Eindhoven University of Technology

BACHELOR

Inception of Streamers near Dielectric Material

Broekman, Britt E.T.

Award date:2018

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Eindhoven University of technology

Final Bachelor Project

Inception of Streamers near DielectricMaterial

Britt Broekman

Supervised byShahriar Mirpour and dr.ir. Sander Nijdam

August 5, 2018

Abstract

This paper shows and discusses the results of observing of inception near a dielectric particle. Ahigh voltage is used to create a potential in the area between two electrodes. Here a particle hangsfrom which initiation is observed using a photo-multiplier and an ICCD camera. The ICCD cameradid generate only one useful image showing initiation on the top and breakdown on the bottom ofthe particle. This lack of results could be improved by calibrating the PMT and ICCD together, orby using a focused PMT (on bottom or top of the particle). However, the PMT itself generated lotsof useful results.

Firstly, the PMT signal of initiation shows under some conditions a discrete number of possiblewidths, separated by a constant of approximately 60 nanoseconds. The reason for this is still un-known and could be explored further using single-photon experiments. The shortest width has thehighest probability and gets even more probable with higher applied voltage, which is in line withthe expectation that a higher applied voltage produces initiation faster.

Secondly, the deviation from the mean delay between the applied voltage and the observation ofinitiation gets lower for higher pressure and higher frequency independently, as expected. Neverthe-less, the delay measured with the dielectric particle is found to be lower than the metal and coatedmetal particles. This seems to contradict the theory about dielectric material, but was caused by alower distance between upper electrode and particle.

Thirdly, the figures that present the delay of initiation as a function of the applied voltage at 100mbar show a linear relation, which again defends the expectation that a higher voltage causes fasterinitiation.

Furthermore, the results showing the initiation voltage as a function of frequency are useless sincethe uncertainty in the measurements is bigger than the variations in the graphs.

In addition, the empirical density function is used to learn more about the trend of the delaytime. The results show the probability on a certain delay time or lower. The probability of havinga very short delay time with a dielectric particle at 200 mbar is found to be very low. This could bethe result of the dielectric property: it takes time for the charges to align with the electric field. Thiswould take, considering the results, about 0.5 milliseconds. Another surprising result is found fromthe measurements with the coated metal. It shows a nod in its ECDF, which can not be explained.It may have something to do with the different tested frequency or shape.

Finally, the derivative of the delay time as a function of iteration number gave interesting results.Under some, unrelated, conditions a sudden drop or rise in the consistency of the delay time is ob-served. The cause of this observation yet remains unknown.

To conclude, more theoretical and practical research is needed to explain all observations.

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Contents

1 Introduction 1

2 Theory 22.1 Initiation of streamers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22.2 The circumstances of inception: the Raether-Meek criterion . . . . . . . . . . . . . . . . . 32.3 The dielectric property . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

3 Method 63.1 Experimental Setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63.2 Signal observation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83.3 Tested parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

3.3.1 Material . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93.3.2 Pressure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103.3.3 Distance between electrode and particle . . . . . . . . . . . . . . . . . . . . . . . . 103.3.4 Voltage . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113.3.5 Pulse duration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113.3.6 Frequency . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

4 Results and discussion 124.1 Results photomultiplier . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12

4.1.1 Width of inception PMT signal . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124.1.2 Delay of initiation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14

4.2 Influence of applied voltage . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 154.3 Influence of frequency . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16

4.3.1 Initiation voltage and frequency dependence . . . . . . . . . . . . . . . . . . . . . . 164.3.2 Empirical Cumulative Density Function over trend of delay time . . . . . . . . . . 164.3.3 Trend of the trend of the delay of initiation . . . . . . . . . . . . . . . . . . . . . . 17

4.4 Results ICCD camera . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19

5 Reflection 215.1 Improvements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 215.2 Further research . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21

6 Summary and conclusion 22

AResults 23A.1 Results width of inception PMT signal . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23A.2 Results delay time . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25

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1 Introduction

Ice crystals are formed in cold and moist regions. Thunder clouds form an ideal surroundings since theyconsist mostly of water vapor. These water particles bind to other particles and form, under very specificconditions, perfectly symmetric ice crystals. These beautiful crystals have many more applications be-sides being the base of every snow fight. In particular, covering the motive of the subject of this BachelorEnd project; they play a part in lightning.

Despite the progress achieved in the last thirty years in the science of lightning, the exact detailsof how lightning initiates are still unknown. Nevertheless, a few theories were formed under which the’hydrometeor theory’ seems promising. This particular theory is based on the so called hydrometeorswhich float in a cloud region with a high electric field. While doing so, these hydrometeors interact:they feel friction due to the wind which blows them towards each other. During this process electronsare transferred from the hydrometeor with the weakest binding to the one with the strongest binding.This causes charge transfer which could be responsible for a magnification in the electric field neededfor breakdown. Since this theory can not be proven by means of in situ measurements, physicists haveaddressed smaller parts of the bigger initiation problem in laboratories.

Early measurements where done by Griffiths and Latham [1] and later on Coquillat et al [2] and Pe-tersen et al [3] also investigated the corona streamer formation in conditions similar to thunder clouds.First of all, Griffiths and Latham found that the minimum temperature for streamers to initiate on afrozen particle was around - 20 ◦ C which implies that lightning could not initiate in the coldest regionsof clouds, but Latham reviewed this and concluded some other settings were needed. Controversial ex-periments observing the locations where lightnings starts by Proctor [4], Shao and Krehbiel [5] showedthat initiation was in fact seen in regions colder than - 20◦C. Also Petersen et al [6] and Petersen et al[3] found by means of laboratory experiments that streamers can start on ice crystals at - 38◦C.

Since ice crystals are the most probable type of hydrometeors, the influence of the structure, in partic-ular the dielectric property, in an electric field will be investigated for a material with similar properties.First of all the known physics about streamer initiation and the dielectric property will be explainedin chapter 2. Hereafter, in chapter 3 the followed method using the experimental setup as shown inparagraph 3.1 will be clarified. Furthermore, the results including an interpretation of these experimentswill be shown in chapter 4. Chapter 5 will reflect on the experiments and propose some further research.Finally, in chapter 6 a summary is given and some important conclusions are drawn.

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2 Theory

2.1 Initiation of streamers

As mentioned in the introduction, the details constructing a solid inception theory are still missing.Nevertheless, sticking to the hydrometeor theory, the foFpllowing can be derived from the fundamentalsof electrodynamics [11].

The initiation considered in this paper is defined as the origin of a streamer. A streamer always startsform an avalanche discharge. An avalanche discharge on its turn starts with electrons getting acceleratedby a high external electric field. These electrons bump onto other molecules and ionize them while doingso. More electrons are now created and a chain reaction is set in motion. If now a critical value of freecharges is created in the surroundings a streamer can be initiated [7]. Meek found a value for this criticalvalue which will be discussed in the following paragraph.

The known theory describing the initiation of lightning states that two types of streamers exist; pos-itive and negative ones. A streamer traveling in line with the direction of the electric field is called apositive streamer, while the streamer moving against it is a negative streamer [7]. In the setup schemat-ically shown in figure 1 both streamers should be present.

Figure 1: Schematic overview of present charges and electric field that induce positive and negative streamersin the setup

A positive high voltage is applied on the top electrode, so since the bottom one is grounded an electricfield pointing downwards will be created in the space between them. The particle hanging in this fieldwill get polarized which causes the electrons in the particle to move upwards and create a negative tipon the upper and a positive tip on the lower side of the particle. The polarization of the material causesthe external field to get amplified at the tips of the particle as the distance between positive and negativepole is decreased. A higher local electric field will accelerate the electrons faster, which makes initiationmost probable on the tips of the particle.

For the region above the particle, the electrons present in the surroundings will get attracted by thepositive electrode and rejected by the negative tip of the particle. On their way to the positive electrode,electrons ionize air molecules. The streamer begins to flow upwards, which is in the opposite directionof the local electric field. A negative streamer should thus be created above the crystal.

As for the region below the crystal, electrons in the surroundings will get attracted by the bottomtip of the crystal. Just as for the streamer above the crystal, the electrons ionize the molecules on theirway to the tip but now create a downwards propagating streamer. This is in the same direction as theelectric field so the streamer initiated below the crystal will be a positive one.

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2.2 The circumstances of inception: the Raether-Meek criterion

The roots of inception are explained in the previous paragraph theoretically. But practically, there aremore components to encounter with. The ability of the material to conduct electrons or the amountof space charge in the surroundings for example. Meek found a critical value for this latter one. Hepostulated that a streamer will propagate if the positive ion space charge close to the positive electrodeis equal to K times the impressed field. Here K should be a constant independent of the pressure andthe configuration of the gap between the electrodes [12].

This particular value for K is modeled in a condition for streamer inception by the following integral[13];

∫ x

0

αeff(z)dz (1)

in which αeff = (α−η) if α > η and zero otherwise. This is the effective ionization coefficient consisting ofα, the Townsend first ionization coefficient and η, the attachment coefficient. Furthermore, x representsthe distance an avalanche can travel. If the assumption is made that the streamer propagates along afield line the integral can be written as follows [14];

K = ln

(12πε0De

qeµe

)+ ln

(x

x0

). (2)

In this equation x0 = 1 cm, ε0 is the dielectric permittivity of vacuum, qe the charge of an electronand De

µerepresents the characteristic energy of an electron in an avalanche consisting of De, the diffusion

coefficient and µe the mobility of that electron. Putting some constants together gives

K = K0 + ln

(x

x0

), (3)

where K0 ≈ 19 for a typical value of the characteristic electron energy of 1 eV. Equation 3 could besimplified even more by using the fact that at laboratory scales x ≈ x0 = 1 so the latter term becomesnegligibly small and K ≈ K0.

However it is very important to mention that this equation only holds for a homogeneous field, whichis not the case for the case sketched in figure 1. It should thus be taken into account that this derivationcould result in nothing more but a approximation of the system. Other calculations, for example the oneof Mikropoulos taking into account a cylindrical electrode orientation [16]; values for K varied between8 and 18, depending on the condition of air and the orientation of the gap between the electrodes. Fur-thermore the value of K as derived above is based on averages. It is thus still possible to have initiationat lower values due to the statistical behavior of nature [15].

New insights on this topic are recently published by Casper Rutjes. He proves in his work that theold criteria as explained above do not hold for experiments near objects. A new method is presentedand shows that charges can accumulate near these objects, which results in initiation at lower voltagesthan assumed before [8].

2.3 The dielectric property

As briefly mentioned in the introduction this paper focuses on dielectric materials since ice crystals inthunderclouds share those properties. So, the inception as explained in the previous paragraphs couldbe taken one step closer to reality by adding the properties of a dielectric. What these properties are,how they relate to (coated) metals and how they might influence the experiments will be explained below.

Let’s start at the basics: a dielectric material is an electrical insulator that can be polarized by anapplied electric field. If an electric field is applied to the system, the charges won’t conduct through thematerial as would be the case for a metal. A dielectric does not have loosely bound or free electrons,

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so they just change their orientation causing the material to get polarized. This polarization induces anelectric field itself that reduces the total electric field within the material. The relative permittivity ordielectric constant εr is a measure for the ability of a material to polarize. This value equals infinity fora metal, but varies between approximately 3 and 100 for ice crystals [9].

The dielectric constant of ice varies because of its frequency dependence. As explained before, thecharges in the dielectric material re-align due to this field. However, this will not happen instantaneousbut will take time: the relaxation time τ . The polarization P after switching of the electric field and thetime in which the material adjusts to the surroundings τ are related by the following equation :

P (t) = P0 ∗ exp(−tτ

)(4)

which is an exponential decay looking like figure 2 shown below. Of course, the opposite will be the casewhen the electric field is suddenly turned on again.

Figure 2: The relaxation time of the polarization after switching off the electric field.

But, as there exist both slow and fast changing fields in a step function it is more interesting to lookat polarization as a function of the frequency ω. This can be obtained using a Fourier transform onequation 4 which gives

P (ω) =P0

ω0 + i ∗ ω, (5)

with the constant ω0 = 1τ . So, if now the electric field would be changed very fast ω >> ω0, the mechan-

ics of the system cannot follow. This causes the dielectric strength, the maximal electric field a materialcan withstand without breaking down, decreases with the frequency of the applied field. A quantificationfor this is given in figure 3, which shows the dielectric constant as a function of the frequency for ice.

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Figure 3: The dielectric constant as a function of the frequency of ice [10].

As for a coated metal, the theories of conductors and dielectric materials can be combined as bothexist in the material. There are free moving electrons that create a polarization inside the material, butthe insulation coating prevents the particle from conducting a current.

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3 Method

In order to find inception the general method explained below was used. Furthermore, paragraph 3.1will illustrate this method and specify the particular role of all components in the experimental setup.Finally, an overview of all tested parameters with corresponding characteristics will be explained inpargraph 3.3.

3.1 Experimental Setup

All experiments were performed using the general setup as shown below in figure 4. In this paragraphthe experimental setup will be explained step by step while giving an overview of the contributions ofeach component to the complete system.

Figure 4: Schemetic overview of the general setup used to find initiation of streamers.

(1) General PC The general PC controls the setup and uses Matlab 2017a. The program AppFi-nal.Matlab (made by Shahriar Mirpour) is used to control the function generator (2), the high voltage(6) and to read out the oscilloscope (13). From this program several factors like the HV pulse function,the pulse width, the rise time, the amplitude and the offset level and amplitude of the applied voltagecan be varied. Furthermore, the script has a function that automatically saves the data acquired fromthe photo-multiplier (10).

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(2) Function generator The function generator, controlled by the general PC (1) produces a givenfunction (a step function in this particular case) and sends this to a set of optical signal transformers (3)and to the ICCD camera (11).

(3) Signal transformers The signal transformers transform electrical signals into optical ones andback. They are placed between the function generator (2) and the switch to ensure a good Electro-Magnetic Compatibility between the different devices.

(4) Switch The switch is the main component controlling whether or not high voltage is applied tothe probe (7), since its input (red wire) is connected through some resistors to the high voltage supply(6) and the output (yellow wire) is connected to the upper electrode. This system is in turn regulatedby the function generator (2). Furthermore the black wire is used for grounding.

(5) Low voltage generator The low voltage generator is connected to the power supply and regulatesthe high voltage power supply (6).

(6) High voltage generator The Spellman SL150 high voltage supply generates the high voltage forthe system.

(7) Probe The Northstar PVM-1 high voltage probe measures the exact value of voltage appliedto the upper electrode in the vessel. This value is recorded by the oscilloscope (13) on channel 4.

(8) Flat electrodes In the vessel two flat electrodes with a radius of approximately 8 centimeters arelined up above each other. On the upper one a high voltage can be applied, the lower one is connectedto ground. A particle (9) is hung between the electrodes, after which an electric field can be created.Furthermore, the current is measured from the lower electrode and is sent to the oscilloscope (13) throughchannel 2.

Figure 5: A more detailed view on the vessel including the particle which is observed with a photo-multiplier(on the right) and an ICCD camera (in the bottom).

(9) Particle A crystal shaped particle with a length of about 2 centimeters is placed between thetwo electrodes (8) as shown in figure 5 in order to observe initiation in the applied electric field underadjustable conditions. The particle has sharpened tips and can be made from various materials. A morein depth description is given in paragraph 3.3.1.

(10) Photomultimplier The initiation in the vessel is observed using two different techniques. Oneof those is through means of photo-multiplication. Photons originated from discharge initiation arecaught by a sensor and multiplied in order to create a observable signal for the system. This PMT signalis sent to channel 1 of the oscilloscope (13).

(11) Intensified Charge-Coupled Device The other method used to capture initiation is by imagingit using the 4 Quik E ICCD camera from Stanford computer optics. This ICCD is controlled by the

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ICCD PC (12) and the function generator (2). A 105 mm Nikon lens is mounted which ensures a sharp,fully zoomed image.

(12) ICCD PC The ICCD can be controlled using 4Spec. This program enables the variation ofthe opening time of the gate, the delay of the gate compared to the trigger generated by the functiongenerator (2) and the gain of the signal. The gate of the ICCD signal can be observed from the oscillo-scope (13) as well using channel 3.

(13) Oscilloscope As explained above, the oscilloscope monitors the complete system; the PMT sig-nal, the current in the vessel, the ICCD gate and the high voltage. It collects all data and sends it back tothe main PC (1), where it is stored using Matlab. For this setup the Teledyne LeCroy oscilloscope is used.

(14) Pump Additionally a vacuum pump is installed and connected to the vessel to enable theusage of lower pressures.

3.2 Signal observation

The previous paragraph explains that inception near the particle is observed using the PMT and theICCD camera. The data from the PMT that describes this is typically collected by the oscilloscope asfollows:

Figure 6: The upper graph shows a red line which corresponds to a voltage of 16.8 kV applied by Matlab andthe measured high voltage applied to the upper electrode as measured by the probe (blue line) a function of time.The lower graph shows the PMT signal in the same time interval of the graph above.

As can be seen from the upper graph, the measured value of the high voltage is not completely aperfect step function; it converges from the red horizontal line at 16.8 kV, which is the manually appliedvoltage on the system. For sake of unity it is chosen that the highest voltage measured counts in theresults. The deviation of this measured value from the applied value varies between 0.4 and 1.2 kV fordepending on the frequency of the applied voltage.

The large peak observed in the lower graph shows inception. The signal is saved and defined asinception if the peak is higher than the threshold value of the oscilloscope. This value depends on thescale of the PMT signal on the oscilloscope. In the experiments a scale of 10 V per devision is used,which corresponds to a trigger value of 0.0 V. The initiation peak should thus be bigger than 99 mVin order to be saved. Also, a very small peak occurs at 0 seconds, when the voltage is applied to thesystem. This is not initiation, but is probably caused by a signal mismatch of devices in the setup.

3.3 Tested parameters

There are four parameters which will be tested: the type of material of which the particle is made, thepressure of the air inside the vessel, the high voltage applied to the upper electrode and the frequency

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at which this pulse is applied to the system. All variables and corresponding ranges in which they willbe tested are shown schematically in figure 7 below. The setup is show in the form of a tree to enablethe exploration of all possible relations between the parameters. However, for the sake simplicity, onlyone branch is fully drawn but of course all materials will be tested at all pressures and at each pressureall frequencies will be tested and so on. Furthermore, the range of tested the repetition rates and thevoltages vary with the other parameters.

Figure 7: Schemetic overview of the parameters tested in the experiments.

In the next few paragraphs the (expected) influence of all important parameters, including the oneskept constant like the distance between the electrode and the crystal and the pulse duration will beexplained.

3.3.1 Material

Three types of material will be tested during the experiments; a metal, a semi dielectric and a dielectric.The important difference between them obviously is the dielectric property, as explained in paragraph2.3. This particular property of the crystal is chosen because of its similarities with common ice crystalsin thunderclouds [9]. The influence of this property on the inception on or near the particle is investigatedby comparing the three materials which properties are discussed below.

Figure 8: A photo of the dielectric, metal and coated semi dielectric particle respectively.

To start off, the metal particle is made from stainless steel, has a cylindrical middle part and roundedtips as can be seen from figure 8. The length of the particle is 2.00± 0.05 centimeters, has a diameter of4.00 ± 0.05 millimeter in the middle part and can be hung in the setup using a thin plastic wire.

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The dielectric particle is handmade from Titaniumdioxide. Titaniumdioxide has a dielectric propertyvery similar to the one of ice as can be seen by comparing figure 3 with figure 9. When the dielectricparticle is compared with the other, machine produced ones, it can be concluded that it is about 2millimeters longer and has a diameter of 6.00±0.05 millimeter, but has approximately the same roundedtips as the metal one.

Figure 9: The permittivity as a function of the frequency for Titaniumdioxide, as found by Shahriar Mirpour.

Finally, the coated metal particle is a particle made of stainless steel but with a sharper tip, coatedin MR8008 insulating varnish from Electrolube. Electrons within this coating will not move freely incontrast to the metal part which it covers, which causes the complete particle to act like a semi dielectric.Important to mention is the fact that the coating did not happen completely even; the varnish is thickeron the cones than on the cylindrical part of the particle. Also, the tips do not seem to be coated at all(or very thin). Nevertheless, tests on the resistance of the three materials show that the coated metal,just as the dielectric do not conduct current. The coating works successfully, also on the tips.

3.3.2 Pressure

The gas used for all experiments is ambient air. The pressure in the vessel simply determines the numberof air molecules present. As explained before in paragraph 2.1, electrons collide with these moleculesand ionize them; the air molecules could be seen as obstacles for electrons on their way to or from thetip of the streamer. If the pressure is reduced, the vessel contains less molecules and the electrons havea larger mean free path, are more mobile and thus initiation is expected to happen faster. Pressure alsoobviously plays a role in background ionization: a higher pressure enables a higher density of ionizedparticles left over after one initiation. This could result in the fact that a second initiation happensfaster. The experiments are executed in both 100 mbar and 200 mbar.

3.3.3 Distance between electrode and particle

The distance between the electrodes and the particle is another parameter which influences the delaybetween the high voltage pulse and the initiation. If this distance is decreased and both tips are closer tothe electrodes, the electric field as sketched in figure 1 will be stronger causing fast polarization, electronflow and thus it is expected to find faster initiation.

However, it is important to make sure that both electrodes are not too close to each other. Since, ifthey are, a path along which a current can flow, connecting the electrodes, is now produced very fast.This causes breakdown, which is not the goal of this experiment so this should be avoided when possible.So the optimal distance will be used during the experiments and varies with the type of material. Forthe dielectric particle this optimal distance is 165 mm, for the metal and the semi dielectric particle itis almost twice this value; 300 mm.

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3.3.4 Voltage

A higher difference in charge and thus a higher potential induces initiation faster. Electrons in the envi-ronment get attracted or rejected more and will travel faster from or to a streamer tip. So, at a higherapplied voltage it is expected to see initiation faster. Furthermore, when a higher voltage is appliedto the system, more molecules in the surrounding air get excited due to the collision with acceleratedelectrons. If these excited molecules fall back in their ground state, they excite photons. A higher voltagewill probably result in a higher amount of captured photons. For the experiments at the lower pressureof 100 mbar, the particle is observed at voltages around 9 kV. For the experiments in 200 mbar, voltagesof around 15 kV are needed to find initiation.

3.3.5 Pulse duration

The pulse duration is the time interval that high voltage is applied to the upper electrode. If this time islonger, electrons with a long mean free path also have the opportunity to reach the tip of the streamerand electrons with a short mean free path are able to ionize more molecules and reduce the delay time.It is thus expected that at a longer pulse duration an avalanche is more probable because the chanceson success are bigger. Nevertheless, this parameter is kept at a constant value of 50 milliseconds for thedielectric and metal particle and 10 milliseconds for the semi dielectric particle. The reason a differentvalue is chosen for the semi dielectric particle is due to the fact that the combination of pulse durationand frequency did not work for at 50 milliseconds; the system stops acquiring data after about 240acquisitions.

3.3.6 Frequency

The frequency of the high voltage, or repetition rate, has somewhat the same effect as the pulse duration.When there are more high voltage pulses applied per second, there are more possible trials for initiation,so the chance on one being successful is higher. Furthermore, the repetition rate has an influence onthe background. After one repetition, several molecules in the air get ionized to create an avalancheas explained in paragraph 2.1. As the time passes, these ions diffuse or become neutral. If the timebetween two repetitions is very long (low repetition rate), every avalanche has to be created in the sameenvironment with an equal number of ions. But, if the repetition rate is very high, the number of ions inthe background grows with each pulse. With more ions in the background an avalanche is created moreeasily. So, the expectation follows that there will be more initiation observed at higher frequencies.

In the experiments of this paper different frequencies are used for different materials; the dielectricparticle is tested at 5 Hz and 15 Hz, the metal particle is tested at 5 Hz, 8 Hz and 10 Hz and thesemi dielectric particle is tested at 4 Hz and 8 Hz. This inconsistency is the result of an error in savingthe data; Matlab did not accept some combinations of pulse duration and frequency which caused theacquisition to stop.

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4 Results and discussion

As explained in paragraph 3.3, three different types of materials were tested in order to learn moreabout the dielectric behavior in initiation and its effect on it. This paragraph will give the results andinterpretation of those experiments in the form of the PMT signal and the image obtained from theICCD camera. An overview of all additional results is attached in the appendix A. For all presentedresults shown below, the data of 1000 initiations are combined.

4.1 Results photomultiplier

The main source of data describing inception near the particle is the photo-multiplier. First of all para-graph 4.1.1 will show the width of the PMT signal as observed on the oscilloscope. Hereafter, paragraph4.1.2 will show the delay of the initiation. This was obtained by comparing the time at which the highvoltage was applied and the time of initiation as can be extracted from figure 6 in the previous chapter.Furthermore, the influence of the applied voltage and the frequency on initiation is presented in para-graph 4.2 and 4.3 respectively.

4.1.1 Width of inception PMT signal

The following graphs show a histogram of the width of the PMT signal as observed on the oscilloscope.An example of this width is given in figure 10 below.

Figure 10: The PMT signal containing photons from initiation. The red arrow defines the width of the PMT asused in the results below.

The most surprising result is that the width, which quantifies the initiation, has not only one valueunder specific conditions. For example, the width in the experiments performed with the dielectricparticle at 100 mbar and 5 Hz can typically have three different values as follows from figure 11.

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Figure 11: The width of the PMT signal for a dielectric particle at 100 mbar and 5 Hz.

The width here is 30± 20, 100± 20 or 160± 10 nanoseconds, with a constant of approximately 65± 5seconds separating them. Furthermore it can be seen that the smallest width gets more probable withhigher applied voltage, in contrary to the secondary peaks which get lower. This same patern is observedfor the dielectric at 100 mbar at 15 Hz as can be seen from figure 28 in appendix A.1. Also, for thecoated metal particle at 100 mbar at 8 Hz (figure 32) and at 200 mbar the dielectric particle at 15 Hz(figure 34), the metal particle at 10 Hz (figure 36) and the coated metal at 4 Hz (figure 37) the histogramshows a double peak. Again a pattern is visible with this same constant 65± 5 between the primary andsecondary peaks.

A possible explanation for this pattern could be as follows. As explained in paragraph 3.3.4, it isexpected that a higher voltage would result in (1) a larger amount of captured photons (2) faster initi-ation. The first expectation can only be measured using the amplitude of the PMT peak, which is notvisible here. But the second expectation states that at a higher voltage, molecules get excited (and thusfall back into their ground state) faster which makes the time between the first and the last capturedphoton, the width of the PMT, shorter.

The other observation, considering the fact that the time between the peaks seems constant and thatfor example in figure 11 not one single inception is captured with a PMT width of 70 nanoseconds couldhave something to do with the signal processing of the PMT itself but remains unclear.

The other measurements: at 100 mbar the metal particle at 10 Hz (figure 30) and the coated metalat 4 Hz (figure 31) and at 200 mbar the dielectric particle at 5 Hz (figure 33) and the metal particle at5 Hz (figure 12 here below) do not show this repeated signal.

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Figure 12: The width of the PMT signal for a metal particle at 200 mbar and 5 Hz.

These results have in common that at a higher applied voltage the average PMT width gets smaller.This again could be the result of faster excitation as already explained above. But why exactly theseexperiments only return one peak is still unclear since there does not seems to be any consistency invaried parameters. To learn more about this phenomenon, single-photon experiments could be veryuseful in order to be able to quantify the signal achieved from the photon-multiplier in discrete steps.

4.1.2 Delay of initiation

The delay of the initiation is the time between when the high voltage is applied to the system and wheninitiation is observed by the photo-multiplier. Since the delay time was observed to be approximatelyindependent of the applied voltage, the results will be presented as follows. At each pressure the differentfrequencies will be compared at the lowest measured voltage.

For the dielectric material the distribution of the delay time looks as follows:

Figure 13: Dielectric particle, 100 mbar Figure 14: Dielectric particle, 200 mbar

As can be seen from the axis in figure 13 and 14 the deviation from the mean delay time gets lower ata higher pressure. The experiment at higher frequency returns this same result. Except for the measure-ment at 10 Hz with the metal particle and the measurement with the coated metal at 100 mbar, all otherexperiments, which can be found in figures 40 till 43 in appendix A.2, support these two observations.Furthermore, figure 14 shows that the delay time itself gets lower at a higher frequency. Nevertheless,this is the only result that might implement that relation, other experiments show an approximately

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constant average delay time for different frequencies.

An explanation for the fact that the deviation from the mean delay time gets lower for a higherpressure could be as follows. As explained in paragraph 3.3.2 could a higher pressure result in fasterinitiation. This implies shorter delay times and makes deviations from the mean delay time, like at lowerpressure, less probable.

The relation between the delay time and the frequency can be explained as well using the theory(paragraph 3.3.6): a higher frequency results in a lower delay time because of a higher density of ionizedmolecules in the vessel.

Finally, by comparing the three materials, the average delay time is lower for the dielectric particlethan for the metal and coated metal which is intuitively wrong considering the dielectric property eval-uated in paragraph 2.3. Nevertheless, this conclusion may not be drawn since a larger distance betweenelectrode and particle was used for the metal and coated metal particle as stated in paragraph 3.3.3.This section also explained that a larger distance would cause initiation to happen more slowly, as foundin the results.

4.2 Influence of applied voltage

This paragraph gives some additional results and compares the three materials with respect to the ap-plied voltage and its influence on inception.

The following results show the mean and standard deviation of the delay time as a function of theapplied high voltage. Figure 15 and 16 show how fast initiation was observed with the PMT after ap-plying a high voltage pulse and how this depends on the amplitude of this voltage.

Figure 15: The mean and standard deviation ofthe delay time at a constant frequency of 5 ± 1 Hzand a constant pressure of 100 mbar of differentmaterial.

Figure 16: The mean and standard deviation ofthe delay time at a constant frequency of 5 ± 1 Hzand a constant pressure of 200 mbar of differentmaterial.

For the experiments in 100 mbar with the metal and semi dielectric particle the relation looks almostlinear; when a higher voltage is applied to the upper electrode, initiation is observed faster. The dielectricparticle, on the contrary, does not show this dependence, which is not the case for the experiments in200 mbar. But, at this higher pressure less measurements were performed, which makes it impossible todraw any conclusions based on figure 16.

The linear dependence of the average delay time and applied voltage as observed in figure 15 wasexpected. As explained before in paragraph 3.3.4, will a higher voltage on the upper electrode induceinitiation faster. This is the result of a higher potential difference, which causes electrons to be acceler-

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ated more and create an avalanche within a shorter amount of time.

The fact that the dielectric particle has shorter average delay times comparing to the metal andcoated metal one, is discussed in the previous chapter. The distance between the electrode and particlehas shown to be an important parameter to investigate in further research. The line presenting thecoated metal particle lies above the metal particle because of the isolation in which it is covered in.

4.3 Influence of frequency

The following few sub-paragraphs will give some additional results comparing the three materials withrespect to the frequency and its influence on inception.

4.3.1 Initiation voltage and frequency dependence

As explained in paragraph 3.3.6 the voltage at which inception occurs could be frequency dependent.Since this gives information about when in the applied step function initiation occurred, it supplies moreinformation on the polarization of the material. In the figures 17 and 18 below the mean initiation volt-age (with corresponding standard deviation) is shown for the different tested frequencies for the threematerials.

Figure 17: The mean and standard deviation ofthe initiation voltage at a constant voltage of 10.2±0.1 kV and a constant pressure of 100 mbar fordifferent materials.

Figure 18: The mean and standard deviation ofthe initiation voltage at a constant voltage of 16.4±0.2 kV and a constant pressure of 200 mbar fordifferent materials.

From 18 it looks like the average initiation voltage is independent of the frequency. Which can notimmediately be concluded from figure 17. But, while reading these figures it is important to keep inmind that the applied voltage varied a few hundreds of volts for different frequencies and was thus notcompletely constant. Also the applied voltage itself varies a little in time as explained in paragraph 3.3.4.Therefore, no proper conclusions can be drawn based on these results. Perhaps, by taking bigger stepsin the frequency (of about 20 Hz), a dependence between these parameters can be found.

4.3.2 Empirical Cumulative Density Function over trend of delay time

The results in this paragraph show the delay time, as presented in paragraph 4.1.2, in the form of anempirical cumulative density function of the delay time. This means that at each delay time on thex-axis, the corresponding probability on this delay time or less will be shown on the y-axis. For exam-ple, following the dielectric particle in figure 19, zero percent of the initiations has a delay time of zeromilliseconds, 50 percent of the initiations has a delay time of 2 seconds or shorter and all initiations have

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a delay time shorter than 15 milliseconds.

Figure 19: The ECD function for the delay timeat 100 mbar, 5 ± 1 Hz and 10.4 ± 0.1 kV

Figure 20: The ECD function for the delay timeat 200 mbar, 5 ± 1 Hz and 16.4 ± 0.2 kV

It is interesting to see that for the dielectric particle at 100 mbar the probability for having a shortdelay time is higher than for the metal particle and the coated metal particle. This is obviously not thecase for the higher pressure where the probability for the dielectric particle catches up with the metaland coated metal one only at a delay time of 0.7 milliseconds. Also the green line representing the coatedmetal particle looks interesting; its shape is divergent from the other two for both pressures. This couldhave something to do with the fact that this particle is tested at 4 Hz, while the others were tested at5 Hz. The divergent shape could have some influence as well: the coated metal has sharp, metal tipson one hand, but is coated in an insulating varnish on the other. Furthermore, at 100 mbar the coatedmetal particle reaches its maximum before the metal one does, which is the opposite of what happensat 200 mbar. This again is the result of a divergent looking curve of the coated metal, since the curveof the metal particle look similar at both pressures. The reason for this particular shape of the coatedmetal is still unknown and should be investigated in the future.

The first observation, considering the delay time of the dielectric particle in comparison with themetal and coated metal particles, is explained two times before (in paragraph 4.1.2 and 4.2) and iscaused by the difference in distance between the electrode and particle. The result at 200 mbar is not inline with this conclusion. Here the probability of a delay time below 0,5 millisecond is very low, whichis in line with the theory of a dielectric as explained in paragraph 2.3. A dielectric always needs somesort of an installation time to re-align its charges with the applied electric field. So, it could be the casethat in figure 20 this installation time is about 0.5 milliseconds. However, to able to make a conclusionon such an installation time, other experiments need to support this theory. This, for example, could bedone by performing more experiments with other values for the pressure and applied voltage and zoomin on these shortest delay times.

4.3.3 Trend of the trend of the delay of initiation

The following results again concern the delay time between the applied voltage and the observed ini-tiation. But now the derivative of the delay is presented as a function of the iteration number, whichapproximately shows its behave over time. This should give a better insight in the influence of thefrequency on the background ionization as explained in paragraph 3.3.6.

For the measurements with the dielectric particle at 200 mbar, some sort of a pattern is found in thedelay of the inception. In figure 21 the delay time seems to get lower and more constant as the timepasses. This contradicts figure 22, which shows that the delay time gets more chaotic in time.

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Figure 21: The derivative of trend of the delaytime of a dielectric particle at 200 mbar, 5 Hz and16.9 kV

Figure 22: The derivative of trend of the delaytime of a dielectric particle at 200 mbar, 15 Hz and17.5 kV

For experiments with the metal particle at 100 mbar this derivative of the trend of the delay timeseems to be all random, but at a higher pressure they are more interesting. Divergent results are found,which are presented below in figure 23 and 24. Figure 23 shows halfway the experiment a very constantdelay time, which suddenly also becomes more chaotic very soon. Figure 24 shows a similar result butwith a longer period.

Figure 23: The derivative of trend of the delaytime of a metal particle at 200 mbar, 8 Hz and 16kV

Figure 24: The derivative of trend of the delaytime of a metal particle at 200 mbar, 8 Hz and17.1 kV

Just as for the metal particle, the trend of the trend of the delay time for the coated metal particlelooks completely random at 100 mbar, but has an interesting shape for the experiment at 200 mbar ascan be seen in figure 25 below.

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Figure 25: The derivative of trend of the delay time of a coated metal particle at 200 mbar, 4 Hz and 16.2 kV

This figure shows a sudden constant value for the delay time in the middle of the experiment. Thechange in delay time goes from a stochastic process to a constant value exponentially as shown using thered fit curve. This drop in chaos could be the result of background ionization produced by one iterationthat leaves a a sort of ”memory” for the next iteration. This could result in more constant delay timesas observed in figure 25.

However, there is no good explanation yet for the sudden built up in chaos again as observed infigures 23 and 24. It could be that some other process disturbs the process as described above, due tothe change of an unknown parameter. Nevertheless are these results very interesting and it would bevery valuable if more experiments would be done with more parameters kept constant. Furthermore,a quantitative measurement of the ionization density during the experiments would be very useful as well.

4.4 Results ICCD camera

This paragraph will visualize the results from the PMT as presented above. However, capturing initia-tion with the ICCD camera was really hard and only one useful image was found. This image is shownbelow in figure 26, in which the yellow color identifies light captured by the ICCD camera. The darkpink contour is the focused particle as captured before the experiment.

Figure 26: Initiation observed with the ICCD on the bottom of the dielectric particle at 200 mbar, 5 Hz and16.5 kV

Interesting is the fact that breakdown is observed on the lower tip of the particle, which correspondswith a positive streamer as explained in paragraph 2.1. And a streamer is observed in top of the particle,which is a negative one. This is in line with the expectations, since positive streamers develop fasterthan negative streamers [7]. Furthermore, the yellow dots spread all over the image are considered to be

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background noise.

Unfortunately, not much can be concluded from figure 26 because it is the only visual evidence foundclosest to initiation. A proper image of initiation is hard to capture since the ICCD and PMT are notcalibrated: it is almost impossible to set a proper delay time for the camera. The timescale for theinitiation process is about nanoseconds (paragraph 4.1.1), so the time in which the camera is open (theshutter time) should be in the same order. However, the delay of this process is about milliseconds(paragraph 4.1.2), which makes the probability of setting a good delay time for the camera and findinginitiation very low. Furthermore, even if a image is found, there is no information describing it sinceit is unknown at what moment in time, or with which PMT signal it corresponds. A solution for thisproblem could be a focused PMT: if only the upper tip or only the lower tip is observed, a quantitativedistinction can be made of initiation of positive and negative streamers.

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5 Reflection

5.1 Improvements

In order to have more reliable and meaningful results, some parts of the experimental setup, method oranalysis could be improved.

To start off, the general success of initiation for different sets of parameters could be tested easilyby calculating the ratio of pulses that caused initiation over the total of applied pulses. However, didthe current set up not measure the total number of applied voltages nor the total measurement time(which could be multiplied by the frequency to obtain the needed result as well). A simple addition tothe experiments could thus give more insight. Also, to be able to really compare the three materials itis important that all the particles have exactly the same shape. In particular the curvature of the tipshould be alike since this is crucial to the inception. Furthermore, it would be an improvement if theMatlab code, which is now used to acquire the data from the oscilloscope, would be able to observe dou-ble initiation (which was observed, but unfortunately could not be captured). Besides, the code couldbe adjusted in such a way that also smaller peaks in the photo-multiplier signal are captured. Afterall it are these peaks that represent the very first inception. Finally, for the visual observation of theinception there should be some improvements on the use of the ICCD camera. It is useful for example tofigure out what the exact time delay is between the PMT and the ICCD. This would make it a lot easierto set a proper delay time for opening the ICCD and will thus increase the chances on capturing inception.

5.2 Further research

So, what could be the next step in learning more about inception? The experiments in this paper couldbe continued in some different ways.

First of all, the experimental setup could be made safer to allow high voltage pulses above 16 kV, thiswould enable tests in higher pressure which is more in agreements with the reality in a thundercloud.If experiments with higher voltages are possible, increasing the distance between the electrodes and theparticle could return relevant results. In this paper the coated metal particle is tested on a shorterdistance which makes comparison more difficult. Furthermore, it would be interesting how the set upbehaves in different types of gases. It is already known that streamers propagate differently in other gastypes, which perhaps has some roots in the initiation. Also, other shapes of the particle could createinteresting results as well. Ice crystals for example have all sorts of beautiful symmetric shapes.

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6 Summary and conclusion

The experiments in this paper observe the initiation near a particle using a photo-multiplier and an ICCDcamera. This particle is placed between two electrodes on which a high voltage is applied to create apotential. For this a dielectric, metal and coated metal particle are used. Here the amplitude of theapplied high voltage pulses, the repetition rate of these pulses and the pressure of air in the vessel werevaried. The ICCD camera generated only one single useful image presenting initiation on the top andbreakdown on the lower tip, which lacks data describing the initiation with the PMT at that momentin time. This is due to the fact that the PMT and ICCD are not calibrated. However, from the PMTsignal itself some interesting things are observed.

First of all, it is found that the pulse width of the PMT signal can have more than one value and comesin discrete steps with a constant of about 60 nanoseconds separating them. This happened under some,random looking, conditions. Single-photons experiments could give more insight to this phenomenon.Also, it is found that the shortest PMT width gets more probable when a higher voltage is applied. Thisconfirms the theory that a higher voltage causes faster initiation.

Furthermore, the results of the delay time between the applied voltage and the initiation observed bythe PMT show the following. The deviation from the mean delay time gets lower for higher pressure andalso for higher frequencies, which is in line with the expectations. However, the fact that the averagedelay time is lower for the dielectric particle than for the metal and coated metal particles does notfollow the theory. This is most likely the result of a shorter distance between electrode and particle forthe dielectric material.

While investigating the influence of the applied voltage on the delay of initiation, a linear relation isfound for the experiments at 100 mbar. This follows the expectation as the theory explains that highervoltages cause initiation to happen faster.

Moreover, no conclusions can be drawn on the relation between the frequency and the initiationvoltage. The applied voltage needed to observe initiation varies a few hundreds of volts for differentfrequencies. Furthermore, the applied high voltage is not a perfect the step function and varies as well.

When the empirical cumulative density function is used to analyze the trend of the delay time as afunction of the iteration number, an interesting result occurred: the shortest delay times have a verylow probability for the dielectric particle at 200 mbar in comparison with the metal and coated metalparticle. This could be caused by the dielectric property which suggests that there exists some sort of”installation time” of about 0.5 milliseconds in which charges in the dielectric material realign as reactionon the change of electric field. Furthermore, the coated metal particle shows a nod in its ECDF which isnot observed for the dielectric or metal particle. A suggestion is that this is due to the different testedfrequency, or shape.

Finally, the derivative of the delay time as a function of the iteration number is observed. This givesa better inside in the consistency of the delay time; is it approximately constant or is it completelyrandom? The results show for some, not directly related, sets of variables a sudden drop in chaos. Thisholds on for a random number of iterations, after which the delay time starts to vary a lot again. It isstill unclear which parameters or circumstances give rise to this effect. However, these results could givea better inside in initiation, so further research with more constant and other parameters would certainlybe useful.

To conclude, a lot of results are presented, yet none could be explained properly. In order to be ableto say anything about initiation near dielectric materials for certain, more theoretical studies in this fieldare needed.

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AResults

A.1 Results width of inception PMT signal

At a pressure of 100 mbar the results of the PMT signal are as follows:

Dielectric particle:

Figure 27: Dielectric particle, 100 mbar, 5Hz

Figure 28: Dielectric particle, 100 mbar, 15Hz

Metal particle:

Figure 29: Metal particle, 100 mbar, 5 Hz Figure 30: Metal particle, 100 mbar, 10 Hz

Coated metal particle:

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Figure 31: Coated metal particle, 100 mbar,4 Hz

Figure 32: Coated metal particle, 100 mbar,8 Hz

If more air is allowed in the vessel and the pressure rises up to 200 mbar, this signal was is shown inthe following few figures.

Dielectric particle:

Figure 33: Dielectric particle, 200 mbar, 5Hz

Figure 34: Dielectric particle, 200 mbar, 15Hz

Metal particle:

Figure 35: Metal particle, 200 mbar, 5 Hz Figure 36: Metal particle, 200 mbar, 10 Hz

Coated metal particle:

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Figure 37: Coated metal particle, 200 mbar, 4 Hz

A.2 Results delay time

Dielectric particle:

Figure 38: Dielectric particle, 100 mbar Figure 39: Dielectric particle, 200 mbar

Metal particle:

Figure 40: Metal particle, 100 mbar Figure 41: Metal particle, 200 mbar

Coated metal particle:

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Figure 42: Semi dielectric particle, 100 mbar Figure 43: Semi dielectric particle, 200 mbar

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