probability for BDs to occur during this time wascalculated as breakdowns per pulses. III. RESULTSA. Studies of different ramping scenarios
Copper electrodes with 40 mm anode against 60 mmcathode and 40 µ m gap were used in this experiment.Seven different ramping scenarios and one withoutramping were investigated in the flat mode at a voltageclose to the saturation value, with ∼ pulses in each run. Each flat mode run waspreceded by a short feedback mode run in order to checkthat there were no drastic changes in the conditioningstate of the electrodes which would affect the saturationvoltage. All the ramping experiments were conductedwith a repetition rate of 2 kHz.The ramping scenarios are listed and visualized inFig. 2. They include four step-wise voltage ramps andthree cases where the voltage was ramped in slopes. In each of these cases, the ramping parameters were cho-sen to match the shape of the voltage ramp used in theprevious experiments [33, 35] (20 steps over 2000 pulseswith F = 4). For comparison, we also performed anexperiment without any ramping, i.e. the voltage wasset to the target value immediately. In all scenarios, theelectrostatic field reached at the end of the ramp wasalways between 126 MV / m and 128 MV / m. The resultsare listed in Table I and visualized in Fig. 4.In the table, each voltage ramp scenario is described bythe number and the method of the voltage changes, e.g.
20 steps or , until the voltage reaches the targetvalue. F parameter specifies the shape of the rampingcurve, see Eq. 1; BDR is the breakdown rate measuredin BDs per pulse.We also show the fitting parameters α and β (see Eq.2), which are essentially the BDRs of the primary andsecondary events, respectively. The fit was done with up-per limit at 20 000 pulses and lower limit at the numberof pulses where the ramping voltage exceeds 95 % of thetarget value, except 5 slope and 3 slope scenarios wherethe limits had to be manually adjusted. N cross in the ta-ble indicates the number of the pulses, at which the twoexponents describing sBDs and pBDs (see Section II B)intersect. All BDs, which were registered before N cross ,were defined as secondary ones. These are shown as thefraction of the total number of BDs in each run in percent( N sBD ). For the type with no ramping, the two-term ex-ponential model was impossible to fit and the cross-pointwas assumed at 1000 pulses, around the value where thePDF drops below 1 × − . The last column of the ta-ble shows the number of the sBDs that took place aftereach pBD on average ( µ sBD ). All the uncertainties arecalculated from the standard error of the mean.The lowest BDR and the lowest sBD fraction can al-ready point out the best ramping scenario. However, wenote that these values, which are found for the ramp with20 steps ( F = 4) and the one with a single slope, are alsostrengthened by the lowest rates of the primary events α = 1 . × − and the smallest mean number of thesBDs per a primary one, µ sBD < . F parameter specifies the shape of the ramping curve, BDR is breakdowns per pulses, α and β arefitting parameters of the two-exponential model, N cross is the number of pulses at which those exponentials intersect,N sBD is the fraction of all BDs that occur below N cross and µ sBD is the mean number of consecutive BDs belowN cross . The uncertainties are calculated as the standard error of the mean. For the scenario with no ramping, thetwo-exponential fit was impossible, meaning that the values denoted with † are not fully comparable to the others. Ramp scenario F BDR [bpp] α β N cross N sBD [%] µ sBD
20 steps 4 1 . × − . × − .
002 2467 70 ± . ± .
120 steps 1000 7 . × − . × − .
010 2304 82 ± . ± .
29 steps 1 8 . × − . × − .
011 1205 88 ± . ± .
65 steps 1 2 . × − . × − .
025 1385 84 ± . ± .
45 slopes 1 3 . × − . × − .
010 1357 90 ± . ± .
83 slopes 0 . . × − . × − .
013 899 95 ± . ± .
91 slope 100 5 . × − . × − .
003 3666 67 ± . ± . . × − - † - † † ± † . ± . † Number of pulses between BDs -8 -6 -4 -2 B r ea k do w n p r obab ili t y den s i t y
20 steps, F=420 steps, F=10009 steps, F=15 steps, F=15 slopes, F=13 slopes, F=0.51 slope, F=100No ramping -6 -5 -4 -3 -2
20 steps, F=4:A=6.4e-06, =1.1e-04B=7.2e-04, =2.0e-031 slope, F=100:A=1.5e-05, =1.1e-04B=2.5e-01, =2.8e-03
FIG. 4: Probability for a breakdown to occur at each number of pulses between breakdowns for each of the rampingscenarios. The vertical lines indicate the cross-points of the two-exponential fit for each run. Visualization of the fitfor the data points of 20 steps, F =4 and 1 slope, F =100 is shown in the inset. There the legend also shows the fitparameters.The vertical lines in Fig. 4 show the cross-points of thetwo-term exponential fits. The colors of these lines matchthe color of the markers chosen for each ramping run. Itis clear that all of these lines are close to one another andare about 2000 pulses, which was the number of pulsesused in all ramping procedures.Since the voltage ramp always follows a post- breakdown pause, it is difficult to separate the effect ofsurface modifications caused by the preceding BD eventand possible effect of residual deposition during the pausetime. The data showing the experiments with no ramp-ing and with a single slope ramping cast some light onthis issue. We see that, restoring the same voltage valueimmediately after the post-BD pause (no ramping), re-sults in the highest BDR, showing practically a singleexponent behavior of ρ BD ( n ) in Fig. 4. Meanwhile, thelinear increase in the voltage after a BD even with a post-breakdown pause resulted in the least secondary break-downs during the ramping. This observation suggeststhat some relaxation effects take place on the surfaceduring the gradual increase of surface charge.We note that all the major ramping peaks appear be-fore the cross-points, hence concluding that almost all ofthe sBDs occurred during the ramping period. This alsomeans that the sBDs barely separate from one another bymore than 2000 pulses which the duration of the rampingprocedure. Clearly, the changes taking place during theramping affect the probability of triggering subsequentbreakdowns, while at the target voltage, where all elec-tric parameters are kept unchanged, the sBDs practicallydo not take place. In some runs, however, the cross-pointwas found at a number of pulses greater than 2000, whichmeans that in these cases, the changes that took placeduring the ramping period still affect the surface behaviorshortly after the pulsing at the target voltage has begun.The breakdown probability was also analyzed as afunction of voltage, as shown in Fig. 5. Here we seethat during the step-wise ramping, breakdowns start tak-ing place already at lower voltages, whereas the linearincrease in the voltage without pausing leads to an in-creased BD probability at higher voltages and typicallyonly after a slope change, i.e. a small pause in the puls-ing. The type with no ramping was not evaluated as allthe breakdowns occurred at the target voltage. Target voltage [V] -7 -6 -5 -4 -3 -2 -1 B r ea k do w n p r obab ili t y den s i t y
20 steps, F=420 steps, F=10009 steps, F=15 steps, F=15 slopes, F=13 slopes, F=0.51 slope, F=100
FIG. 5: Probability for a breakdown at a givenramping voltage. The x-axis values have been beenscaled so that V target =5000 V in each measurement. B. Experiments on pulsing repetition rates
Since we observe a clear correlation between the break-down probability and the pause duration between the pulsing runs, we now turn out attention to the analy-sis on the effect of the repetition rate which we appliedin different orders. All the repetition rate experimentswere concluded using 40 mm Cu electrodes separated bya 60 µ m gap.
1. Increasing order of repetition rates
The pulsing was done with repetition rates rangingfrom 10 Hz to 6000 Hz. The repetition rate was changedto the next one after every 100 BDs. The usual flat modealgorithm was used during each such step. The electricfield was chosen to keep the BDR between 10 − bpp and10 − bpp. The results are shown in Fig. 6.Figure 6a shows that the BDR (bpp) decreases as therepetition rate increases. With the same electric field,the BDR at 10 Hz is 7 . × − bpp while at 6 kHz itis 6 . × − bpp, which is by two orders of magnitudelower. The difference is observable, but less remark-able when the BDR is expressed as breakdowns per sec-onds (bps), as shown in the same figure. In the latter,we see a five-fold increase in the BDR from the lowestto the highest repetition rate (from 7 . × − bps to3 . × − bps). The increase in the number of BDs persecond is expected since the idle time between the pulsesdecreases with an increase in the repetition rate. How-ever, this difference in the idle time the between pulsesof both regimes is much greater (600) compared to theobserved increase. Hence, the two graphs presented inFig. 6a corroborate one another in spite of the differencein the measured rates.Since sBDs show the correlation with the precedingevents, we plot the percentage of these events (N sBD )separately in Figure 6b along with the mean number ofsBDs after a pBD ( µ sBD ), as function of the repetitionrate. Although the dependence is not as monotonic as inFig. 6a, the graphs clearly show that the values of bothN sBD and µ sBD are higher at lower repetition rates anddecrease strongly at the higher pulsing frequencies.
2. Swap repetition rates
During the pulsing experiments, the electrode surfacesare continuously conditioned and this may affect theBDR measurements at different repetition rates, con-fusing the possible conclusions. To avoid the effect ofchange in the surface conditioning state between the mea-surements from screening the results, we applied a modewhere the repetition rates were swapped between 100 Hzand 2 kHz after every three consecutive BDs that oc-curred at the target voltage. Fig, 7 shows the cumulativenumber of BDs vs the number of pulses in the repeti-tion rate swap regime (solid line). For comparison, wealso show the same value accumulated during the 100 Hzrepetition rate (red dash-dot line) and that accumulatedduring the 2 kHz repetition rate (blue dash-dot line). Repetition Rate [Hz] -5 -4 -3 -3 -2 -1 -3 -2 -1 Idle time [s] (a) Repetition rate [Hz] s B D [ % ] s B D -3 -2 -1 Idle time [s] (b)
FIG. 6: BD experiments with variable repetition rates.a) shows the BDR as BDs per pulses and as BDs persecond for each repetition rate. b) shows the fraction ofsecondary, BDs N sBD and the mean number ofsecondary BDs after a primary one, µ sBD for eachrepetition rate. In each graph, the uncertainties areestimated from the standard error of the mean, thoughmany of the error bars are too small to be visible.We see that the BDR (in bpp) is approximately twiceas high with the lower repetition rate, while it is prac-tically the same as for the higher repetition rate in theexperiments with the swapped repetition rates. It is clearthat the system was running for longer number of pulseswhen the repetition rate was high (blue segments) andstarted practically immediately breaking down, when therepetition rate was switched to the lower value (red seg-ments in the shape of steps) Number of Pulses N u m be r o f B D s Combined BDR: 9.56e-06BDR @ 100 Hz: 1.59e-05BDR @ 2 kHz: 8.06e-06
FIG. 7: Evolution of the cumulative number of BDsagainst the number of high-voltage dc pulses with theswapping of repetition rates. The solid line shows theresult from the whole experiment while the blue and reddash-dot lines show the results for the repetition ratesof 2 kHz and 100 Hz, respectively.
3. Burst mode
An additional burst mode was implemented in thehardware of the generator in order to further study theeffect of the repetition rates as described in Section II C.For the analysis, the breakdowns that occurred at theodd and the even pulses were separated. In this case, thepause before an odd-numbered pulse was 10 ms and thepause before an even-numbered pulse was 0 . R BDR shows the BDR ratio with the lower repetitionrate divided by that of the higher repetition rate.
E [MV/m] Pause [ms] BDs BDR [bpp] R BDR
62 10 197 2 . × − . × −
61 10 116 9 . × − . × −
62 10 57 8 . × − . × − C. Pause between pulsing
The pause between measurements with the pulsed dcsystem was measured using the feedback mode and byimplementing a randomly selected pause between 15 and100 000 seconds ( ∼
28 h) in length, each following a 50 000pulsing period without a BD. The pause lengths weregrouped into 8 bins and the BD probability was estimatedfrom the fraction of cases that lead to a BD within thefirst second of pulsing (2000 pulses) after the pause. It isalso important to note that no voltage ramping was usedafter the pause as there was no preceding BD.For the rf test stand, the effect of the pause was es-timated by presenting the number of BDs that occurredwithin the first two hours of operation at 50 Hz (360 000pulses) following a long pause in operation ranging from11 to 68 hours. With the rf test stand, the vacuum levelis typically maintained at around 1 × − mbar duringthe pauses i.e. 2–3 magnitudes lower than in the pulseddc systems.The results of both tests are presented in the Fig. 8and both show that the BD probability increases withthe length of the pause. This result indicates that thereare processes, which take place during the pause and con-sequently affect the probability of BDs after the pause,when the electric field is restored at the surface.FIG. 8: a) BD probability within the first second ofrunning (2000 pulses) after a predetermined pausebetween pulsing runs, not preceded by a BD, with apulsed dc system. The horizontal blue error barsindicate the range of the pause length values where thedata were averaged. The vertical red error bars, again,indicate the uncertainty as the standard error of themean. b) Shows the probability of BD i.e. the BDRduring the first two hours of operation after a longpause in pulsing with a rf test stand. The blue verticalerror bars indicate the uncertainty as the square root ofthe number of the BD events. IV. DISCUSSION
In the present study, we clearly see that the idle timesbetween the pulsing runs and during the pulsing itselfhave a great impact on the BD probability. Several inde-pendent measurements show the same result: the longerthe idle time between the pulses, the higher the BDRmeasured in bpp becomes.Analysis on the different voltage ramp scenarios canshed some light on this effect. First of all, we see that both the shape of the ramping curve and the pauses be-tween the ramping steps or slopes play important roles.While ramping the voltage step-wise, two changes appearbetween the steps: the voltage level increases and the sys-tem pauses for 20 seconds to set the new voltage value. Inthe multi-slope voltage ramp, the voltage changes gradu-ally, however, the system pauses for the same 20 secondsto set a new slope of the voltage ramp. Hence, by keepingone of the parameters, for instance the number of pauses,intact, we are able to separate the effect of pauses andthe voltage change on the BD probability.Assuming that vacuum residuals could explain the in-creased BD probability in the system during the voltageramp, one could suggest reducing the number of possiblepauses to reduce the number of BDs and, hence, improvethe efficiency of the surface conditioning. However, theresults presented in Table I show that the 9 and 5 pausesin the 9 steps and 5 steps/slopes scenarios resulted inhigher BDR and fraction of sBDs as well as in longer BDseries compared to the 20 steps voltage ramps with bothcurvatures F = 4 and F = 1000. Moreover, the voltageramp with 3 slopes, which required only three pauses,resulted in the worst result. Almost all the BDs werecounted as secondaries and the average number of sBDin the series after a pBD is one of the largest. This in-dicates that the pauses (vacuum residuals) alone cannotexplain the higher activity of the surface during the volt-age ramp. The step height for the voltage ramp plays animportant role as well.As we see in Fig. 2a, both 9 and 5 steps voltage rampsbring the voltage to 70 % (and the 3 slopes to 90 %) of thetarget value already at end of the very first step. Suchhigh voltage values following after the mandatory pausemake these scenarios very similar to that with no ramp-ing at all. Hence we conclude that, although intuitively,the large steps at low voltages are rather reasonable, theexperiments show that the voltage should not change dra-matically during the voltage ramp. In the following, wewill obtain a deeper insight of the effect of the voltagechange in the voltage ramps where the number of pauseswas the same.In Fig. 9 we zoom in the data presented in Fig. 4 toanalyze the behavior of ρ BD for the sBDs, i.e. BDs withthe enhanced probability that take place before the cross-point of the two exponents. We selected four scenariosthat can be grouped in pairs. The pairs are defined by thesame number of pauses during the voltage ramp, either5 or 20. However, within the pair, the voltage ramp wasdone differently. In the pair with 5 pauses the voltagewas ramped either in steps (5 steps ramp) or in slopes (5slopes ramp). Both height of the steps and the value ofthe slopes were modified during the ramp to follow theexponential shape of the ramp applied in [33].In the pair of with 20 pauses, the voltage was rampedin steps in both scenarios. The difference was in theheight of the steps. In the ramp with F = 4, the stepheight varied similarly as it was done in [33], while in theramp with F = 1000, the step height was kept constant,0so that the overall ramping shape was linear.Comparison of the curves for the 5 pause pair in Fig. 9reveals a striking similarity: Both curves have peaks atthe same number of pulses between the consecutive BDs,at 400 and 800 pulses. Since, a single step before chang-ing the voltage value or the slope consists of 400 pulses, itis clear that the first two pauses create conditions favor-able for a BD to occur in the first pulse after the pause.In Fig. 2 we see that the voltage values right after thepauses in 5 steps and 5 slopes scenarios are the same.It is clear that the BD probability during the first pulseafter a pause is increased due to increased value of thevoltage and due to exposure of the surface to the resid-ual deposition during the pause. Although the systemsees the increased value of the voltage already before thepause in the slope-wise ramp, a BD is more probable totake place after the system paused. It is evident thatthat the cleaning of the surface takes place even withoutBDs, otherwise, the BD events would be nearly equallyprobable in the slope-wise ramping before and after thepause.
200 400 800 1200 2000
Number of pulses between BDs -8 -6 -4 -2 B r ea k do w n p r obab ili t y
20 steps, F=420 steps, F=10005 steps, F=15 slopes, F=11 slope, F=100
FIG. 9: Zoom-in for Fig. 4 showing the breakdownprobability PDF against the number of pulses betweenbreakdowns for the scenarios with 20 stairs, 5 stairs,5 slopes and 1 slope.The second peak can be explained in a very similarmanner as the first one. However, the further increasein the voltage values during the system pausing, showsdifferent behavior for both voltage ramps. The step-wiseramp exhibits two more peaks at 1200 pulses and at 1600pulses, while the slope-wise ramp does not show increasedprobabilities related to the pauses in the system. It isclear that the smoother change in the voltage of the slopeprovides gentler cleaning of the surface close to the targetvoltage value, compared to the step-wise changes, evenif the system still pauses to change the slope. The lessernumber of peaks in the ρ BD ( n ) for the 5 slopes voltageramp does not, however, result in better overall perfor-mance. The data in Table I indicates that the step-wisevoltage ramp gives slightly smaller fraction of sBDs and lower total BDR and can hence be considered as a moreoptimal scenario for the voltage ramp. This is due tohigher intensity of the BD in the first pulse after thevery first pause during the ramping. It is clear that thepulsing with the steep linear voltage increase activatesmore spots for subsequent BDs ( µ sBD for the 5 slopesramp is almost twice as high as for the 5 steps one) inthe vicinity of the preceding ones, than the pulsing at thesame voltage.The ρ BD ( n ) functions for both 20 steps scenarios donot have identical peaks, although the number of pausesin both ramping scenarios is the same. The large steps inthe voltage ramp in the beginning of the ramping proce-dure result in increased BD probability for the ramp with F = 4. We do not register any breakdowns in the rampwith F = 1000 for the first 6 steps, however, we observea strong increase of the BD probability with the well-pronounced peaks during the first pulse after the pausesat higher voltage steps. Moreover, the peaks are growingin height, illustrating that the voltage increase should beslower when approaching the voltage target value.Despite of the higher BD probability at the beginningof the voltage ramp, we see that overall, the conditioningachieved in the voltage ramp with curvature F = 4 ismore optimal as it results in lower total BDR and lowerfraction of the sBDs in the pulsing run. The BDs trig-gered at the voltage values closer to the target value aremore intense and may result in larger number of nucleifor the subsequent BDs. However, the difference in per-formance of the voltage ramps with 20 steps is not asdramatic as for the ramps with 5 steps and 5 slopes.Based on the obtained results, we conclude that thepulsing at the lower voltage values is essential for clean-ing the surface. If the surface was exposed to a sufficientnumber of lower voltage pulses, the increased BD proba-bility at higher voltage values is less detrimental for thesurface conditioning than in the reverse case (less lowvoltage pulsing, but reduced BD probability at the highervoltages). This conclusion is strengthened by the resultsshown in Fig. 9 for 1 slope. In this scenario, no pauseswere allowed in the system and the voltage was slowlyramped from the initial to the target value after a BD.The slope of the voltage increase is, however, very similarto that for the 20 steps voltage ramp with F = 1000. Weobserve that the data looks very similar between the tworamps, however, the peaks at the first pulses after thepauses in the 20 steps ramp are missing in the ramp witha single slope. We see again that the BD probability ishigher at the voltages closer to the target value, but theoverall result is the best for this run.We also note here that the two-term exponential fitsfor the ρ BD ( n ) support the previously proposed hypoth-esis of two mechanisms triggering a BD event, hence theBDs can be classified as ”primary”, which are indepen-dent of other events and occur at random place on thesurface, and ”secondary”, which have an enhanced prob-ability and found to correlate stronger with the precedingBDs [33, 39, 42]. The best fits are with the scenarios with11 slope and the one with 20 steps and F = 4 ( R = 0 . R = 0 . × s for the rf case. These valuescorrelate with the roughly estimated monolayer forma-tion times, based on the impingement rate [43] of watermolecules which are 80 s and 6 × s, respectively, atthe internal pressure of each system. This supports thenotion that some of the breakdowns may be triggered byvacuum residuals migrating to the high field regions ofthe surface during the idle time. The surfaces are con-sequently cleaned by the high voltage pulses and break-downs. Also electrostatics of the surface impurities mayplay a role in the atom redistribution on the surface viasurface migration processes [17].We also observe a strong dependence of the BDR mea-sured in bpp on the pulsing repetition rate, which wasdramatically decreasing with the increase of the repeti-tion rate. The trend is relatively smooth on the loglogscale over the whole frequency range, except for an un-expected data point, measured at a frequency of 4 kHz.In Ref. [41] it was concluded that the repetition rate hasonly negligible effect on the BDR, i.e. increase in thepulsing frequency has no effect on the conditioning pro-cess. However, the conclusion was derived for the rangeof repetition rates from 25 Hz to 200 Hz, while the widerrange of repetition rates in the present study reveals theexistence of such dependence. In Fig. 6, we see that theresponse over this narrower range is less significant, com-pared to the extremes of 10 Hz and 6 kHz.Figure 6b shows that both the fraction of sBDs (out ofall BDs) and the mean number of consecutive sBDs aftera pBD decrease as the pulsing frequency increases, i.e.the idle time between the pulses decreases. This suggeststhat the idle time during pulsing affects especially thesecondary BDs. We note that, again, the response isthe greatest at the lowest and highest repetition rates.Between 50 Hz and 1000 Hz, i.e. with idle times rangingfrom 20 ms to 1 ms, this trend is not visible. The studies with the burst mode show that the idletime between the high-voltage pulses has also a signifi-cant effect on the BDR. In the last column of Table II weshow the ratio of the BDRs, R BDR during the odd andeven-numbered pulses in the burst mode with the fre-quencies of 100 Hz and 2 kHz. Although the BDR valueobtained for the odd-numbered pulses was consistentlylarger than that measured for the even-numbered pulses,the difference is not dramatic ( < V. CONCLUSIONS
Several methods for investigating the effect of the var-ious aspects of pulse timing on the breakdown rate wereevaluated using the pulsed dc and rf systems. The stud-ies include a comparison of different breakdown recoveryscenarios, measurements of breakdown rates for variablerepetition rates and measurement of the effect of pausesbetween pulsing runs. All the measurements performedwith pauses between pulsing ranging from 0 .
17 ms to 68 hshow that the longer the idle time between pulses, themore prone the system is to breakdowns.In comparison of different post-breakdown voltage re-covery procedures, we observe a correlation betweenthe increased idle time before pulsing, combined witha strong voltage increase, and the average number ofsecondary breakdowns, i.e. those that occur soon afterand in the vicinity of the previous ones.This correlationsuggests that the vacuum residuals must interact withthe modification on the surface caused by the precedingbreakdown, increasing the probability of a breakdown tooccur during the post-breakdown recovery right after thepause and voltage increase.The optimal voltage recovery after a breakdown wasdetermined to be a linear increase in the voltage withthe smallest idle time during the recovery. Thus, thisramping scenario will be used in the future experimentswith the pulsed dc systems.In this work, we observe an enhanced breakdown ratefollowing a period when the system was not pulsed. How-ever, the enhancement is not dramatic and the break-down rate is restored rapidly after the system starts puls-ing again returning to the previous breakdown rate re-gardless of the length of the idle time.2
ACKNOWLEDGEMENTS
The research and collaboration was made possible bythe funding from the K-contract between Helsinki Insti-tute of Physics and CERN. The authors would also like to thank the Paul Scherrer Institute for funding the highvoltage generator that was supported by an SNF/FLAREgrant No. 20FL20 147463. We are grateful to the CLICproduction team for design support on each stage of sys-tem development and samples fabrication. [1] John R. Rumble,
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