Spark Initiation Research Articles

On the modes of nanosecond pulsed plasmas for combustion ignition of quiescent CH4-air mixtures

The effect of transient plasma modes on ignition kernel development are discussed here for a quiescent CH4-air combustion model system. A 10 ns high-voltage pulse was applied to a pin-to-pin electrode in lean fuel-air mixtures at room temperature and atmospheric pressure. High-impedance streamer, transient spark and low-impedance spark discharges were identified based on pulse waveforms of voltage and current. A sustained ignition kernel expansion was observed when the plasma discharge transitioned into a transient spark or spark discharge. The minimum ignition energy was obtained at the transient spark mode, which has less than a third of the energy or Coulomb transfer compared to the low-impedance spark. Employing repetitive 10-pulse sequence at 10 kHz, the lean-fuel limit was extended from an equivalence ratio of 0.6 for the single pulse ignition to 0.5. The use of repetitive pulses also allowed streamer breakdown or spark initiation to occur at a lower voltage.

The Formation of a Flame Front in a Hydrogen–Air Mixture during Spark Ignition in a Semi-Open Channel with a Porous Coating

An experimental study of ignition and flame front propagation during spark initiation in a hydrogen–air mixture in a semi-open channel with a porous coating is reported. The bottom surface of the channel was covered with a porous layer made of porous polyurethane or steel wool. The measurements were carried out for a stoichiometric mixture (equivalence ratio ER = 1.0) and for a lean mixture (ER = 0.4) of hydrogen with air, where ER is the molar excess of hydrogen. The flame front was recorded with a high-speed camera using the shadow method. Depending on the pore size, the velocity of the flame front and the sizes of disturbances generated on the surface of the flame front were determined. Qualitative features of the deflagration flame front at ER = 0.4, consisting of disturbances resembling small balls of flame, were discovered. The sizes of these disturbances significantly exceed the analytical values for the Darrieus–Landau instability. The effect of coatings made of porous polyurethane or steel wool is compared with the results obtained for an empty smooth channel. Depending on the hydrogen concentration in the hydrogen–air mixture, the velocity of the flame front compared to a smooth channel was three times higher when the channel was covered with steel wool and five times higher when the channel was covered with porous polyurethane.

Increasing SERCA function promotes initiation of calcium sparks and breakup of calcium waves.

Increasing sarcoplasmic/endoplasmic reticulum calcium ATPase (SERCA) pump activity enhances sarcoplasmic reticulum calcium (Ca) load, which increases both ryanodine receptor opening and driving force of Ca release flux. Both of these effects promote Ca spark formation and wave propagation. However, increasing SERCA activity also accelerates local cytosolic Ca decay as the wave front travels to the next cluster, which limits wave propagation. As a result, increasing SERCA pump activity has a biphasic effect on the propensity of arrhythmogenic Ca waves, but a monotonic effect to increase Ca spark frequency and amplitude. Waves of sarcoplasmic reticulum (SR) calcium (Ca) release can cause arrhythmogenic afterdepolarizations in cardiac myocytes. Ca waves propagate when Ca sparks at one Ca release unit (CRU) recruit new Ca sparks in neighbouring CRUs. Under normal conditions, Ca sparks are too small to recruit neighbouring Ca sparks where Ca sensitivity is also low. However, under pathological conditions such as a Ca overload or ryanodine receptor (RyR) sensitization, Ca sparks can be larger and propagate more readily as macro-sparks or full Ca waves. Increasing SERCA pump activity promotes SR Ca load, which promotes RyR opening and increases driving force of the Ca release flux from SR to cytosol, promoting Ca waves. However, high sarcoplasmic/endoplasmic reticulum calcium ATPase (SERCA) activity can also decrease local cytosolic [Ca] as it approaches the next CRU, thereby reducing wave appearance and propagation. In this study, we use a physiologically detailed model of subcellular Ca cycling and experiments in phospholamban-knockout mice, to show how Ca waves are initiated and propagate and how different conditions contribute to the generation and propagation of Ca waves. We show that reducing diffusive coupling between Ca sparks by increasing SERCA activity prevents Ca waves by reducing [Ca] at the next CRU, as do Ca buffers, low intra-SR Ca diffusion and distance between CRUs. Increasing SR Ca uptake rate has a biphasic effect on Ca wave propagation; initially it enhances Ca spark probability and amplitude and CRU coupling, thereby promoting arrhythmogenic Ca wave propagation, but at higher levels SR Ca uptake can abort those arrhythmogenic Ca waves.

Investigation on cutting of thin carbon fiber-reinforced polymer composite plate using sandwich electrode-assisted wire electrical-discharge machining

This paper presents the experimental investigation on cutting of thin carbon fiber-reinforced polymer (CFRP) composite plate by wire electrical-discharge machining (WEDM) with the aid of sandwich assisting-electrodes. The difficulties such as incomplete cut and deviation in machining path during WEDM of CFRP were avoided by using metal plates (H13 steel) as assisting-electrodes. The spark initiation during WEDM of CFRP is difficult without exposing the carbon fiber as fibers are embedded into nonconductive polymer in CFRP. Thus, in this work, assisting-electrode was used to initiate the sparking without changing the surface integrity of the CFRP. The one-factor-at-a-time analysis was applied to study the effect of input parameters namely input current (2, 4, 6, 8, 10, and 12 A), pulse on time (10, 20, 30, 40, 50, and 60 µs), pulse off time (10, 20, 30, 40, 50, and 60 µs), and voltage (70 and 90 V) on the cutting time and the machined surface morphology. A decreasing trend was observed for cutting time with an increase in the current. Whereas, the cutting time was increased with an increase in the pulse off time. It was also observed that the cutting time initially increased with the pulse on time (10 to 30 µs) and then started decreasing with a further increase in the pulse on time (40 to 60 µs). The cutting time was significantly reduced at a higher level of voltage (90 V) when compared one-on-one with lower voltage level (70 V). In this study, microscopic analysis of the surface morphology was also extensively investigated which was not investigated earlier. The investigation showed damages such as breakage of carbon fibers, fiber-matrix debonding, and matrix cracking during WEDM of CFRP using sandwich assisting-electrode.

Features of haloalkane effect on the concentration limits and induction time for the ignition of methane–oxygen mixtures

A strong difference in the character of admixture effect on ignition by shock wave and spark initiation has been revealed using the haloalkane effect on the ignition of methane–oxygen mixtures as an example. It has been shown that the difference is determined by the presence of considerable concentrations of reactive intermediate species in an initial mixture, the qualitative difference in gas heating modes, and the strong difference between the temperature ranges of the process for two these methods.

Surface and porous recast layer analysis in µ-EDM of MWCNT-Al2O3 composites

ABSTRACTMachining of ceramic materials has been a major challenge owing to high hardness and brittleness. The reinforcement of a conducting filler allows permissible machining in electrical discharge machining (EDM) process. The current effort analyses the impact of multi-walled carbon nanotubes (MWCNT) of concentrations of 2.5 and 5 vol. %, as conducting filler towards machinability of alumina composites in µ-EDM process. The influence of tool materials and its rotation are closely analyzed. A successful machining process is observed in both the two composites, with a higher material removal rate (MRR) in 5 vol. % MWCNTs. When the tool starts to rotate at 750 rpm, an increment of around 60–65% is observed in MRR for both the two composites. Similarly, the surface roughness (Ra) decreases by a factor of 20−25%. The brass tool is observed to yield better machining capabilities due to the frequent initiation of sparks. A highly porous machined surface is observed in both the two composites. This scenario depicts the spalling effect as more dominant than melting-evaporation effect. The extent of porous recast layer on the drilled edges is found to reduce with increasing the speed of tool rotation.

Size Matters: Ryanodine Receptor Cluster Size Heterogeneity Potentiates Calcium Waves

Ryanodine receptors (RyRs) mediate calcium (Ca)-induced Ca release and intracellular Ca homeostasis. In a cardiac myocyte, RyRs group into clusters of variable size from a few to several hundred RyRs, creating a spatially nonuniform intracellular distribution. It is unclear how heterogeneity of RyR cluster size alters spontaneous sarcoplasmic reticulum (SR) Ca releases (Ca sparks) and arrhythmogenic Ca waves. Here, we tested the impact of heterogeneous RyR cluster size on the initiation of Ca waves. Experimentally, we measured RyR cluster sizes at Ca spark sites in rat ventricular myocytes and further tested functional impacts using a physiologically detailed computational model with spatial and stochastic intracellular Ca dynamics. We found that the spark frequency and amplitude increase nonlinearly with the size of RyR clusters. Larger RyR clusters have lower SR Ca release threshold for local Ca spark initiation and exhibit steeper SR Ca release versus SR Ca load relationship. However, larger RyR clusters tend to lower SR Ca load because of the higher Ca leak rate. Conversely, smaller clusters have a higher threshold and a lower leak, which tends to increase SR Ca load. At the myocyte level, homogeneously large or small RyR clusters limit Ca waves (because of low load for large clusters but low excitability for small clusters). Mixtures of large and small RyR clusters potentiates Ca waves because the enhanced SR Ca load driven by smaller clusters enables Ca wave initiation and propagation from larger RyR clusters. Our study suggests that a spatially heterogeneous distribution of RyR cluster size under pathological conditions may potentiate Ca waves and thus afterdepolarizations and triggered arrhythmias.

Late Ca2+ Sparks and Ripples During the Systolic Ca2+ Transient in Heart Muscle Cells.

The development of a refractory period for Ca2+ spark initiation after Ca2+ release in cardiac myocytes should inhibit further Ca2+ release during the action potential plateau. However, Ca2+ release sites that did not initially activate or which have prematurely recovered from refractoriness might release Ca2+ later during the action potential and alter the cell-wide Ca2+ transient. To investigate the possibility of late Ca2+ spark (LCS) activity in intact isolated cardiac myocytes using fast confocal line scanning with improved confocality and signal to noise. We recorded Ca2+ transients from cardiac ventricular myocytes isolated from rabbit hearts. Action potentials were produced by electric stimulation, and rapid solution changes were used to modify the L-type Ca2+ current. After the upstroke of the Ca2+ transient, LCSs were detected which had increased amplitude compared with diastolic Ca2+ sparks. LCS are triggered by both L-type Ca2+ channel activity during the action potential plateau, as well as by the increase of cytosolic Ca2+ associated with the Ca2+ transient itself. Importantly, a mismatch between sarcoplasmic reticulum load and L-type Ca2+ trigger can increase the number of LCS. The likelihood of triggering an LCS also depends on recovery from refractoriness that appears after prior activation. Consequences of LCS include a reduced rate of decline of the Ca2+ transient and, if frequent, formation of microscopic propagating Ca2+ release events (Ca2+ ripples). Ca2+ ripples resemble Ca2+ waves in terms of local propagation velocity but spread for only a short distance because of limited regeneration. These new types of Ca2+ signaling behavior extend our understanding of Ca2+-mediated signaling. LCS may provide an arrhythmogenic substrate by slowing the Ca2+ transient decline, as well as by amplifying maintained Ca2+ current effects on intracellular Ca2+ and consequently Na+/Ca2+ exchange current.

Corrosion resistance in artificial saliva of titanium anodized by plasma electrolytic oxidation in Na3PO4

Abstract In order to improve the chemical and electrochemical resistance of titanium as well as its potential bioactivity, coatings were formed by using plasma electrolytic oxidation under galvanostatic conditions in a phosphate containing electrolyte. The grown anodized layers were characterized at different stages of the oxidation process, corresponding to different voltages. The structure and composition of the coatings were investigated by XRD, SEM-EDS and μ-Raman spectroscopy. The electrochemical behaviour of the coated materials was evaluated in acidified artificial saliva by using classical stationary methods and electrochemical impedance spectroscopy. Before the initiation of sparks, an inner layer is formed by a classical anodizing mechanism. This layer plays the role of barrier, improving the corrosion resistance of titanium in artificial saliva. As soon as the sparking phenomenon starts, a more compact overlayer grows. Due to the presence of large cracks, the corrosion resistance is no more improved.

On the Adjacency Matrix of RyR2 Cluster Structures.

In the heart, electrical stimulation of cardiac myocytes increases the open probability of sarcolemmal voltage-sensitive Ca2+ channels and flux of Ca2+ into the cells. This increases Ca2+ binding to ligand-gated channels known as ryanodine receptors (RyR2). Their openings cause cell-wide release of Ca2+, which in turn causes muscle contraction and the generation of the mechanical force required to pump blood. In resting myocytes, RyR2s can also open spontaneously giving rise to spatially-confined Ca2+ release events known as “sparks.” RyR2s are organized in a lattice to form clusters in the junctional sarcoplasmic reticulum membrane. Our recent work has shown that the spatial arrangement of RyR2s within clusters strongly influences the frequency of Ca2+ sparks. We showed that the probability of a Ca2+ spark occurring when a single RyR2 in the cluster opens spontaneously can be predicted from the precise spatial arrangements of the RyR2s. Thus, “function” follows from “structure.” This probability is related to the maximum eigenvalue (λ 1) of the adjacency matrix of the RyR2 cluster lattice. In this work, we develop a theoretical framework for understanding this relationship. We present a stochastic contact network model of the Ca2+ spark initiation process. We show that λ 1 determines a stability threshold for the formation of Ca2+ sparks in terms of the RyR2 gating transition rates. We recapitulate these results by applying the model to realistic RyR2 cluster structures informed by super-resolution stimulated emission depletion (STED) microscopy. Eigendecomposition of the linearized mean-field contact network model reveals functional subdomains within RyR2 clusters with distinct sensitivities to Ca2+. This work provides novel perspectives on the cardiac Ca2+ release process and a general method for inferring the functional properties of transmembrane receptor clusters from their structure.

Calcium Sparks in the Heart: Dynamics and Regulation.

Calcium (Ca2+) plays a central role in the contraction of the heart. It is the bi-directional link between electrical excitation of the heart and contraction. Electrical excitation initiates Ca2+influx across the sarcolemma and T-tubular membrane that triggered calcium release from the sarcoplasmic reticulum. Ca2+sparks are the elementary events of calcium release from the sarcoplasmic reticulum. Therefore, understanding the dynamics of Ca2+sparks is essential for understanding the function of the heart. To this end, numerous experimental and computational studies have focused on this topic, exploring the mechanisms of calcium spark initiation, termination, and regulation and what role these play in normal and patho-physiology. The proper understanding of Ca2+ spark regulation and dynamics serves as the foundation for our insights into a multitude of pathological conditions may develop that can be the result of structural and/or functional changes at the cellular or subcellular level. Computational modeling of Ca2+ spark dynamics has proven to be a useful tool to understand Ca2+ spark dynamics. This review addresses our current understanding of Ca2+ sparks and how synchronized SR Ca2+ release, in which Ca2+ sparks is a major pathway, is linked to the different cardiac diseases, especially arrhythmias.

Laser ignition in internal-combustion engines: Sparkless initiation

Laser ignition has been implemented in a single-cylinder internal combustion engine fueled by gasoline. Indicator diagrams (cylinder pressure versus crank angle) were obtained for laser ignition with nano- and microsecond pulses of an Nd:YAG laser. The maximum power of microsecond pulses was below critical for spark initiation, while the radiation wavelength was outside the spectral range of optical absorption by hydrocarbon fuels. Apparently, the ignition starts due to radiation absorption by the oil residues or carbon deposit in the combustion chamber, so that the ability of engine to operate is retained. This initiation of spark-free ignition shows the possibility of using compact semiconductor quantum-cascade lasers operating at wavelengths of about 3.4 μm (for which the optical absorption by fuel mixtures is high) in ignition systems of internal combustion engines.

Initiation of detonation of fuel-air mixtures in a flow-type annular combustor

Initiation of detonation in a fuel-air mixture flow formed in an annular cylindrical combustor 306 mm in diameter is studied. The source of detonation initiation is the detonation wave entering the annular channel from a plane-radial vortex chamber, a jet of products, or a low-power heat pulse. It is demonstrated that continuous spin detonation (CSD) can be ensured by all these methods. Its formation is accompanied by a transitional process with a duration up to 10 ms, which is associated with violation of injection of the species (initiation by the detonation wave) or with the time of evolution of tangential instability in CSD (jet or spark initiation). Transfer of detonation to a flow of fuel-air mixtures with low chemical activity (propane-air, methane-air, kerosene-air, and gasoline-air mixtures) by the initiating detonation wave formed within fractions of a millisecond by a low-energy pulse or as a result of self-ignition of the hydrogen-air mixture in the plane-radial vortex chamber is realized. It is found that organization of CSD in these mixtures requires combustors with greater (than 306 mm) diameters. A possibility of CSD in kerosene-air and gasoline-air mixtures with low chemical activity by means of air enrichment by oxygen ahead of the combustor entrance is demonstrated.

Dynamics of Calcium Sparks and SR Calcium Leak During Excitation-Contraction Coupling in Mouse Heart Cells

Stable calcium-induced calcium release (CICR) is critical for maintaining normal cell contraction during cardiac excitation-contraction (EC) coupling in heart cells. The fundamental element of CICR in heart is the calcium (Ca2+) spark which arises from the regenerative release of Ca2+ from a cluster of ryanodine receptors (RyR2) in the junctional sarcoplasmic reticulum membrane. We have shown how stochastic gating of RyR2s could produce an SR Ca2+ leak capable of balancing SR Ca2+-ATPase (SERCA2a) activity under quiescent conditions (Williams et al. BJ 2011). This investigation suggested the surprising finding that a single, or even multiple, RyR2 openings could fail probabilistically to trigger a Ca2+ spark. To further investigate this effect, we expanded upon that formulation to create a detailed, local control model of EC coupling in mouse heart. A number of features were added or modified, including the addition of a novel seven-state Markov chain model of the sarcolemmal L-type Ca2+ channel (LCC). This model features dynamic action-potential (AP) generation, robust Ca2+ spark initiation and termination, realistic [Ca2+]i transients, and true SR Ca2+ pump/leak balance. The model suggests that numerous LCC openings are often required to trigger a single Ca2+ spark. This is consistent with our prior work where multiple RyR2 openings were needed to trigger a spontaneous Ca2+ spark during quiescent conditions. We also investigated how RyR2 mutations associated with catecholaminergic polymorphic ventricular tachycardia (CPVT) influence the dynamics of Ca2+ sparks, “invisible” non-spark Ca2+ leak, [Ca2+]i transients, and SR Ca2+ content. We observe that CPVT mutations can lead to unstable Ca2+ spark dynamics, altering SR Ca2+ content and promoting [Ca2+]i signaling instability. Our new model provides significant insights into the dynamics of local control of CICR under physiological and pathological conditions.

Influence of an acoustic resonator on flame propagation regimes in spark initiated H2 combustion in a cylindrical reactor near the lower detonation limit

It is experimentally shown that an acoustic resonator like Helmholtz's resonator connected with a cylindrical reactor can provide a significant flame acceleration under spark initiation in lean (15%) hydrogen–oxygen mixtures close to the lower detonation limit.

Control of Sarcoplasmic Reticulum Ca2+ Release by Stochastic RyR Gating within a 3D Model of the Cardiac Dyad and Importance of Induction Decay for CICR Termination

The factors responsible for the regulation of regenerative calcium-induced calcium release (CICR) during Ca2+ spark evolution remain unclear. Cardiac ryanodine receptor (RyR) gating in rats and sheep was recorded at physiological Ca2+, Mg2+, and ATP levels and incorporated into a 3D model of the cardiac dyad, which reproduced the time course of Ca2+ sparks, Ca2+ blinks, and Ca2+ spark restitution. The termination of CICR by induction decay in the model principally arose from the steep Ca2+ dependence of RyR closed time, with the measured sarcoplasmic reticulum (SR) lumen Ca2+ dependence of RyR gating making almost no contribution. The start of CICR termination was strongly dependent on the extent of local depletion of junctional SR Ca2+, as well as the time course of local Ca2+ gradients within the junctional space. Reducing the dimensions of the dyad junction reduced Ca2+ spark amplitude by reducing the strength of regenerative feedback within CICR. A refractory period for Ca2+ spark initiation and subsequent Ca2+ spark amplitude restitution arose from 1), the extent to which the regenerative phase of CICR can be supported by the partially depleted junctional SR, and 2), the availability of releasable Ca2+ in the junctional SR. The physical organization of RyRs within the junctional space had minimal effects on Ca2+ spark amplitude when more than nine RyRs were present. Spark amplitude had a nonlinear dependence on RyR single-channel Ca2+ flux, and was approximately halved by reducing the flux from 0.6 to 0.2 pA. Although rat and sheep RyRs had quite different Ca2+ sensitivities, Ca2+ spark amplitude was hardly affected. This suggests that moderate changes in RyR gating by second-messenger systems will principally alter the spatiotemporal properties of SR release, with smaller effects on the amount released.

Interaction of Spherical Flames of Hydrogen-Air and Methane-Air Mixtures in the Closed Reactor at the Central Spark Initiation with Closed Meshed Obstacles

It is shown that spark initiated flames of lean hydrogen-air mixtures (8%-15% Н2) pass through close-meshed aluminum spherical obstacles with the cell size 0.04-0.1 mm2; the flame of 15% Н2 in air after an obstacle is accelerated; acoustic gas fluctuations occur in the reactor. The flame of 7.5% hydrogen-air mixture does not propagate through the obstacles the flame of 8% natural gas-air mixture is not accelerated after an obstacle; acoustic fluctuations are missing. It is shown that active centers of methane and hydrogen combustion, determining flame propagation, have different chemical nature.

Spark Characteristics Investigation of a Gas Turbine Igniter

A spark-induced hot gas jet of a gas turbine combustor igniter has been investigated using high-speed schlieren, stereo, and stereoscopic shadowgraph imaging visualization techniques. The schlieren images show that the spark-induced local high pressure generates a spherical shockwave. The energy released by the spark initiation combines with the igniter tip geometry to produce a hot gas jet. The hot gas front velocity was obtained from the high-speed schlieren images. The results have shown that the input voltage does not have much effect on the propagation speed of the hot gas front. It was observed that each spark had caused the erosion of some melted tiny metal bits flying off the igniter tip. The 3D velocity vectors of the flying off metal bits are calculated by a stereo reconstruction and evaluation algorithm. It has been found that the amount and velocity distributions of the eroded metal bits are very different even at a fixed input voltage to the igniter, which contrasts with the quite consistent hot gas jet development. The 3D structures of the interaction boundary between hot gas and ambient air are reconstructed for the first time using a stereoscopic shadowgraph technique.

Thermite Initiation Processes and Thresholds

ABSTRACTThe objectives of this work are to characterize thermite initiation processes and thresholds, and to develop thermite reactive trains, where a sensitive nanothermite ignites an insensitive micron thermite, which produces little gas. Nanothermites, including Al/AgIO3, Al/Bi2O3, Al/MoO3, Al/Fe3O4, and Ti/AgIO3, were characterized for their ignition behavior by spark and resistive heating. Energies for spark and thermal initiation were as low as 9 and 140 μJ, respectively. Thermal initiation results were consistent with local temperature as the main controlling factor. The propagation rate of the Al/Fe3O4 nanothermite was about 100X slower than that of the other nanothermites. This low reactivity is attributed to the high volatilization temperature and high melting point of the oxidizer. Mixing of 90% Al/Fe3O4 nanothermite with 10% of a more sensitive, high-gas-producing nanothermite gave materials with the same sensitivity as the sensitive nanothermite. Thus, the mixture provides a safer sensitive nanothermite. Thermites with micron-scale ingredients were pressed into pellets and ignited with small amounts of nanothermite. Gas production of micron thermite compositions was reduced by adding the intermetallic composite, Ti/2B, or excess iron. In both cases, a single hot mass was produced, while the pure micron Al/Fe2O3 produced a dispersion of particles.

Nanosecond repetitively pulsed discharges in air at atmospheric pressure—the spark regime

Nanosecond repetitively pulsed (NRP) spark discharges have been studied in atmospheric pressure air preheated to 1000 K. Measurements of spark initiation and stability, plasma dynamics, gas temperature and current–voltage characteristics of the spark regime are presented. Using 10 ns pulses applied repetitively at 30 kHz, we find that 2–400 pulses are required to initiate the spark, depending on the applied voltage. Furthermore, about 30–50 pulses are required for the spark discharge to reach steady state, following initiation. Based on space- and time-resolved optical emission spectroscopy, the spark discharge in steady state is found to ignite homogeneously in the discharge gap, without evidence of an initial streamer. Using measured emission from the N2 (C–B) 0–0 band, it is found that the gas temperature rises by several thousand Kelvin in the span of about 30 ns following the application of the high-voltage pulse. Current–voltage measurements show that up to 20–40 A of conduction current is generated, which corresponds to an electron number density of up to 1015 cm−3 towards the end of the high-voltage pulse. The discharge dynamics, gas temperature and electron number density are consistent with a streamer-less spark that develops homogeneously through avalanche ionization in volume. This occurs because the pre-ionization electron number density of about 1011 cm−3 produced by the high frequency train of pulses is above the critical density for streamer-less discharge development, which is shown to be about 108 cm−3.