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Nov 26, 2012 - High-resolution measurements of the electric field at the streamer arrival to the cathode: A unification of the streamer-initiated gas-breakdown ...
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PHYSICAL REVIEW E 86, 055401(R) (2012)

High-resolution measurements of the electric field at the streamer arrival to the cathode: A unification of the streamer-initiated gas-breakdown mechanism ˇ ak,2 Jean Paillol,3 Detlef Loffhagen,1 and Ronny Brandenburg1 Tom´asˇ Hoder,1,* Mirko Cern´ 1

2

Leibniz Institute for Plasma Science and Technology (INP Greifswald), 17489 Greifswald, Germany R&D Center for Low-cost Plasma and Nanotechnology Surface Modifications, Masaryk University, 611 37 Brno, Czech Republic 3 LGE University of Pau, 64000 Pau, France (Received 2 March 2012; revised manuscript received 11 October 2012; published 26 November 2012) A time-correlated single-photon counting technique was used to verify the formation of a cathode-directed streamer inside the narrow cathode region following the interpulse phase of regular negative corona Trichel pulses in ambient air. A purely experimental approach was used to determine the spatiotemporal development of the electric field during the Trichel pulse rise with an extremely high resolution of 10 μm and tens of picoseconds. The results confirm the positive-streamer mechanism for Trichel pulse formation and provide supportive evidence for the hypothesis that the formation of a primary cathode-directed streamer occurs always in any streamer-initiated breakdown and prebreakdown phenomena associated with cathode spot formation. DOI: 10.1103/PhysRevE.86.055401

PACS number(s): 52.80.Hc, 51.50.+v, 52.25.Jm, 52.70.Kz

Typically, at gas pressures above roughly 10 kPa, the sequence of events leading to an arc formation consists of the bridging of the gap by primary streamers, and the subsequent heating of the initial channel created by the streamers. The transition between these two stages is determined by the formation of an active cathode spot capable of feeding an increasing current of electrons into the discharge channel [1–6]. The mechanism for cathode spot formation still remains somewhat obscure [4,6–9], and it is the important and still missing segment in a unified theory consistently integrating the extensive results pertaining to the streamerinitiated-breakdown phenomena: Except for the prebreakdown phenomena in negative corona gaps [9–15] and for cathode spot formation by a breakdown of cathode sheaths of pulsed high-pressure discharges [16–19], the primary-streamer arrival to the cathode is accepted to be a turning point in the streamerinitiated-breakdown development leading to the final arc formation [1–8]. In the mentioned exceptional cases, cathode spot formation is related to fast phenomena (∼0.1–1 ns) inside of a narrow (∼0.1 mm) high-field region in the cathode vicinity [1,13,18,19]. Because of an apparent contrast with the RaetherMeek criterion for the avalanche-to-streamer transition [20,21] and the technical difficulties of viewing such a small area with a subnanosecond time resolution, the formation of cathodedirected streamers in such very narrow cathode regions is obviously not considered [9–16,19]. This causes the mentioned inconsistency in theory concerning cathode spot formation and contrasts with the results of a recent computer simulation study [17] by the coauthors of this Rapid Communication, which provide a strong indication that at conditions close to those used in transversely-excited atmospheric-pressure (TEA) lasers the cathode spots are formed by positive-streamer breakdowns of the cathode sheath. Also, it was hypothesized [4,17,21] that the regular in time and spatially stabilized cathode spot formation during the so-called negative corona Trichel current pulses [9,14,16,20–22], which are well amenable to time- and space-resolved optical and current measurements,

*

Corresponding author: [email protected]

1539-3755/2012/86(5)/055401(5)

are of a positive-streamer-based mechanism very similar to random cathode spot formation that is due to cathode sheath breakdowns. This hypothesis has been supported, for example, by recent studies of pulsed breakdowns in high-pressure negative corona gaps [9,23]. On this basis we believe that an experimental verification of the proposed [4,17,20,21,24] but not yet generally accepted positive-streamer-based mechanism for Trichel pulse (TP) cathode spot formation can also provide an indication that the streamer-initiated breakdown is always and in any conditions associated with a cathode spot formation by the positivestreamer arrival at the cathode. To examine the cathode region of the repetitive TPs a time-correlated single-photon counting technique called cross-correlation spectroscopy (CCS [25,26]) providing high spatiotemporal resolution of the spectroscopic recording was used. The experimental conditions were chosen to be typical of those used for studies of TPs and amenable to CCS-based measurements of the electric-field strengths: The corona discharge setup consisted of a grounded cathode with a tip curvature of 190 μm and a positive dc voltage (+7.8 kV) connected plate, both made of stainless steel with a gap of 7 mm. This setup resulted in TPs with a frequency of approximately 200 kHz and a current amplitude reaching 4 mA. For current measurements, the cathode was grounded through a 50- resistor to a digital oscilloscope. The discharge was driven in dry air flow of 300 SCCM (where SCCM denotes cubic centimeter per minute at STP) at atmospheric pressure. The shape of the TP cathode spot recorded using an intensified CCD camera and a microscope is shown in Fig. 1. The measurements of electric-field strengths during the TP rise, which is of particular interest because the streamer develops due to intense ionization in a strong electric field around its head, was performed as illustrated in Fig. 1: The CCS was calibrated by the emission from a Townsend discharge with known reduced electric-field strengths E/n according to the proven kinetic model [25,27–29]. Use was made of the fact that the E/n can be estimated from the ratio of band intensities of 0-0 vibrational transitions of the first negative system of nitrogen (band head at 391.5 nm, FNS) and the

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©2012 American Physical Society

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FIG. 1. Experimental setup for the E/n determination in TP discharge. The embedded intensified CCD picture was taken with an exposure time of 1 ms. PMT stands for photomultiplier, and TS-SPC for time-correlated single-photon counting module.

second positive system of nitrogen (band head at 337.1 nm, SPS) [25,27,29]. The non-self-sustaining Townsend discharge was operated under UV irradiation in the same setup as used in Ref. [28]. To obtain more direct results, the measurement of the TPs and the E/n calibration were performed on the same setup using an adjustable mirror. The spatial and temporal resolution of the CCS reached 10 μm and approximately 10 ps. In order to justify the use of the hydrodynamic equilibrium approximation by measurements with such a high temporal and spatial resolution, the collision frequencies νm (U ) and νe (U ) for momentum and energy dissipation as well as the mean free path λm (U ) and the energy dissipation length λe (U ) were determined (see Fig. 2) according to Ref. [30] as a function of the kinetic energy U of the electrons. These quantities were obtained using the recommended collision cross-section data given by Ref. [31]. Because both the dissipation frequencies are larger than the highest frequency of the electric-field change of about 1.13 × 1010 s−1 (see below) for almost all relevant energies, a quasistationary evolution of the distribution function of the electrons with respect to the energy and momentum takes place. This result is in agreement with Refs. [32,33] and has also been justified by corresponding temporal relaxation studies. In addition, the mean free path and energy dissipation length are smaller than the smallest length of the electric-field change of about 7.6 × 10−6 m for almost all relevant energies, so that the electrons can be assumed to be in equilibrium with the local field. The spatiotemporally resolved intensity distributions for the SPS and the FNS during the TP rise are shown in Fig. 3. The two main parts of the discharge are already visible on the SPS intensity distribution [Fig. 3(a)]. The maximum intensity (from 50 to 400 μm) is created by the propagation of the negative streamer. The measurement of the SPS was done for a PMT gain of 65%. Thus, as shown in Fig. 3(a), only the most intensive light signal was obtained to identify the clearly visible negative-streamer propagation towards the anode. The temporal correlation of light and current signals revealed that the maximum light emission (spatially integrated) appears at the same moment as the current pulse maximum, whereby the maximum light emission correlates with the propagation of the negative streamer. The FNS signal distribution shown

FIG. 2. (Color online) Collision frequencies νm (U ) and νe (U ) for momentum and energy dissipation and the mean free path λm (U ) and the energy dissipation length λe (U ) in comparison with the highest frequency of the electric-field change νf (U ) and the smallest length of the electric-field change λf (U ).

in Fig. 3(b), which can be interpreted as the spatiotemporal distribution of electrons with energy 18.7 eV [25], contains much more information about the discharge development at close proximity to the cathode. Taking into account the local field approximation and direct electron impact excitation of radiating states, the trace of the maximum E/n can be visualized [25]. The increase of the signal starts 90 μm apart from the negative point. A few nanoseconds later the positive streamer is ignited and propagates towards the cathode. As the positive streamer reaches the cathode, the current rises to its maximum. From FNS and SPS measurements we estimated the velocity of the positive and negative streamers to be 6 × 104 and 7 × 105 m/s, respectively. In consistency with literature [34], shortly after ignition the velocity of the positive streamer is smaller than that of the negative one. Comparing the plots in Fig. 3 it can be seen that there is no high FNS signal where the SPS signal has its maximum. Thus it can be concluded that within the negative streamer the E/n is lower than in the positive one (see below) while the electron density is higher. Based on the kinetic model [25,27,29] the relation between the measured intensities of the FNS and the SPS and their ratio RFNS/SPS (E/n) is in our case given as  FNS   FNS IFNS τeff + dIFNS /dt τeff  SPS = RFNS/SPS . (1) SPS ISPS τeff + dISPS /dt τeff The letter I denotes the measured light intensity. The effective lifetimes τeff are given in Ref. [35] and computed from data in

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FIG. 4. (Color) Electric-field strength distribution in repetitive TP in atmospheric-pressure air. The values corresponding to E < 3 × 106 V/m seen for x < 60 μm and t < 16 ns are at the noise level.

FIG. 3. (Color) (a) SPS and (b) FNS signal distribution in TPs of negative corona in atmospheric-pressure air with a simultaneous current measurement (black line).

Refs. [35–37]. In order to be more accurate, a spatially resolved spectrum was taken with a spatial resolution of 10 μm and the intensity of the FNS close to the cathode was corrected on the overlap with the neighboring spectral band of the SPS (transition 2-5). The spatiotemporal distribution of RFNS/SPS has been computed from the measured spatiotemporal signal distributions of the FNS and the SPS according to Eq. (1). Subsequently, the adjustable mirror (see Fig. 1) was turned towards the Townsend discharge and for known E/n the dependency RFNS/SPS (E/n) for the CCS setup was determined. As the TP measurements were done at atmospheric pressure, the spatiotemporal distribution of E/n was multiplied by the number gas density and the electric-field strength distribution was obtained, as is shown in Fig. 4. The electric-field evolution in the close vicinity of the cathode is shown in Fig. 4. At the coordinates x = 90 μm and t = 14 ns one can trace the ignition of the positive streamer with an electric-field strength of about 8 × 106 V/m, rapidly increasing to 88 × 106 V/m at the streamer impact. At approximately the same time, at x = 120 μm the negative

streamer with an electric-field strength of approximately 13 × 106 V/m propagates towards the anode. The values of the reduced electric-field strength in the cathode layer created by the streamer arrival are in good agreement with the simulations of Odrobina et al. [5] and Braun et al. [38]. In order to better understand the ignition of the streamers in the TP we adjusted our setup to record the emission far preceding the TP. SPS emission data obtained with a cathode of 520-μm curvature and a voltage of 9 kV are shown in Fig. 5. In such conditions the weak emission of the SPS was detectable even 800 ns before the positive-streamer start. Just 200 ns before the TP leading edge, the detected SPS signal started to increase exponentially. In this setup the long-lasting emission has its center 300 μm in front of the cathode. The observed ionization processes leading to the positive space-charge accumulation in front of the cathode and for the creation of the so-called plasma zone [39] have a long duration, which is orders of magnitude longer than the TP itself and can be attributed to a Townsend discharge with the light density distribution corresponding to the Laplacian field [39,40]. In summary, therefore, the characteristics of the cathodedirected ionizing wave illustrated in Fig. 3, as well as the measured spatiotemporal development of the electric field shown in Fig. 4, persuasively indicate that the ionization processes leading to the fast current rise to the TP maximum are associated with the formation of a positive streamer in the immediate vicinity of the cathode. It is important to say that this fact is not considered in a great majority of recent computer

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FIG. 5. (Color) SPS signal recording preceding the TP.

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simulation studies (see, for example, Refs. [7,11,14,15]). As shown in Fig. 5, the positive-streamer onset was preceded by the formation of a few hundreds of micrometer thick cathode sheath and, consequently, the observed phenomenon can be envisaged as a positive-streamer breakdown inside the cathode sheath of a Townsend discharge. It is noteworthy that very recently a transient cathode spot formation due to the positive-streamer ignition in a narrow cathode sheath with a striking similarity to the results in Figs. 3 and 4 was revealed on the falling voltage slope of a pulsed dielectric barrier discharge in an atmospheric-pressure nitrogen-oxygen mixture [41]. In light of these our observations it is rather surprising that the occurrence of positive-streamer breakdowns or positive-streamer-like instabilities of the high-pressure cathode sheaths is largely neglected by workers in the field of gas discharges, except for only sporadic attention in the literature, for example, in relation to the breakdown of the cathode region of abnormal glow discharge formed in positive corona gaps [42,43] and TEA lasers [17,19,44]. Contrary to the commonly held belief, we suppose that such phenomena occur in many practical situations and their consideration offers the attractive feature of the theoretical unification of all streamer-initiated breakdown processes. As a first step to such unification we claim that the results presented here, taken

together with the discharge current measurements and analysis published in Refs. [21,24,43], and with unique studies [45,46], indicate that any streamer-initiated breakdown phenomenon in a discharge gap with a highly stressed cathode (“negative corona gap”) is always associated with the positive-streamer formation in the cathode surface vicinity. Subsequently, in line with the computer simulation results [17,44] and experimental observations [9,19,23] of the cathode sheath instabilities resulting in cathode spot formation in pulsed high-pressure gas discharges, we hypothesize that these phenomena can also be ascribed to positive-streamer breakdown phenomena that are very similar to those seen in Figs. 3 and 4. We believe that this Rapid Communication will provide the motivation and serve as a guide for further studies aimed at the development of a more consistent and simplified theory of streamer-initiated breakdown phenomena.

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The authors are grateful to Kirill V. Kozlov and HansErich Wagner for useful consultations. This work was partly supported by the Federal German Ministry of Education and Research (BMBF) within project InnoPlas FKZ 03FO1072 and by CZ.1.05/2.1.00/03.0086 funding of European Regional Development Fund.

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