A brief review of the problem of lightning initiation and a hypothesis of initial lightning leader formation

2.1. Branching Positive Streamer System

[7] The fundamental mechanism of dielectric breakdown in a gas is the electron avalanche. In a gas of number density N subject to an electric field E, free electrons are accelerated, and if E is sufficiently strong, cause a net increase in free electrons by impact ionization of neutral gas particles. A net ionization coefficient α′ can be defined as

where α and η are functions of E/N and represent production and removal, respectively, of free electrons per unit distance along a path s parallel to E. The number of free electrons N_e changes along s according to

Integration of equation (2) over the distance Δs (= s_f − s_o) parallel to E yields

For α′ > 0, N_e increases exponentially with distance forming an “avalanche” of electrons. In air α′ = 0 at E/N ≈ 1.24 × 10⁻¹⁹ V·m² [Bazelyan and Raizer, 1998], yielding a threshold breakdown value or “dielectric strength” of E_b = 3 MV·m⁻¹ for air at STP.

[8] Localized regions of strong E near highly curved electrodes can result in localized discharges called “coronas”. In a corona discharge, free electrons that are accelerated by E in the region where α′ > 0 yield electron avalanches. For the anodic case in air, the avalanching electrons are quickly collected by the anode, leaving behind a relatively immobile positive space charge around the anode that alters the local electric field. If electron avalanches occur uniformly across the anode surface, the resultant positive space charge tends to be smoothly distributed causing an overall reduction of electric field strength near the anode. If, however, a local nonuniformity of positive space charge develops, a localized region of intensified electric field will exist around it (Figure 1). New electron avalanches that develop in this intensified electric field will expose more positive space charge, effectively extending the positive space charge region into the electrode gap. If the background electric field in the electrode gap is strong enough, the positive space charge region can continue to extend into the electrode gap.

[9] An anodic discharge that continues to propagate in the manner described above is called a “positive streamer” [Meek, 1940]. Dawson and Winn [1965] modeled a positive streamer as an electrically isolated volume of positive space charge tailed by a net-neutral plasma tail of negligible conductivity. They estimated the net positive charge and density required for propagation to be around 10⁸ positive ions concentrated in a sphere of 30 μm radius. Phelps and Griffiths [1976] described the streamer plasma tail as initially conductive, becoming rapidly nonconductive due to attachment and recombination processes. Effective conductive lengths of the plasma tail were estimated to be on the order of centimeters. Allen and Mikropoulos [1999] empirically determined the minimum electric field necessary for the stable propagation of a positive streamer in air, or the “stability field”(E_st), as

where h is the absolute humidity in grams per cubic meter and δ is the ratio of the local air density to the density of air at STP. For a standard atmosphere at water saturation and an altitude of 5 km, δ ≈ 0.74 and h ≈ 1.6 g/m³ yielding E_st ≈ 330 kV/m. They also empirically determined positive streamer velocities v_str in ambient electric fields E_a as

where E_a is greater than E_st.

[10] Just as electric charge has two polarities, so does the streamer discharge. Cathodic streamer discharges, called negative streamers, are very similar to positive streamers, with the primary difference being the orientation of the electron avalanches relative to the streamer head. In the case of positive streamers the electron avalanches are directed toward the streamer head, while for negative streamers they are directed outward. The electric field required to sustain negative streamers is about twice that of positive streamers due to the self-diffusing nature of the discharge [Bazelyan and Raizer, 1998]. Because of this larger electric field requirement, negative streamers are much less likely to occur than are positive streamers given the same conditions. This asymmetry between positive and negative streamers leads to the favoring of positive streamers as the most likely streamer discharge in weak thundercloud electric fields.

[11] Phelps [1974] studied the behavior of positive streamers when subjected to electric fields in excess of E_st, and found that they increase in positive charge and radius with distance and deposit negative charge in their wake equal to the positive charge gained. Phelps constructed a simple analytical model describing a system of intensifying and branching streamers by extending the streamer model of Dawson and Winn [1965] where a streamer is represented as a propagating compact volume of positive space charge (the “tip”) followed by a tail of negligibly conducting plasma. For a single positive streamer propagating in the direction s of the ambient electric field E_a, the streamer energy budget is formulated as

where q is the net positive charge carried in the streamer tip, u is the potential energy stored in the streamer tip, E_a is the ambient electric field strength, and E_st is the electric field strength required for stable propagation of positive streamers (the “stability” field). This model is extended to a system of N intensifying and branching positive streamers, each streamer characterized by a potential energy 〈u〉 and a tip charge 〈q〉, propagating in the direction of E. For simplicity, a static equilibrium is assumed between continuous growth of individual streamers (increasing 〈u〉 and 〈q〉) and streamer branching (decreasing 〈u〉 and 〈q〉), allowing 〈u〉 and 〈q〉 to be formulated as constants. A further simplifying assumption is made that assumes the electrostatic potential energy between the positively charged streamer tips and the deposited negative charge to be negligible in comparison to the potential energy stored in the streamer tips. Under these simplifying assumptions, the total streamer system potential energy can be defined as U = N〈u〉 and the total streamer system charge as Q = N〈q〉, yielding the final energy budget equation:

Substituting U = (〈u〉/〈q〉)Q, rearranging and integrating over a distance Δs = s_f − s_o yields

where Q_o and Q_f are the initial and final charges of the system “front”. It can be seen that when E_a > E_st, Q increases exponentially with distance. Since the individual positive streamers are assumed to have a constant charge 〈q〉, the exponential growth of Q is manifest as an exponential increase in the number N of positive streamers comprising the streamer system. More interestingly, charge conservation requires that a quantity of negative charge is deposited in the wake of the system with the total charge equal to the quantity −(Q − Q_o).

[12] Griffiths and Phelps [1976] formulated a discrete approximation to this model as a basis for a computer simulation, including a potential energy term to account for the electrostatic interaction of the positively charged streamer tips and the deposited negative space charge. A schematic of their discretized model is shown in Figure 2, showing a conical geometry characterized by a forward stepwise propagation of a growing disk-shaped streamer front and the deposition of negatively charged disks in the passed cone volume. In this computer simulation, an additional feature is added whereby multiple streamer systems are propagated through the same volume in a serial fashion. Each streamer system passage alters the local electric field environment due to the associated charge separation, setting the stage for the next streamer system pass. This feature allows for investigation of the cumulative effect of multiple streamer systems on the overall electric field, especially at the streamer system origin. Results from their model runs yielded two results of interest:

[13] 1. After the passage of a small number of streamer systems, typically less than 10, an order-of-magnitude intensification of the electric field is generated near the streamer system origin over a distance scale of a few meters.

[14] 2. The majority of streamer system intensification occurs over the first few meters of development, along with the associated electric field intensification.

[15] The first result suggests that a sequence of positive streamer systems propagating through the same volume can significantly intensify the electric field over a region spanning a few meters, perhaps to the level of direct dielectric breakdown. The second result suggests that the size scale across which this mechanism operates may be on the order of tens of meters or less, requiring that such regions of high ambient electric field may be quite compact. One of the primary concerns with this mechanism is the fact that the streamer stability field as given by equation (5) appears to be about a factor of two larger than observed peak thundercloud electric fields for a given altitude. It may be the case that the necessary regions of high electric field do exist by ordinary means but, due to being compact, have simply eluded observation. It may also be that such regions are rapidly created by the more exotic discharge mechanism known as runaway breakdown.

2.2. Runaway Breakdown

[16] When a free electron moves through a material medium such as a gas, it undergoes elastic and inelastic collisions that result in an effective frictional force. A graph of this frictional force as a function of electron kinetic energy K is given in Figure 3. Up to electron energies of about 0.1 keV, this frictional force is a rapidly increasing function of electron energy. An electron in this energy regime that is subject to an electric field less than E_c will remain in this regime, continually gaining energy from the electric field and losing it due to collisions. However, between about 0.1 keV and 1 MeV, the frictional force is a decreasing function of electron energy. In this energy regime, if the force on the electron due to the electric field is greater than the frictional force due to collisions, the electron will gain energy and accelerate. Such an electron will continue to gain energy and accelerate as long as it exists in the state where the energy gained from the electric field is larger than the energy lost due to friction. As the electron approaches relativistic energies, the friction once again becomes an increasing function of electron energy and the electron eventually reaches equilibrium where energy gained from the electric field is equal to energy lost due to friction. These electrons are termed “runaway” electrons, and are characterized by relativistic energies on the order of 1 MeV. C.T.R Wilson [1924, 1925] first suggested that energetic electrons in Earth’s atmosphere could become runaways under the influence of a strong thundercloud electric field, and that they could generate additional runaway electrons via ionizing collisions with neutrals. Gurevich et al. [1992] suggested that runaway electrons could precipitate a runaway avalanche and that if seeded in the optimal location in a thundercloud by a highly energetic cosmic ray shower, could result in a significant electrical breakdown of the thundercloud environment. They termed this discharge “runaway breakdown” to set it apart from the ordinary types of electrical breakdown that are characterized by low-energy electron avalanches. In addition, they suggested that runaway breakdown may be a crucial process in the initiation of lightning.

[17] The population of energetic (MeV) electrons in a runaway avalanche can be characterized as:

where L is the length traversed by the runaway avalanche, λ is the characteristic avalanche length, N_o is the initial quantity of runaway electrons and N_re is the final quantity of runaway electrons. On the basis of computer simulations, Dwyer [2003] has estimated λ as

and E_rb, the minimum electric field necessary to support a runaway avalanche, as

where δ is the ratio of the local air density to the density of air at STP. The values of E_rb given by equation (11) are comparable to the maximum observed thundercloud electric fields [Marshall et al., 1995, 2005], suggesting that runaway breakdown may be an important form of electrical breakdown in thunderclouds. However, the values of λ given by equation (10) are on the order of tens of meters or more for the strongest observed thundercloud electric fields, suggesting that runaway avalanches require distances on the order of a kilometer for a significant increase in runaway electrons.

[18] An important feature of runaway breakdown is the generation of large quantities of low energy (<100 eV) electrons produced in the discharge wake by inelastic collisions of runaways with neutrals. Gurevich et al. [2002] has estimated that the ionization of air by a runaway electron ranges from 30 to 50 ions per centimeter of travel under typical atmospheric conditions. These ions form a nonLTE (local thermodynamic equilibrium) plasma that is characterized by rapid electron attachment with characteristic attachment times on the order of 10⁻⁷ s [Gallimberti, 1979]. During this short free-electron lifetime, polarization of the plasma may be induced by the thundercloud electric field as illustrated in Figure 4. Gurevich et al. [1999], and Gurevich and Zybin [2001] have suggested that a large runaway discharge, initiated by a powerful cosmic ray shower (K > 10¹⁵ eV), could result in polarization of this plasma sufficient to induce a significant local intensification of the electric field at the plasma extremities. It is further suggested that the core of this plasma could be polarized sufficiently to mimic the structure of a streamer tip, perhaps then developing into a lightning leader. Dwyer [2005] has argued against this possibility, suggesting that the seed electrons produced by a cosmic ray shower should encompass a large lateral extent thereby producing a relatively diffuse runaway avalanche. Dwyer hypothesized another form of runaway breakdown, whereby positron and gamma ray feedback spread and sustain a runaway discharge event until collapsing the large-scale electric field to subrunaway strength. Dwyer's simulations suggest that a linearly compact but significant intensification of the electric field may form at the boundary of the discharge region, perhaps enough to support the “conventional” processes of lightning initiation.

2.3. Hybrid Scenario for Locally Intensifying the Thundercloud Electric Field

[19] Based on the outcome of the positive streamer system model of Griffiths and Phelps [1976], it appears that the positive streamer system mechanism is capable of boosting the electric field by up to an order of magnitude over a distance of a few meters. Such a boosting, however, requires an initial background electric field about 2 times larger than observed maximum electric fields. Even more important, a seed streamer must be provided in order to initiate the streamer system. The best candidate for the creation of a seed streamer is a corona streamer from a nearby hydrometeor.

[20] Since both the solid and liquid phases of water are electrically conductive, hydrometeors tend to polarize in electric fields causing enhancement of the electric field around their extremities. Observations have shown that, under the proper conditions, this local electric field enhancement is sufficient to support various corona processes, including positive streamers. Early studies of corona on hydrometeors focused on water drops, because of their presence in regions of known lightning development. When subject to strong electric fields, water drops are observed to deform into elongated shapes, with the elongated ends extending and disrupting into a spray of droplets. Richards and Dawson [1971] investigated corona on water drops of radius >2 mm that were falling through air at 1000 mb pressure while subject to positive vertical electric fields. They reported discharge threshold electric field values for positive corona to be around 950 kV·m⁻¹ for uncharged water drops and 550 kV·m⁻¹ for highly positively charged water drops. Griffiths and Latham [1972] investigated corona on water drops of radius 2.7 mm falling through air at 1000 mb and 500 mb pressure and subject to horizontal and positive vertical electric fields. At an air pressure of 1000 mb, threshold electric field values for positive corona on were around 900 kV·m⁻¹ for positive vertical electric fields and around 630 kV·m⁻¹ for horizontal electric fields. At an air pressure of 500 mb, field values changed to 550 kV·m⁻¹ for positive vertical electric fields and 690 kV·m⁻¹ for horizontal electric fields. Crabb and Latham [1974] investigated corona on pairs of colliding water drops in air pressure of 1000 mb and subject to electric fields, using drops of radius 2.7 mm and 0.65 mm that traveled toward each other at a velocity of 5.8 m·s⁻¹. The collisions were often observed to produce temporary elongations of the interacting drop pairs in the form of water filaments up to 20mm in length, with the longer water filaments resulting from more glancing collisions. Threshold electric field values for positive corona ranged from about 500 kV·m⁻¹ for water filaments of length 10 mm, down to about 200 kV·m⁻¹ for water filaments of length 20 mm. The measurements of Crabb et al. represent the lowest corona threshold values for known individual and interacting hydrometeors. Coronas from ice hydrometeors have been less extensively studied, with the most important work done by Griffiths and Latham [1974]. In their experiment, they studied various habits of ice hydrometeors with lengths ranging from 4 to 25 millimeters in length. They found that the electric field required for positive streamer emission for vapor-grown ice crystals ranged from 600–800 kV·m⁻¹ at sea level pressures down to about 400 kV·m⁻¹ at 500 mb. Hailstones provided only slightly lower electric field requirements, with a 25 mm long hailstone yielding threshold fields of 500 kV·m⁻¹ at 1000 mb down to about 360 kV·m⁻¹ at 500 mb. In one of their oft-quoted findings, they found that continuous corona currents could be induced on ice crystals only at temperatures above −18°C. This finding is often taken as evidence that ice crystals cannot contribute to streamer production at colder temperatures such as occur in the upper regions of thunderclouds. However, if we consider that a positive streamer system requires only a single seed streamer and that less than 10 systems may create an order-of-magnitude increase in the local electric field, it may only be necessary for an ice crystal to produce a small number of positive streamers to be viable for lightning initiation. A more recent study by Petersen et al. [2006] showed that individual positive streamers can indeed be generated from ice crystals at temperatures as low as −38°C, in contrast to the misunderstood result of Griffiths and Latham.

[21] Based on the available studies, it appears that the electric fields required for positive streamer generation on hydrometeors exceeds the electric fields required for the positive streamer mechanism of local electric field intensification hypothesized by Griffiths and Phelps [1976]. If we assume that a small population of hydrometeors is capable of going into corona at around 400–500 kV·m⁻¹, then it follows that the emerging seed streamer will immediately develop into an intensifying positive streamer system and possibly lead to a local intensification of the electric field.

[22] As is well known, observations of thundercloud electric fields suggest that no such strong electric fields exist in thunderclouds. It could well be that such regions do exist by ordinary means, and that they have simply eluded observation due to being quite compact. Alternatively, such regions may be formed by action of the runaway breakdown mechanism. Evidence in support of the runaway breakdown hypothesis includes, among other things, a close match between runaway breakdown electric fields and maximum observed thundercloud electric fields. Indeed, runaway breakdown may be one of many viable mechanisms for locally boosting the thundercloud electric fields.

[23] We propose a hybrid mechanism of local thundercloud electric field intensification that takes advantage of both runaway breakdown and hydrometeor-initiated positive streamer systems. This mechanism could equally well conform to the notion of preexisting yet undetected local pockets of strong electric field, with such regions replacing the role of runaway breakdown in the sequence. One scenario begins with an extensive cosmic ray shower seeding a runaway breakdown event that proceeds to generate a region of cool plasma in the high electric field region of the thundercloud. Before attachment renders the plasma nonconductive, the plasma polarizes and creates a local intensification of the electric field that reaches or exceeds the value required for coronas on nearby hydrometeors. A nearby hydrometeor then goes into corona, generating a single positive streamer. This streamer rapidly develop into a positive streamer system, quickly filling the newly formed high-field region of the polarized plasma and further intensifying the electric field near the streamer system origin (Figure 5). The positive feedback on the electric field at the streamer system origin leads to a continued succession of positive streamer systems, rapidly boosting the electric field near the streamer system origin. With the propagation velocity of positive streamers being around 10⁵ m·s⁻¹ and the length scale of interest being around 10 m, the timescale of this process would be on the order of a millisecond.

[24] Another scenario involving runaway breakdown involves the mechanism of Dwyer [2005]. In this case, when the background thundercloud electric field exceeds the runaway threshold, positive feedback on the runaway breakdown creates a forward-propagating region of intensified electric field at the runaway breakdown discharge front. Dwyer's simulation suggests that the electric field in this front can exceed 430 kV·m⁻¹ at around 7000 m above sea level, corresponding to around 1 MV·m⁻¹ at sea level pressure and about 500 kV·m⁻¹ at 500 mb. An important issue with this scenario is the speed with which the discharge front propagates. It is suggested that a well-developed discharge front may attain speeds up to about 10⁶ m·s⁻¹, with the region of electric field exceeding 500 kV·m⁻¹ at 500 mb having a linear extent of around 100 m. The local residence time in this field would be about 0.1 milliseconds, somewhat smaller in magnitude than the estimated time for development of hydrometeor-initiated positive streamer systems. However, it may be possible that this short duration is sufficient to support a brief burst of positive streamer activity that is itself sufficient to support further positive streamer system development and associated local electric field intensification well after the runaway discharge front has passed.

3.1. Positive Leader

[25] Various studies have characterized the initiation of positive and negative leaders from conducting electrodes [Gallimberti, 1979] as well as initiation of leaders from long (>1 m) conductors floating in electrode gaps [Castellani et al., 1998; Lalande et al., 2002]. Leaders, both in the laboratory and in nature (lightning), consist primarily of a channel of air that is electrically conductive due to thermally driven electron detachment and ionization processes. Laboratory investigations have indicated a minimum temperature for sustained electrical conductivity to be in the range of 1000–2000 K [Aleksandrov et al., 2001; Gallimberti et al., 2002]. The issue of importance in the formation of a leader is the means whereby the leader channel is heated and propagated forward. Figure 6 illustrates the anatomy of the active region of a typical positive laboratory leader. This region consists of the terminal end of the highly conductive leader channel, the growing tip of this channel, and the surrounding streamer zone. Because of the high conductivity of the conductive leader channel, it acts as an anode and generates a very intense electric field ahead of the tip. This intense electric field exceeds the dielectric strength of air near the tip, resulting in the formation of positive streamers that rapidly propagate away from the tip over a distance of a few meters. As the streamers exit the tip, they produce a concentrated current in and around the tip that further heats the tip and propagates it forward. The quantity of streamers necessary for continued positive leader development is constrained to a range of intermediate values. If a leader does not produce enough streamers, it cannot adequately heat the leader tip and channel and thus cannot extend. If the leader produces too many streamers it becomes shrouded in a field-choking positive space charge. This constraint can be quantified as a streamer charge production per unit length of leader development, or Q/L, with laboratory results indicating it to be on the order of 50 μC·m⁻¹ [Gallimberti et al., 2002]. The electric field required for stable positive leader propagation at sea level air pressure varies from 100–200 kV·m⁻¹ for laboratory leaders down to about 10–50 kV·m⁻¹ for lightning leaders, and the propagation rate of positive leaders varies from 10⁴ m·s⁻¹ for laboratory leaders up to 3 × 10⁵ m·s⁻¹ for lightning leaders [Lalande et al., 2002].

3.2. Negative Leader

[26] The active region of a negative laboratory leader has the same general anatomy as a positive laboratory leader, consisting of a leader channel, tip and streamer zone. There is, however, a significant addition to the negative laboratory leader extension process, illustrated in Figure 7. In the negative laboratory leader case, an initial burst of negative streamers is emitted from the main leader tip and propagates through the strong local electric field for a few meters. As illustrated on Figure 7a, this results in the creation of small heated and positively charged stems along the negative streamer paths corresponding to regions of vigorous streamer intensification and/or branching [Reess et al., 1995]. As illustrated on Figure 7b, the positive space charge in these regions leads to the rapid formation of a retrograde positive streamer that propagates back to the main negative leader tip. If the positive streamer emission is energetic enough, a compensatory quantity of negative charge is deposited back into the space stem, resulting in a forward-propagating negative streamer. This discharge sequence is called a “pilot”, and often occurs in a repetitive forward-propagating series with a repetition period of tens of nanoseconds and a propagation velocity on the order of 10⁵ m/s. Pilots serve as a continuous source of retrograde positive streamers that feed into the main negative leader tip. This coupling of pilots to the main negative leader tip provides the majority of the electric current that heats and extends the main negative leader tip.

[27] The situation can arise whereby two or more pilots may exist simultaneously in a linear series in front of the main negative leader tip. This situation is of great interest because it creates the condition whereby one of the pilots may transition into a hot bipolar leader segment [Ortega et al., 1994]. Figure 7c illustrates a linear series of two pilots, with the outer pilot generating positive streamers that are fed into the inner pilot. By being fed current from an upstream pilot and in turning feeding that current downstream to the main negative leader channel, the inner pilot stem is continuously heated via joule heating. After reaching the critical temperature for sustaining electrical conductivity, the inner pilot stem begins to lengthen at both ends in much the same way as the tip of the main negative leader. This elongating conductive structure is called a “space leader”, and is essentially a floating bipolar leader. As illustrated in Figure 7d, the lengthening space leader eventually attaches to the main negative leader channel. At this moment, the space leader is rapidly brought to the potential of the main negative leader tip. This is accompanied by a surge of current and luminosity, and is commonly referred to as a “step”.

[28] Typical Q/L values for negative laboratory leaders are around 100 μC·m⁻¹ [Gallimberti et al., 2002]. Ambient electric fields of 200–300 kV·m⁻¹ are required for propagation at sea level air pressure, nearly double that of positive leaders [Lalande et al., 2002]. The elongation of negative laboratory leaders typically occurs in step lengths on the order of 1 m, with a stepping period of 10–20 μs and velocity of 1–5 × 10⁵ m·s⁻¹. In comparison, negative lightning leaders have step lengths that can exceed several tens of meters and velocities that approach 10⁶ m·s⁻¹. While it may superficially appear that the mechanisms of lightning and laboratory stepped leader extension are identical, debate still exists due the more extreme nature of lightning and the apparent lack of sufficiently detailed observational evidence.

3.3. Hypothesis for Lightning Leader Initiation

[29] While most laboratory studies provide insight into leader initiation on electrodes and large floating conductors, lightning leader initiation usually occurs in regions devoid of such structures and is thus not trivially comparable. Instead of attempting to explain lightning leader formation in terms of electrode-initiated leaders, it may instead be more accurate to consider a comparison to the laboratory space leader as the laboratory space leader shares with lightning the constraint of being initiated in regions devoid of conducting electrodes.

[30] We suggest that the local conditions required for the onset of the pilot process and subsequent formation of a laboratory space leader may also exist in a thundercloud environment. Specifically, we suggest that these conditions may arise in the strong electric field regions that are hypothesized to result from the positive streamer system mechanism of Griffiths and Phelps. Figure 8 illustrates the process as conceived, based on hypothesized properties of positive streamer systems and know properties of the laboratory space leader. According to Griffiths and Phelps [1976], a series of overlapping positive streamer systems may boost the electric field to levels exceeding 1 MV·m⁻¹ over the distance of a few meters. In such conditions, hydrometeors likely undergo both positive and negative corona discharges. The positive streamer discharges would continue to reinforce the positive streamer system effect of locally intensified electric field, while the negative streamers might create space stems in the same way as in the case of the laboratory negative leader (Figure 8b). These space stems could undergo a series of pilot discharges, with the positive streamers continuing on into positive streamer systems (supplanting the hydrometeors as initiators of seed positive streamers). If a small number of pilots becomes serially connected via positive steamers (Figure 8c), then the downstream pilot stems could undergo heating until becoming electrically conductive. These electrically conductive stems could then be further heated by continued pilot-generated streamer activity, resulting in their extension into space leaders. Further growth and extension of a number of serially connected space leaders could lead to their attachment, creating a substantially longer space leader segment (Figure 8d). This attachment process would be very much analogous to the stepping process of the laboratory negative leader, with the role of the main negative leader channel as a positive charge drain being taken by the continuing positive streamer generation on the anodic end. As the space leader channel continues to lengthen, the potential gradient along the conductive leader channel would continue to drop due to continued joule heating, further intensifying the electric field at the leader channel extremities. Given that the local electric field at the leader extremities can sustain continued development, the space leader should continue to lengthen until emerging as a lightning leader channel.

[31] In order for this hypothesized lightning initiation sequence to succeed, a number of constraints must be accommodated. First, the electric field strength required for space stem formation must be met. Observations of laboratory pilot formation have shown that pilots can form in the outer regions of the streamer zone of a laboratory negative leader [Ortega et al., 1994; Reess et al., 1995]. It can be assumed that the electric field in these regions is comparable to the minimum field required for negative streamer propagation, around 750 kV·m⁻¹ at sea level pressure [Gallimberti et al., 2002]. This value, adjusted to 500 mb pressure, is less than the field strength hypothesized to occur near the positive streamer system mechanism. Additionally, the streamers created by the pilots should not develop a local space charge shield that reduces the local electric field and quenches the discharge. In the case of a laboratory negative leader, this constraint is fulfilled via removal of positive charge through the highly conductive leader channel. However, in the case of lightning initiation, no such conductive channel exists. Instead, positive charge removal must be carried out by the propagation of positive streamers away from the pilot. The positive streamer system mechanism is hypothesized to propagate positive space charge to distances on the order of 10 m or more, in addition to further intensifying the electric field at the system origin due to positive streamer intensification. This should, in effect, fulfill the role of positive space charge removal. However, unlike the case of a laboratory negative leader, the embryonic lightning leader must eventually develop its positive end in the general direction of this large deposit of positive space charge. If the accumulated space charge is too great, it may interrupt the positive leader development which would end the discharge. One possibility is that, as the embryonic lightning leader extends out toward the deposited positive space charge, the reduced potential gradient inside the lengthening leader channel results in intensification of the electric field at the positive leader tip sufficient to overcome the shielding effect. Another possibility is that the embryonic lightning leader simply develops around, and thus avoids, the deposited positive space charge. Finally, the emerging embryonic lightning leader must be capable of continued development under the weaker background thundercloud electric field. This constraint depends primarily on the polarization of the leader channel upon emergence into the weaker background field, and is a function of the leader channel length and conductivity. If the leader channel is able to emerge under these constraints, it may be properly stated that lightning has initiated.