INSTITUTE OF PHYSICS PUBLISHING
JOURNAL OF PHYSICS D: APPLIED PHYSICS
J. Phys. D: Appl. Phys. 35 (2002) 2169–2179
PII: S0022-3727(02)33941-X
Pulsed positive corona streamer propagation and branching E M van Veldhuizen and W R Rutgers Department of Physics, Technische Universiteit Eindhoven, 5600 MB Eindhoven, The Netherlands E-mail:
[email protected]
Received 19 February 2002, in final form 11 June 2002 Published 16 August 2002 Online at stacks.iop.org/JPhysD/35/2169 Abstract The propagation and branching of pulsed positive corona streamers in a short gap is observed with high resolution in space and time. The appearance of the pre-breakdown phenomena can be controlled by the electrode configuration, the gas composition and the impedance of the pulsed power circuit. In a point-wire gap the positive corona shows much more branching than in the parallel plane gap with a protrusion. In air, the branching is more pronounced than in argon. The pulsed power circuit appears to operate in two modes, either as an inductive circuit creating a lower number of thick streamers or as a resistive circuit giving a higher number of thin streamers. A possible cause for branching is electrostatic repulsion of two parts of the streamer head. The electric field at the streamer head is limited, the maximum values found are ∼170 kV cm−1 in air and ∼100 kV cm−1 in argon. At these maximum field strengths, the electrons have 5–10 eV energy, so the ionization is dominated by two-step processes. Differences between argon and ambient air in the field strength at which streamers propagate are ascribed to the difference in de-excitation processes in noble and molecular gases. The fact that the pulsed power circuit can control the streamer structure is important for applications, but this effect must also be taken into account in fundamental studies of streamer propagation and branching.
1. Introduction Electrical discharges play a key role in technologies such as semiconductor fabrication, high-efficiency lighting, arc welding, high-voltage switchgear, plasma displays and chemical treatments of gases, liquids and surfaces. Due to the complexity of the plasma created by such discharges, their application is still largely based on empirical knowledge. In this paper, the case of the pulsed positive corona is addressed. This non-thermal, chemically active plasma is one of the options for gas treatment at atmospheric pressure and it offers more perspective for large gas flows than the alternatives such as the dielectric barrier and the packed bed discharge [1]. This perspective has made a large gain recently with the development of power supplies up to 75 kW with high efficiency and good reliability [2]. Despite these recent improvements, the pulsed corona discharge itself is still not fully understood and is therefore being investigated experimentally and theoretically. 0022-3727/02/172169+11$30.00
© 2002 IOP Publishing Ltd
Experiments face the difficulty of the high space and time resolution and sensitivity that are required. Simulations face the same problem and their state-of-the-art is the two-dimensional approach [1, 3]. Recent improvement of equipment now facilitates more detailed experimental research. Early recordings of the development of streamer corona have been made by cloud chamber tracks [4]. This method is, however, very limited in applicability. Photographs with intensified cameras have been made in the past but with limited sensitivity and resolution in space. In [5], for instance, it is mentioned that pre-breakdown streamers in argon were not observed. Occasionally, the Schlieren technique is used [1, 6] but this requires heating of the gas and therefore has very limited time resolution. Recently, laser spectroscopic techniques have been employed to determine in detail the distribution of species such as OH [7, 8], NO [9, 10], N [11] and O [12]. Further, the electric field is determined from emission spectroscopy [13] or from polarization effects [14, 15]. These methods also still have restrictions in resolution, are
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difficult to calibrate and can be applied only in very special arrangements. Questions that are still not addressed till now are: how efficient are radicals produced by one electrical pulse, and, are there ways to optimize this production. A crucial role is played here by the phenomenon of the branching of discharge channels. Many streamers can emerge from one anode tip and this number varies with conditions. This effect is known since the start of streamer research [16] but it has hardly been studied in detail till now. One of the first attempts is probably the Monte Carlo approach for the branching probability given in [17]. Later, the fractal approach has been used to simulate the two-dimensional discharge pattern of a surface discharge in SF6 [18]. With the addition of graphic post-processing, the simulation appears very similar to the experimental observation [19]. Recently, branching is predicted for negative streamers using a fully deterministic model [20]. In this paper, we present experimental results of streamer branching recorded with a CCD camera having a high sensitivity and a good resolution in space and time. The recording of the optical emission of a single corona pulse is feasible with this system [21]. Several parameters on which the branching phenomena strongly depend can thus be investigated: the gap configuration, the gas composition and the electrical impedance of the pulsed power circuit.
2. Theoretical background A large number of papers and books on the behaviour of corona streamers is available. Here, we give a short review of the stateof-the-art of the theory on pulsed positive corona in order to facilitate the interpretation of the measurements presented in section 4. Three basic subjects can be identified: the start of a streamer, usually called inception, the propagation and the branching. To avoid confusion, we also indicate the difference between streamers and sparks and the transition of streamers to ionization waves.
occasional avalanche will be relatively slow and the so-called inception time-lag not only becomes long but will also have a considerable stochastic spread, called jitter. 2.2. Stability field Once the avalanche has developed into a space charge cloud of positive ions, the local field may be high enough to start a new avalanche closer to the cathode. The required initial electron is considered to originate from photoionization. Whether or not this process continues until the cathode is reached depends again on the applied field strength. The lowest value at which stable propagation appears to be possible in a homogeneous field is called the stability field, Est [1, 6, 22, 23], although this term is not used by all authors. Its value in ambient air is 5 kV cm−1 . It is shown from theory that the field inside the streamer channel, Ech , is equal to the stability field [1, 22]. If a streamer head cannot propagate for some reason then the space charge will diffuse and recombine. The current will go to zero and the discharge extinguishes. The streamer discharge only exists as long as the streamer is propagating, therefore it is called a transient discharge. 2.3. Maximum field It is clear that an avalanche must stop its exponential growth at some point. According to [22], this maximum field, Emax , is found from the inflection point of the ionization coefficient versus the field strength. In figure 1 these curves are given for air and argon, based on empirical literature data [24–26]. In the figure the tangent lines to the curves are drawn in order to determine the inflection point. The values obtained from figure 1 for Emax are 520 ± 60 Td for air and 320 ± 50 Td for argon, which is equivalent to ∼170 kV cm−1 and ∼100 kV cm−1 respectively. The two curves of argon show a significant difference, the result given here is their average. At these field strengths, the average electron energy will be of the order of 5–10 eV, so one may wonder why the ionization already saturates when the ionization threshold is 15 eV and its
2.1. Inception probability An electron that moves in a sufficiently high electric field develops into an avalanche. This avalanche becomes a streamer head when the electric field of the ions that are left behind dominates the applied field. So, three conditions must be met to obtain streamer inception: (1) a free electron, (2) applied field above the so-called critical field strength, Ecr , and (3) sufficient or critical distance, dcr . The free electron can originate from detachment of a negative ion or from ionization through cosmic rays. The critical field in ambient air is roughly 30 kV cm−1 [5] and the critical distance is a fraction of a millimetre. If one or more of these conditions is only marginally met then the streamer may or may not start. Similar to the case of spark breakdown [5], we define here the inception probability, Pinc , which gives the chance for a streamer to occur upon a single high-voltage pulse. In most practical corona applications, the inception probabilty is one because the electric field at the sharp electrode is far above the critical field. Under conditions where Pinc is low, the growth of an 2170
Figure 1. The reduced ionization coefficients as a function of the reduced electric field. ‘1’ is an empirical formula for air from [24], ‘2’ is a table for Ar from [25] and ‘3’ is an empirical formula for Ar [26]. The bending points give the maximum field strength at the streamer head.
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maximum cross section is at ∼100 eV. This is explained from the fact that the energy of these electrons is very efficiently absorbed by creating metastables and excited states. Ionization then easily occurs by two-step processes. A streamer head is a positive space charge region which carries 108 –109 ions. This head is shaped as a disk of 200 µm diameter and 20 µm thickness [1, 3, 22, 27]. This roughly leads to the same Emax as obtained from figure 1. A large streamer head may split in parts which will separate due to electrostatic repulsion [20]. This force is strong enough to cause a separation of a few millimetres in tens of nanoseconds. Other mechanisms such as magnetic forces or diffusion are orders of magnitude too small. 2.4. Spark breakdown A streamer head can propagate until the cathode when the applied voltage is high enough. Then a conducting path is created between the electrodes and a current will flow when the voltage is maintained. If this current is very low then recombination will reduce the conductivity and the discharge will extinguish. If the current is high enough it will heat the gas, decrease its density and increase its conductivity. The current will grow to a maximum value which is determined by the pulsed power circuit, it can be orders of magnitude higher than the corona current. The same is the case for the intensity of its optical emission. The pulsed power circuit will usually maintain this high current only for a short time, therefore this type of discharge is called spark breakdown. Besides the high current, a major difference with streamer corona is that the plasma of the spark discharge tends to go to a thermal plasma, whereas in the streamer channel the gas remains close to room temperature. 2.5. Ionization waves Pulsed corona discharges at atmospheric pressure require voltages of the order of 0.1 MV cm−1 in order to initiate. The velocity of the streamer ranges from ∼0.1 to 1 mm ns−1 [1]. This implies that in a short gap of 25 mm a voltage pulse is required of 25 kV with a rise time of not more than 25 ns. In such a case, the full voltage is across the gap before the streamer has propagated from anode to cathode. The typical diameter of positive streamers in this situation is ∼200 µm. If the rate of rise of the voltage is made much higher, i.e. ∼10 kV ns−1 , one enters into a different regime of discharge, sometimes called ionization wave [28]. In that case the electron energy goes up considerably and the streamer diameter can increase to ∼1 cm [29].
cost. The alternatives were either thyratrons, which were very expensive with limited lifetime, or thyristors followed by a magnetic compression step. These last ones do have a good lifetime but are even more expensive. Stacked highvoltage MOSFET transistors are another possibility that have recently become available. Although quite modest in terms of power, their parameters make them very suitable for smallscale investigations as presented here. The Behlke HTS-301 is used for a part of the measurements presented in this paper. It has a maximum withstand voltage of 30 kV and a minimum turn-on rise time of 20 ns. Besides this, it has a trigger jitter of only 0.1 ns, which makes it much easier to synchronize its pulses with lasers or cameras than a spark gap. A scheme of the circuit used in the experiments is given in figure 2. The negative output of the DC high-voltage supply, HV, is connected to the 10 M charging resistor. The 1 nF energy storage capacitor is connected to ground by the triggered switch. This leads to a positive pulse on the discharge gap. This pulse is measured by a voltage probe, V , and a current probe, I . The signals are measured by a digital oscilloscope with 1 GHz sampling rate. Both signals are slightly filtered in the oscilloscope to give the probes the same rise time. This also gives some reduction of noise and oscillations. The 50 M resistor across the gap serves to bring the potential of the point electrode back to zero between pulses. This circuit is by no means designed for high-energy efficiency. Its flexibility is much more important here and the circuit can be altered by introducing additional resistance or inductance between the storage capacitor and the HV electrode and/or capacitance, as indicated with dotted lines in figure 2. The fibre optics and the shielding box are installed for interferencefree operation of the measuring equipment. The corona gap indicated here consists of a point-to-wire gap of 25 mm with the wire parallel to the CCD. This is an attempt to let the streamers propagate more or less in a plane to get them well focused on the camera. Photos with the wire perpendicular to the CCD show that the streamers bend outwards quite strongly in the middle of the gap but they return to the wire [30]. The point-wire gap can be replaced by a parallel plane gap with a protrusion as indicated in figure 3 in order to study streamer propagation in an (almost) homogeneous electric field. The point is always the same tungsten tip with a radius of 15 µm. No changes were observed at this tip because a low number of pulses is made with low energy. Oscilloscope
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3. Pulsed corona power circuit and diagnostics In this paper, corona streamers are studied using a pulse circuit with voltage rates of rise of approximately 1 kV ns−1 . This value is common and leads to good efficiencies in pulsed corona applications [1]. One way to obtain such a pulse, with a limited number of components and a good flexibility to change parameters, is to discharge a high-voltage capacitor by a fast switch. In the past, mostly spark gap switches have been used because of their ease of construction and their low
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The corona enclosure is either open to ambient air or it is flushed, after evacuation, with high purity argon (5.0) at 1 bar. It has a 50 mm diameter quartz window on one side. The CCD camera is fitted with a Nikon UV-Nikkor, 105 mm f/4.5 lens; so, also the UV part of the spectrum is recorded. The main specifications of the camera (Andor Technology ICCD-452) are • 1024 × 1024 pixels, • 13 µm × 13 µm pixel size, • 21 µm spatial resolution (determined by the fibre coupling of the intensifier) • 0.8 ns minimum optical gate time, • up to 3600× gain, • 180–850 nm wavelength range, • Peltier cooling (ensuring a low and uniform background). The electrodes are focused on the camera with a magnification of 0.45 so the complete gap is always photographed. Reading out the camera by a PC takes several seconds and since no highvoltage pulses are given between photos the corona repetition rate is several pictures per minute or less.
4. Results on propagation and branching in a point-wire gap 4.1. Basic pulsed power circuit Figure 4 shows one example of a photo where the shortest possible optical gate time of 0.8 ns is used. One sees that the streamer heads simultaneously moving as spheres through the gas. More examples in [21] and [30] show that the number of heads increases during propagation, clearly indicating the branching. In analytical considerations [22] and in twodimensional simulations [3] the streamer heads appear as disks, which are very thin in the direction of propagation. This shape is not resolved here, it would require an optical gate of less than 0.1 ns. The CCD camera records intensity and the colours in the figures indicate certain levels of intensity. They are a compromise between visibility of low level details and a good dynamic range. This leads to overexposure of high-intensity parts near the anode. These corona pulses are almost invisible to the human eye. Only at the highest voltages and after a long adaptation in the dark they can just be observed. The background of the CCD itself is very constant as can be seen 2172
Figure 4. Photograph of streamer heads of a point-wire discharge in air taken with the intensified CCD camera using an optical gate of 0.8 ns. A pulse of 25 kV with a rise time of 20 ns is applied. The photo is taken 31 ns after the start of the pulse.
from the uniform blue colours. Therefore, no further attempts have been made for background subtraction. If the optical gate time is made longer than 0.8 ns then the streamers appear as line pieces on the photo. The length of such a piece divided by the opening time gives the velocity of the streamer head averaged over this opening time [31]. The streamer velocity in air at 12.5 kV is ∼3 × 105 m s−1 at the anode, it decreases to 1.4 × 105 m s−1 in the middle of the gap and it increases slightly to 1.6 × 105 m s−1 near the cathode. At 25 kV the velocity is quite constant across the gap at 1.2 × 106 m s−1 . Adding a series resistor of 1 k has no influence on the velocity. The series inductance of 10 µH leads to ∼25% increase of the velocity at 12.5 kV and ∼25% decrease at 25 kV. Figures 5–7 show pictures of discharges in air with a 25 mm point-to-wire gap using an optical gate time of 5 µs. The illuminated paths on the photos indicate the positions where the streamer heads have moved along. These pictures are taken asymmetric because then the full discharge development is seen at one side. The reproducilbity of these photos with respect to streamer length and width and the number of branches is remarkably good. Figure 5(a) is taken at a voltage pulse amplitude of 7.5 kV. This is the lowest voltage at which branching is observed. At this voltage, no distinction can be made between pictures obtained with either a spark gap or a semiconductor as switch for the production of the high-voltage pulse. Figures 5(b) and (c) are both taken at a pulse voltage of 12.5 kV, where the semiconductor switch is used in figures 5(b) and (c) the spark gap in figure 5(c). In both pictures one streamer is seen that reaches the cathode and the appearance of the pictures is quite similar except that the streamers are slightly more diffuse in the case of the spark gap. Figures 6 and 7 are both taken at 25 kV, the first one using the semiconductor switch and the second one the spark gap. The difference between figures 6(a) and 7(a), where the basic circuit is used in both cases, is now much larger. About three times more streamers appear in figure 6(a) and they appear to be thinner. Since the thick streamers in figure 7(a) are overexposed in this picture one cannot determine the diameter directly. In [30], it is shown that both high- and low-intensity streamers in the gas have diameters of 160 ± 30 µm, as
Pulsed positive corona streamer propagation
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Figure 5. CCD photos of the point-wire discharge in air using 5 µs optical gate. Applied voltages: (a) at 7.5 kV, (b) and (c) at 12.5 kV. For (a) and (b) the semiconductor switch is used, for (c) the spark gap. (a)
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Figure 6. CCD photos of the point-wire discharge in air at 25 kV using 5 µs optical gate. The semiconductor switch is used here. (a) is taken with the basic circuit, (b) with a 23 k series resistor and (c) with a 10 µH series inductance. (a)
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determined from their full width at half maximum. At the anode, the streamers may be thicker but they are not clearly defined anymore, also because there is a ‘glow’ discharge at the anode (the larger sphere at the top of figure 4) as long as there is a current flow.
4.2. Parameter changes of the pulsed power circuit Additional resistance, inductance and/or capacitance, as indicated in figure 2, has been added to the pulsed power circuit
in order to study the influence of the circuit impedance on the branching behaviour of the discharge. Figures 6(b) and 7(b) show the effect on streamer branching of adding a resistor of 23 k and 1 k respectively, figures 6(c) and 7(c) the same for adding inductance of 10 µH in both cases. It is observed that extra resistance causes thin streamers with more branches, whereas inductance gives thicker and more diffuse streamers with less branching. Additional capacitance has no influence on the appearance of the streamer branching. The influence of these additions on the voltage and current of the pulse is shown in figure 8 for the case of 2173
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the semiconductor switch. The curves obtained for the spark gap are very similar concerning voltage rise time and current amplitude and duration. They have a somewhat more oscillatory behaviour, which is to be expected because the circuit has less damping. Figure 8(a) shows voltage and current of the discharge at a supply voltage of 25 kV. The 10–90% voltage rise time is 22 ns. This rise time is also 22 ns in figure 8(b) where 10 µH is added to the circuit and 29 ns in figure 8(c) where a 1 k resistor is added. Figure 8(d) shows the case of a 23 k resistor in series with the switch. This clearly has a much larger influence on the voltage pulse leading to a rise time of more than 1000 ns. Other effects of the additions are a small oscillation due to the inductance, figure 8(b), and a voltage dip of 3 kV at the anode during the streamer current in case of the 1 k resistor, figure 8(c). The 23 k, figure 8(d), gives a very different behaviour. At 7 kV the slope of the voltage bends, this is an indication that a discharge current starts flowing and it appears to continue for several hundreds of nanoseconds. For the analysis of the current, which flows in the loop of the capacitor, the switch and the discharge gap, it is important to realize that this consists of two parts. The first part is a displacement current, Idispl , which brings the needle to a high potential, given by Idispl = Cgeom
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be recognized. Cgeom is calculated by fitting the calculated dV /dt, the dotted line in figure 8(a), to the first current peak. This gives a value of ∼7 pF. The energy in the second pulse, the real discharge current, is 2 mJ. The time interval between Idispl and Idisch shows that under this condition the inception time lag is ∼100 ns. Figure 8(b) gives an example of a very short inception time lag so that Idisp and Idisch overlap. By using Cgeom from a situation as in figure 8(a) one can calculate Idisch also for figure 8(b). In the cases of figures 8(b) and (c), the energy of the pulse is again 2 mJ. In these three cases, the current duration is equal to the time required by the streamers to cross the gap, i.e. several tens of nanoseconds. The voltage remains at maximum for about 10 µs in all cases but no corona current is observed anymore after the pulses as shown in figures 8(a)–(c). Compared to DC corona the currents observed here may appear to be very high. The typical current of an individual streamer of ∼0.1 A is, however, common for pulsed corona and this value is consistent with model results [1, 3, 22]. The case of figure 8(d) is quite different from the others because the voltage has a long rise time of between 300 and 500 ns, during which approximately half of the voltage is across the resistor. Then the resistance of the corona is also ∼23 k and the current is almost 0.5 A. This value is also obtained as an average of the oscillating current in this period. This leads ∼1 mJ for the energy content of the discharge pulse and a similar amount of energy dissipated in the resistor. It cannot be determined from figure 6(b) if the streamers move more slowly or that different streamers appear after each other in time. At lower voltages, oscillations and noise start
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Figure 9. CCD photos of a point-wire discharge in argon using the semiconductor switch and the basic circuit. The applied voltage is (a) 3.5 kV and (b) and (c) 5 kV. The optical gate is 5 µs.
dominating the pictures. At 12.5 kV applied voltage the energy content of the pulses is estimated to be ∼0.2 mJ. A final remark about the pulses in air is that also the electrical parameters are quite reproducible in all cases. 4.3. Point-wire gap in argon A few photos of positive corona discharges in argon are given in figure 9. Only the semiconductor switch is used for highvoltage pulses in argon because the spark gap is unstable at the relatively low voltages required. The same image intensifier setting has been used here as in figure 5. The lowest voltage where streamers are observed is 3.5 kV. At this low voltage, however, the inception probability is not more than ∼5%. Contrary to air, the streamers can bridge the whole gap at this voltage just above inception, as is shown in figure 9(a). At 5 kV, the inception probability becomes ∼20%. Two examples are given, in figure 9(b) the streamer propagates only ∼5 mm and it develops five branches. In figure 9(c), it crosses the gap almost and there are many fine branches. At 6 kV a spark breakdown occurs every time the pulsed voltage is applied which makes it impossible to observe streamers. These photos show that the streamer length and the number of branches is not reproducible in the case of argon. The measurement of the streamer velocity is impracticable in argon given the statistical behaviour of the streamer inception in combination with optical gates of a few nanoseconds. The current of the corona pulses in argon could not be distinguished from the difference of total and displacement current; their energy is estimated to be below 0.1 mJ.
5. Propagation and branching in a parallel plate gap with protrusion Photographs of streamers obtained with the gap configuration of figure 3 are shown for the case of air in figure 10 and for argon in figure 11. In air, the lowest voltage at which a streamer is observed is 9 kV (figure 10(a)); its length is several millimetres. At 10 kV, the streamer crosses the whole gap and a few branches are observed (figure 10(b) and (c)). A low number of branches is also observed at 12.5 kV. Their number appears to depend on the optical gate of the CCD camera. Figures 10(d) and (e) are taken with 5 µs opening time, showing several branches, and figures 10( f ) and (g) with
50 µs, with roughly three times more branches. This effect was not observed in the point-wire gap. Figure 10(h) is taken at 15 kV pulse amplitude and with the long opening time. For a comparison of the two electrode geometries used one should look at figure 5(b) (∼40 branches) and figures 10(d) and (e) (3 branches) for a situation with the same average value of the applied electric field. A few examples of discharges in argon are given in figure 11. Figures 11(a) and (b) are taken at 4 kV. Again the inception probability for streamers is very low, i.e. ∼2%. Occasionally a very faint spot is observed at the anode (figure 11(a)) and, even more sporadically, a streamer is seen which then always crosses the whole gap (figure 11(b)). At 4.5 kV, a streamer develops more often (figure 11(c)) but it sometimes develops into a spark breakdown (figures 11(d) and (e)). These spark channels have a luminous intensity of roughly five orders of magnitude higher than the streamers in argon as seen on other pictures presented here. Branching is not observed in the plane-protrusion gap in argon.
6. Discussion 6.1. Point-wire gap in air The number of branches observed for positive streamers in air, and their propagation length and velocity, is quite reproducible. The branching is observed already close to the anode but also in the entire gap. The distance that the streamers propagate depends on the applied voltage. The lowest voltage at which the streamers reach the cathode is 12.5 kV so the average applied field is equal to the stability field. However, in a pointwire gap of 25 mm with a point radius of 15 µm the applied field is below 0.5 kV cm−1 in most of the gap as calculated with a boundary element method. Therefore, in the configuration used here, the streamer continues to propagate in an applied field, which is ten times below the stability field. At 25 kV the number and the thickness of the branches appears to depend on the type of switch used, as can be seen from comparing figures 6(a) and 7(a). At 12.5 kV and below, this effect is hardly observed. At such low voltages the energy in the corona pulse is very low and it can take this energy from the local geometric and stray capacitance. This capacitance is estimated at ∼2 pF, so it contains ∼0.2 mJ energy at 12.5 kV, which is equal to the estimated energy of the pulse. At 25 kV 2175
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Figure 10. CCD photos of a plane-protrusion discharge in air using the semiconductor switch. The applied voltage is (a) 9 kV, (b) and (c) 10 kV, (d)–(g) 12.5 kV and (h) 15 kV. The optical gate is (a)–(e) 5 µs, and ( f )–(h) 50 µs. (a)
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Figure 11. CCD photos of a plane-protrusion discharge in argon using the semiconductor switch. The applied voltage is (a) and (b) 4 kV and (c)–(e) 4.5 kV. In (d) and (e) the sensitivity is reduced five orders of magnitude compared to the other pictures in order to observe the spark breakdown without overexposure.
this local contribution is below ∼25%. So at 12.5 kV and below the (remote) switch does not play an important role, but at 25 kV it should because most of the required energy goes through it. The question now is what causes the difference in branching as observed in figures 6(a) and 7(a). The voltage rise time is 20 ns in both cases. Therefore, the rise time, or 2176
the voltage rate of rise, is not the determining factor here. Another possibility is a difference in the impedance of the switches. According to the manufacturer of the semiconductor, this switch has 20 pF capacitance and 60–1000 resistance (depending on the load). For the spark gap these parameters are estimated to be ∼1 pF and ∼10 . With an extra series resistor of 1 k in the spark gap circuit, more and thinner
Pulsed positive corona streamer propagation
branches are created and the picture becomes more similar to the one obtained using the semiconductor switch, compare figures 6(a) and 7(b). The extra resistor gives an increase in the voltage rise time to 29 ns. Since the streamer current starts at almost maximum voltage (see figure 8(c)) this difference in rise time appears not to be the cause of the difference in branching behaviour. The observations can be summarized by stating that the number of branches of positive corona in air increases if resistance is included in the pulse circuit and it decreases when inductance is added. Approximate values of the full width at half maximum of the optical emission intensity for cases that individual streamers are clearly recognized as 0.2 mm for figure 5(a) and 0.8 mm for figure 7(a). With maximum discharge currents of 8 A and 3 A respectively, this leads to currents for a single streamer of 80 mA with the semiconductor switch and 75 mA for the spark gap, so this last streamer has a 16 times lower current density. In both cases, the resistance of one streamer is 0.3 M. The resistance of the discharge is 3 k in case of the semiconductor switch and 8 k in case of the spark gap. Considering these values, a noticeable influence of a 1 k series resistance can indeed be expected. The currents and the diameters found for a single streamer are in the range of the predictions from numerical simulations [1, 3]. A physical reason for the influence of the additional component is not found. One may think that extra resistance will limit the current, but the energy of the pulse does not change due to the 1 k resistor and even the streamer velocity remains the same. Also the inductance does not give a substantial change in energy and velocity. The streamer velocity is, on the contrary, very sensitive to the amplitude of the voltage pulse. When this voltage increases by a factor of 2, the speed goes up by a factor of 10. 6.2. Point-wire gap in argon The streamer in argon requires a much lower voltage to cross the gap. This is consistent with the stability field, which has a value of 0.4 kV cm−1 in pure argon [23]. So already at 1 kV, the gap of 25 mm could be crossed by the streamer in argon. At such a low voltage, however, the streamer does not start because the streamer head has a potential drop of ∼2 kV (under the estimation that the length of the high field region at the streamer head is 200 µm at a field strength of 100 kV cm−1 ). At the experimental value of 3.5 kV for the lowest voltage to cross the gap this leaves, on an average, ∼0.6 kV cm−1 across the gap, which is quite close to the mentioned 0.4 kV cm−1 . The fact that the streamer head requires a major portion of the applied potential is probably related to the low inception probability.
from two-dimensional simulations [1, 27]. This is, however, not seen in the measurements presented here. The fact that more streamers show up when the opening time of the camera is increased can also not be explained from two-dimensional simulations. A complete three-dimensional scheme will be required to simulate such effects. The argon discharge is changed even more by the nearly homogeneous field. No branching at all is observed; this could be because the streamers propagate more easily in argon. From theory and simulations it is expected that Emax does not depend on the electrode configuration. Values found are 150 kV cm−1 for a point-plane gap [3] and 170 kV cm−1 for the parallel plane gap [27]. So the difference in branching behaviour is not due to the local electric field strength at the streamer head. These values for Emax agree very well with the one obtained from figure 1. 6.4. Argon versus air One point that is not yet explained is the big difference between air and argon in the voltage required for streamers to cross the gap. The maximum E fields at the streamer heads are quite similar but their stability fields differ an order of magnitude, i.e. 5 kV cm−1 for air and 0.4 kV cm−1 for argon. Oxygen is often mentioned as the cause for a high stability field in air due to its electronegative character. Pulsed positive corona streamers, however, propagate on a nanosecond timescale, whereas the time constant for attachment of 1% oxygen in 1 bar argon is estimated to be 10 µs [33]. In air it could be shorter, but for corona durations of ∼30 ns one still can expect the attachment to be negligible. The stability field in pure nitrogen is unknown to the authors but an estimate can be obtained from the fact that the stability field is equal to the field in the streamer channel [1, 22]. A value of 10–20 kV cm−1 is then derived from the figures in [27] which again shows that it is not the electropositive character of argon that causes its low stability field. The explanation that is found in [33] to explain the effect of the admixture of oxygen is that molecules offer many pathways for de-excitation than noble gases. Therefore, in argon, electrons can build up energy at low fields because in elastic collisions with neutral argon they hardly lose energy. In molecular gas, on the contrary, the electron must gain the threshold energy for excitation in one mean free path; otherwise, it will lose its energy in rotations and vibrations. Therefore, a much higher stability field is required to keep the discharge going in molecular gases.
7. Conclusions 7.1. Streamers in air
6.3. Plane-protrusion gap A big difference is observed in the branching behaviour in point-wire and plane-protrusion gaps. In the second case, the applied field strength is very uniform except for a region of ∼2 mm around the tip of the protrusion. So stable propagation is expected once the discharge starts. This situation is found to a good extend in figures 10(b)–(c) and 11(b)–(c). The analysis then predicts an increasing diameter of the streamer head during the propagation [22]. This broadening is calculated also
Pulsed corona streamers in a short gap in air are observed with single shot CCD photos. Their appearance, considering streamer number, length and diameter, is quite reproducible. Their propagation and branching depends on the amplitude of the pulse, the divergence of the applied electric field and the impedance of the pulsed power supply. The streamers in air bridge the gap at an applied voltage that corresponds to an average applied field strength equal to the stability field, i.e. 5 kV cm−1 . This is expected from theory in a homogeneous 2177
E M van Veldhuizen and W R Rutgers
field, but in the experiments, it is also valid in a very nonhomogeneous field of the point-wire gap. The maximum electric field strength at the streamer head also does not depend on the shape of the electrodes. Its value, ∼170 kV cm−1 , is derived from the inflection point of the ionization coefficient versus the field strength. Numerical simulations give similar values. The field does not increase beyond this value because the electrons easily lose their energy in excitations of the background gas. Since the average electron energy is 5–10 eV in this situation, the ionization of the gas is mainly a two-step process. If the streamer head tends to become too large, it must increase its speed or it must break up in parts due to electrostatic repulsion. The adaptation of the speed is illustrated by the observation that it increases an order of magnitude when the applied voltage increases by two times. The branching behaviour of the streamers in air is very different in the two geometries used here. About 10 times more branches are observed in the point-wire case compared to the plane–plane discharge at the same average applied field strength. The maximum field at the streamer head is similar in both cases; therefore, the assumption that the branching probability is linear with the local electric field (as used in [17]) cannot explain the discharge behaviour as observed here. The number of streamers depends also on the impedance of the pulsed power circuit: an resistive circuit gives a high number of thin streamers and an inductive circuit gives fewer streamers with a larger diameter. Both circuits have the same voltage rise time and energy per pulse. The current density in a single streamer differs an order of magnitude in these two cases. Another unexplained feature in the plane-protrusion gap is the appearance of more streamers with increased exposure time. A difference with simulations is the observation that the streamers have a constant diameter when propagating through the gap whereas in simulations their diameter increases. 7.2. Streamers in argon The propagation behaviour in a short gap in argon differs a lot from air. Contrary to statements in textbooks, pre-breakdown streamers in argon are observed in the experiments presented here. They are less easily seen for two reasons: the voltage range in which they occur without leading to spark breakdown is much narrower than in air and the inception probability is less than 10% in this voltage range. The streamer lengths and their number show a large variety. These phenomena are related to the low stability field in argon, 0.4 kV cm−1 , due to the absence of de-excitations by vibrations and rotations compared with molecules. Because the streamer propagates at such a low field strength, the inception behaviour is dominating the discharge in argon more than in air. The low inception probability of the positive corona in argon is related to the fact that a major part of the applied voltage is required for the formation of the streamer head. The maximum field strength at the streamer head is found to be ∼90 kV cm−1 which is four times higher than the value obtained from simulations. Branching is much less pronounced than in air, probably because the streamers propagate so easily in argon. In the plane-protrusion configuration, no branching at all has been observed and the margin between corona inception and spark breakdown is even smaller. 2178
7.3. Final remarks The splitting of streamer heads may originate from electrostatic repulsion. For a better understanding of the details of propagation and branching, a three-dimensional simulation is required preferably using collision cross section instead of empirical ionization constants. Such a model appears to be beyond the present calculational possibilities. More measurements and simulations under comparable condition are required to approach the final goal to understand and control the pulsed discharge at high pressure. The fact that the number and thickness of streamer branches can be influenced by the pulsed power circuit may give a handle to control applications. This work shows that also in fundamental studies of streamer propagation and branching one must take into account the impedance of the power supply.
Acknowledgments The authors gratefully acknowledge the assistance of P C M Kemps and N Valette with the experiments. We thank U Ebert for suggesting experiments with the plane-protrusion gap. The discussions with W W Stoffels have been useful and stimulating.
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