a model study of corona emission from hydrometeors

Q. J. R. Mereorol. Soc. (1999), 125, pp. 1681-1693

A model study of corona emission from hydrometeors

By VICKI SCHROEDER1*. M. B. BAKER' and JOHN LATHAM* I Universiv qf Washington, USA

Universily of Manchester Institute of Science and Technology (UMIST), UK

(Received 16 February 1998; revised 16 November 1998)

S IJ MM ARY

The maximum measured electric fields in thunderclouds are an order of magnitude less than the fields required for electric breakdown of the air. Several explanations for lightning initiation in these low-intensity fields exist. One explanation is that electric breakdown first occurs at the surfaces of hydrometeors where the ambient field is enhanced very locally due to the drop geometry. Laboratory experiments have indicated that colliding raindrops which coalesce to form elongated water filaments, can produce positive corona in ambient fields close to those measured in thunderclouds. We calculate the electric field distribution around a simulated coalesced drop, and use a numerical model to study the positive-corona mechanisms in detail. Our results give good agreement with the laboratory observations. At the altitudes and reduced pressures at which lightning initiation is observed, our results show that positive corona can occur at observed in-cloud electric fields strengths.

KEYWORDS: Cloud physics Lightning

1. INTRODUCTION

The mechanism by which lightning initiation in thunderclouds occurs is poorly understood. The maximum measured electric fields (E-fields) in clouds (E,,, - 100- 400 kV m-I; Marshall et al. 1995; Winn et al. 1974) are an order of magnitude smaller than the E-fields required for dielectric breakdown of air (Ebreakdown - 2700 kV m-' at surface pressure).

The basic charge and E-field structures found in thunderclouds are shown in Fig. 1. Field observations of lightning show that it initiates primarily in three regions, which are indicated in Fig. I (Krehbiel 1986; Shao and Krehbiel 1996). One proposed mechanism for lightning initiation is that electric breakdown first occurs at the surfaces of hydrometeors near which the ambient field is enhanced. In initiation regions 1 and 2 the field enhancement by liquid hydrometeors is important while in region 3, where liquid water content is negligible, enhancement of the E-field would occur around ice particles. Our investigation focuses on region 2. However, our method can be applied to corona processes at the surface of ice particles as investigated experimentally by Griffiths and Latham (1974).

Crabb and Latham (1974; hereafter CL) obtained very promising results from a set of laboratory experiments in which they measured the E-fields required to initiate a discharge from the surface of filamentary, coalesced drops created when two water drops collided. They observed pulsed, intermittent discharges in a localized region near the surface of the drop and found that the E-fields required for discharge initiation lay within the range of observed thunderstorm E-fields.

We extended models of the positive discharge process developed by Dawson and Winn (1965); Gallimberti (1979), Bondiou and Gallimberti (1994), and Abdel-Salem et al. (1976) in order to study the discharge processes occurring from hydrometeors. CL's laboratory conditions were used to initialize the discharge model. We varied both the microphysical and environmental conditions to simulate the range of conditions applicable to those found in thunderclouds. In particular, we investigated continuous discharges from the drop surface and we studied the pressure dependence of the discharge initiation E-fields. * Corresponding author: Geophysics Program, University of Washington, Box 35 1650, Seattle 98195- 1650, USA. e-mail: Vicki @geophys.washington.edu

1681

I682 V. SCHROEDER et al.

Figure 1. Schematic of a thundercloud indicating the locations of the charge centres and the E-field distribution. Region 1 indicates the area in which cloud-to-ground lightning typically initiates, while regions 2 and 3 indicate

the locations of intra-cloud lightning initiation.

We begin with a brief description of CL's experimental procedures and results, followed by a discussion of the discharge model we used. Finally we discuss our model results, showing the E-field required to initiate various discharge types as a function of the coalesced-drop properties and air pressure.

2. LABORATORY EXPERIMENTS

Figure 2(a) shows a schematic of the CL experiment-the full details of which can be found in CL. Their chamber, held at surface pressure, had a positive, high-voltage upper plate and an earthed lower plate separated by 50 mm. Voltages of up to 30 kV could be applied-corresponding to a maximum uniform E-field of 600 kV m-l within the chamber. Large water drops (radius R = 2.7 mm) were dropped into the chamber and collided with small drops (radius r = 0.65 mm) which were ejected vertically upwards from a small wind-tunnel, simulating drops moving in updraughts in thunderclouds. A variety of coalesced-drop shapes were observed, depending on the nature of the collision. CL described three basic collision modes: head-on, glancing and intermediate. Glancing and intermediate collisions produced a coalesced drop with a long filament extending from the large drop-see Fig. 2(b). Head-on collisions results in a flattening of the large drop and did not produce these long filaments. The drops remained in the coalesced state for -1 ms.

In CL's set-up, a negative charge was induced on the upper surface of the drop while the lower end had a positive induced charge. In the thundercloud setting, these drops would be located above the negative charge centre of the cloud. CL recorded the size and shape of the coalesced drops as well as the applied E-fields, E , required to initiate discharges for a large number of coalesced drops. They observed discharges from both ends of the drop, but focussed on the positive pulses occurring at the lower surface of the drop. This surface was observed to remain intact. In contrast surface disruption was observed at the upper, negatively charged surface of the drop.

CORONA EMISSION FROM HYDROMETEORS 1683

HV +

0 lARGEDROP R=2.7mm

0 small drop r=0.65mm

Figure 2. (a) Schematic of Crabb and Latham’s (1974) experimental set-up in which two drops (radii R = 2.7 mm and r = 0.65 mm) collided in the presence of an applied electric field. (b) Photograph of the coalesced

drop that formed after the collision.

CL observed that positive-burst pulses occurred for values of E between 250 and 500 kV m-l, depending on the length of the coalesced drop.

3 . MODEL DESCRIPTION

We describe three basic discharge processes that can occur at the surfaces of drops in the presence of strong E-fields.

The first process, su face disruption discharge, occurs when the electrostatic repulsive force on a drop in a strong E-field exceeds the surface tension. This results in the break-up of the drop surface, and an associated discharge. Dawson (1969) observed the surface E-field, Edismption, required to initiate this form of discharge as a function of drop size, and found Edismption to be independent of air pressure.

The remaining processes are often referred to as ‘pure’ corona processes because the discharge initiates without the occurrence of drop surface disruption. These processes fall into two categories:

(i) burst pulse discharges, which are intermittent; and (ii) continuous streamers, which are capable of propagation.

All of these processes result in the deposition of charge on the drop: either positive or negative depending on the sign of the applied E-field. We focussed only on positive corona: it is simpler to model, has a lower initiation threshold and was studied more extensively by CL than negative corona.

(a ) Positive pure corona model Following earlier work (Dawson and Winn 1965; Gallimberti 1979; Bondiou and

Gallimberti 1994) we model the positive discharge as a series of electron ‘avalanches’ (discussed later).

Consider the E-field near the surface of a drop which is situated in an external E-field, Eextemal (see Fig. 3). Initially, the total E-field at a point a distance z from the

1684 V. SCHROEDER et al.

Drop

N1 ions

ionization zone boundary (a-q) = 0

E r external z

Figure 3. Schematic of positive discharge formation near the surface of a drop. Free electrons are accelerated by the E-field and undergo collisions with air molecules. The ionization of molecules within the ionization zone leads to an exponential growth of electrons (‘avalanche’) and the formation of a spherical streamer head. See text

for further details and discussion.

drop surface is

E(z) = E g ( z ) = Eexternal + Edrop(Z) (1)

where Edrop(Z) is the contribution due to charge induced on the drop and E,(z) is referred to as the geometric field.

In the presence of E, free electrons are accelerated and undergo collisions with air molecules. At some radial distance from the drop E is such that:

a(E/p) = V(E/P) (2)

where a (m-’) and q (m-I) are the ionization and attachment coefficients for electrons in air, respectively, and p is the total air pressure. The surface defined by (2) is the ionization zone boundary; inside this boundary a > q and there is a net growth of free electrons. At surface pressure the ionization-zone boundary is the surface along which E = 2700 kV m-l. Figure 4 shows a and q as functions of E/p (Harrison and Geballe 1953; Loeb 1965; Badaloni 1972; Ibrahim and Singer 1982).

In order to simplify the problem, it is common to replace the three-dimensional problem by a one-dimensional one, in which all exponential growths of electrons, or ‘avalanches’, occur along the z-axis (Dawson and Winn 1965; Griffiths and Phelps 1976a; Gallimberti 1979). The point zj marks the intersection of the ionization boundary with the z-axis. When a free electron, starting at zi , accelerates in the E-field towards the drop, the number of electrons grows exponentially with decreasing z . This is referred to as the primary electron avalanche. Due to the exponential nature of the growth, most of the ionizing collisions occur near the surface of the drop. The free electrons are then absorbed by the drop, leaving behind a region of low-mobility positive ions, modelled as a sphere (Dawson and Winn 1965; Gallimberti 1979), and referred to as the streamer head.


1 o2

1 oo 8 E -2 < 10

- L

4-

r Y

1 0" s

(a) Ionization coefficient (b) Attachment coefficient

1 o-6 0 100 200 300 0 100 200 300

E/p [Wcm torr] V p [Wcm torr]

(c) photon creation A (d) photon absorption coefficient

1

b 1000

\ 10 100

1.p [cm.Torr] 1.p [cm.Torr]

rigure 4. \a) Kauo or ionization coemcienr KO pressure, a l p , ror electrons in air (Baaaioni I Y I L ; Loeb 1965); (b) Ratio of attachment coefficient to pressure, q / p , for electrons in air (Badaloni 1972; Geballe 1953); (c) 9 = f1 . f2 . f3 where fl is the number of photons created per ionizing collision, f2 (m-') is the number of photoions created per photon per metre, and 6 is a solid angle, 2rr in our calculations (Penney and Hummert

1970); (d) Ratio of photon absorption coefficient to pressure, p / p , in air (Penney and Hummert 1970).

The number of positive ions formed by the primary avalanche travelling from the ionization zone boundary, zi, to the drop surface, zo, is given by:

I nt: rauius UI me streamer neaa is approximately:

(4)


where D and u are the electron diffusivity and drift velocity, respectively. D and u are functions of the ratio ( E / p ) and thus depend on z (Healey and Reed 1941; Ibrahim and Singer 1982). R, x 30 p m at surface pressure for most of the calculations reported here.

The total E-field at z is now given by:

where the second term is the E-field due to the spherical charge concentration of the streamer head.

In addition to ionization, collisions between the free electrons and air molecules also result in the excitation of the molecules, which then emit photons on decay. A certain fraction of these photons in turn have sufficient energy to ionize molecules that they encounter, creating photoelectrons. These photoelectrons then start a series of secondary avalanches which converge on the drop from all directions.

The number of photoelectrons created per metre at a radial distance, I , from the drop surface is given by:

P ( l ) = fiN1 . e x p ( - ~ O . f2 * G, (6)

where f1 is the number of photons created per ionizing collision, p (m-’) is the photon absorption coefficient in air, f2 (m-’) is the number of photoions created per photon per metre, and G is a geometric factor to account for the fact that some photons are absorbed by the drop.

Both ,u and f1 . f2 are functions of 1 p , the product of the distance from the photon source (the collisions) and air pressure (Penney and Hummert 1970)-see Fig. 4.

Then the total number of ions created in the secondary avalanches is given by:

N2 = P (1) . exp { izo (a - q ) dz ] dl,

where zo indicates the position of the primary streamer-head surface. We now consider the various initiation conditions. A burst pulse discharge is

initiated if the number of photoelectrons created along the ionization zone boundary during the growth of the primary avalanche is equivalent to the number of photoelectrons that started the primary avalanche (commonly taken to be one) (Abdel-Salam et al. 1976).

We consider photoelectron production in a region of depth (1 / p ) along the ionization zone boundary and write the above condition as follows:

This type of discharge is intermittent, since the charge in the primary streamer head is too low to alter the E-field significantly and is thus unable to attract the subsequent avalanches to its surface. Instead, the successor avalanches are directed towards the drop surface-allowing the discharge to ‘spread’ over the drop surface-and there is no propagation away from the drop.

A more stringent initiation condition exists for continuous streamers. In this case the number of positive ions in the primary streamer head must be large enough to attract the secondary avalanches to the streamer head surface. This is achieved when the radial E-field around the streamer head, E , = 4 a t o ~ ~ ~ R , l Z - E, [Abdel-Salam et al. 19761. In addition:


Figure 5 . Schematic of our idealized coalesced drop shape. The size of the drop is characterized by its total length, L , as indicated. Three different shapes were considered for the upper filament tip and are indicated in the inset (aHc). Negative discharge occurred at the upper filament tip, with positive discharge occurring at the lower end of the drop. The E-field distribution around the the drop was calculated using a finite-element method

(Quickfield Software).

(a) N2, the number of positive ions in the streamer head that results from the secondary avalanches, must equal N1, the number of positive ions created by the primary avalanche; the radius of the secondary streamer head must equal Rs, the radius of the primary streamer head (Dawson and Winn 1965).

(b)

These conditions ensure that the initial streamer-head charge density is reproduced in the second streamer head. Continued reproduction of the streamer head in subsequent steps results in propagation of the positive streamer away from the drop surface.

The minimum value of Eexternal necessary to initiate a discharge at pressure p is referred to as Einitiation(P) and depends on the type of discharge (burst pulse or continuous streamer).

(b) Model procedure Our results were obtained using the following procedure. We began by defining

the drop shape and permitivity, E . The idealized shapes that were used are shown in Fig. 5. We set p , and applied an E-field Eexternal to the drop. The E-field distribution around the drop was calculated using a finite-element-method based solving routine (Quickfield Software; e-mail http://www.tor.ru/quickfield). The E-field at the drop’s negative surface was then compared to the known surface-disruption E-field threshold, Edismption (Dawson 1969). If Esufiace > Edismption then Various amounts O f positive charge, Qdrop, were added to the drop. The E-field distribution was recalculated and the position zi was determined. N1 and R1 were computed from (3) and (4) respectively, and P(1) at zi from (6). If 3 = 1 , then Eextemal = Einitiation(P) for burst pulse discharges. We then proceeded to calculate N2 and R2 from (7) and (4) respectively. If Ec - Eg, N2 = N1 and R2 = R1, then Eextemal = Einitiation(P) for continuous streamers.


C 0 Q

c

.- c c .- .- .-

Rayleigh Limit 8 Breakup --->

lo-'* lo-" 1 o-'O lo-*

Figure 6. Einitiation (see text) for positive burst pulse discharges from the lower positive end of the drop as a function of Qdrop. the charge deposited on the drop by the negative corona from the upper end. The drop length is

held fixed at L = 20 mm.

4. RESULTS

(a ) Sulface disruption Dawson (1969) found Edisruption = 8500 kV m-l for a drop of radius r = 0.65 mm.

We investigated the surface E-fields of a series of filament tip shapes (see Fig. 5) and calculated the Eextemal required to produce Esurface > Edismption.

We found that, as expected, Eexternal decreases from a high of 925 kV m-l for the hemispherical shape (Fig. 5(a)) to a low of 200 kV m-l for the sharper shape shown in Fig. 5(c). Photographs of coalesced drops in CL show that the non-hemispherical shapes are the best representations. The shapes in Fig. 5(b) and (c) both met the requirement for disruption for < 500 kV m-' and this is consistent with CL's observations that the filament tip disrupted in E-fields of this magnitude.

(b) Einitiation against Qdrop

Figure 6 gives the Einitiation values for positive-burst pulse discharges from the lower (positive) end of the drop as a function of the charge, Qdrop, deposited on the drop by the negative discharge from the upper end. The drop length is held fixed at L = 20 mm.

Einitiation decreases rapidly once Qdrop exceeds lo-'' C. The Rayleigh stability criterion (Rayleigh 1882; Taylor 1964) gives the Rayleigh limit QRL, the maximum charge that a sphere of liquid can hold before the electrostatic repulsive force overcomes the surface tension. In SI units it is given by:

2 2 3 Qu = 64rc €0 . r cr, (9) where r is the sphere radius and cr is the surface tension.

For our drop dimensions, QRL FZ 4 x lop9 C. Since CL did not observe disruption of the lower surface of the drop, we limited our calculations to Qhop < QRL. For larger allowed values of Qdrop, close to QRL, the values of Einitiation become comparable to CL's experimental values and to those observed in thunderclouds.

CORONA EMISSION FROM HY DROMETEORS

CL ex erirnental values 700. rnodefcaku\ations I . 1689

C 0

.e c

.- 300.

.-

2oo/ J

5 10 15 20 25 loot

[mml Figure 7. Einiriation (see text) for burst pulse discharge as a function of the drop length L , for fixed charge density. Squares are calculated values of ,!?initiation for burst pulse discharges; circles are Crabb and Latham's (CL; 1974)

measured values.

In addition to the burst pulse discharges we also calculated the fields required to initiate continuous streamers. For Qdrop just below QRL, Einitiation X 400 kV m-l for continuous streamers, approximately 50% greater than that required for burst pulse discharges.

( c ) Einitiation against L We now held the charge density, p, on the drop fixed, and varied the drop length,

L. The circles in Fig. 7 represent CL's measured values. We found that our modelled values of Einitiation for the burst pulse discharges (squares) decreased with increasing L , consistent with the trend that CL observed. The agreement between the calculated results and observation is promising and offers validation of our model processes.

In an attempt to understand the scatter in CL's data, we considered the effects of:

(i) (ii)

The outer curves in Fig. 7 show that a 0.01 C mP3 variation in the charge density of the drop is consistent with the variation of the CL data. A gross variation of drop shape- a perfectly spherical lower end-resulted in Einitiation = 750 kV m-l ( p = 0.035 C m-3, L = 20 mm). This point lies well out of the range of CL's data and indicates that the observed variation would be due to much subtler shape variations. It is likely that the scatter in the CL data resulted from a combination of charge and shape variations.

The same calculations were carried out for continuous streamers and the results are shown in Fig. 8. Einitiation decreased with L in much the same way as for burst pulses. The Einitiation values for the continuous streamers were, however, -50% larger than those required for burst pulses.

TO understand the decrease in Einitiation with L we consider two effects (see Fig. 9): first, that for a given ambient E-field, the surface field at the tip of the filament increases with increasing L , which lowers Einitiation; and second, that as L increases E g ( z )

the amount of positive charge deposited on the drop, and the shape of the lower end of the drop.


Figure 8. &tiation (see text) for continuous discharges as a function of both drop length, L (mm), and pressure, P fmb).

breakdown

Figure 9. Schematic of the E-field, E, as a function of distance, z , from the surface of the drop. E,1 and E,, are the surface fields for long (20 mm) and short (10 mm) drops, respectively. The ionization zone boundaries for

long and short drops are indicated by zil and ziS, respectively.

decreases more rapidly with z , which reduces the size of the ionization zone and thus increases Einitiation.

Our results show that the former process dominates; i.e. that the increased average field within the ionization zone compensates for the electron's shortened path-leading to a lowering of Einitjation as the drop's length is increased. However, dEinitiation/ dL decreases as L increases, so that the effect of increased length becomes less significant for L > 20 mm.

(d) The pressure effect All CL's measurements were made at surface pressure (1000 mb). It is, however,

of interest to know what the Einitiation values for continuous streamers would be at the lower pressures found in the regions where lightning initiates. We therefore calculated Einitiation for continuous streamers over a range of pressures.

The variation of Einitiation for continuous streamers with both pressure and drop size is shown in Fig. 8. The dark region in the lower left corner indicates the region in which initiation is most favourable-large L and low p . Over the chosen ranges of p and L, pressure has a greater effect on Einitiation.


0 5 10 18 20

absolute humidity [g/m3]

Figure 10. Epropagation (see text) as a function of absolute humidity and pressure, p (Griffiths and Phelps 1976b).

Fig. 8 indicates that Einitiation varies linearly with pressure. We consider the dependence of the various parameters used by the model: a, q, D and IJ are functions of E/p while the p and f 1 + f 2 are functions of 1 . p. The linear relationship between Einitiation and p suggests that the terms which depend on E/p dominate, and that there is a unique value of the ‘reduced’ E-field, Yinitiation = Einitiation/P for a particular E and p combination.

( e ) Propagation The E-field necessary to sustain stable streamer propagation, Epropagation(P), was

measured by Griffiths and Phelps (1976b) as a function of p. These stable streamers, once initiated, will continue to propagate provided Einitiation 2 Epropagation. Griffiths and Phelps found that Epropagation - 400 kV m-’ for dry air at p = 1000 mb and that Epropagation(P) O( p5 (Fig. 10). At P = 500 mb Epropagation - 150 kV m-l for dry air.

For p = 1000 mb, our calculations yield ,?initiation > 400 kV mU1 for all L (Fig. 8). Streamers initiated under these conditions will therefore be able to propagate over the entire length of the region in which Eextemal remains constant. In thunderclouds this scale is typically hundreds of metres. At lower pressures we find Einitiation > Epropagation over a smaller range of L.

5 . DISCUSSION

In this paper we have shown that continuous, propagating streamers can be initiated from water drops at the pressures and E-fields found in thunderstorms. Furthermore, these streamers are capable of propagating over considerable distances-the distances being limited by the size of the region in which Eextemal is greater than Epropagation(P).

When the electron currents in streamers become large, Joule heating produces a channel in which thermodynamic equilibrium is destroyed and hydrodynamic effects become important (Gallimberti 1979). This is commonly referred to as a leader or as


a ‘stepped-leader’ in the cloud-to-ground lightning context. The currents carried by individual streamers initiated at the drops are several orders of magnitude too low to produce Joule heating effects (Bondiou, private communication). These streamers may, however, still eventually lead to leader formation.

Griffiths and Phelps (1976a) considered the role of small-scale discharges in thunderclouds, calculating the E-field enhancement due to multiple propagations of positive streamers near an electrode. According to their model, a series of three to seven streamers gave rise to an enhanced E-field of up to - 1500 kV m-l over a region of several metres near the electrode. At p - 500 mb this E-field is large enough to lead to large- scale breakdown of the air in this region, and give rise to the high-current streamer needed for leader formation. Griffiths and Phelps (1976b) found that the field was in- tensified on a time-scale of -1 ms, which is comparable to the lifetime of the coalesced drops as measured by CL. It is possible that, in this manner, several continuous streamers initiated from drops in the thundercloud could give rise to a leader. Further investigation is required to determine whether a single drop is in fact capable of initiating multiple streamers, or whether drops in close proximity to one another could have the same effect.

Another mechanism for leader formation, based on the close proximity of initiating drops, that requires investigation is the merging of several streamers to form a single, more vigorous streamer with sufficient current to transform it to the ‘warm’ leader stage. If we think of drops that initiate continuous streamers as ‘electrodes’ then the number of electrodes available increases with increasing E (i.e. the range of acceptable L values increases). Thus the likelihood of several streamers initiating in close proximity increases and the chance of leader formation is increased. This is also in keeping with the observations of large amounts of corona activity in thunderstorms without lightning; i.e. the electrode density must be sufficiently high before streamers are able to merge and form a leader.

The streamers observed by CL and those examined in our model were all positive, occurring at the lower end of drops. This corresponds to drops located above the negative-charge centre in clouds. Drops located below the negative-charge centre have negatively charged lower ends, and investigation of this situation will require the modelling of negative streamers which are much more complex in nature than positive streamers (Castellani et al. 1994). No attempt has been made in this paper to model these negative processes but future attempts should be made to investigate this phenomenon.

Finally, whilst we have concentrated on liquid hydrometeors, future work should incorporate ice particles as possible electrodes. This may provide an explanation for lightning initiation that occurs at higher altitudes, near the upper positive-charge centre in thunderclouds, where there is little or no liquid water available.

ACKNOWLEDGEMENTS

We are grateful for support by NASA # NAG8-1150. We thank Anne Bondiou- Clergerie of ONERA for supplying the ionization and attachment coefficient data and providing helpful comments and advice. We are also very grateful to the late Ron Geballe for his suggestions.

REFERENCES

Abdel-Salam, M., Zitoun, A. G. and 1976 Analysis of the discharge development of a positive rod-plane gap in air. IEEE Transactions on Power Apparatus and Systems, El-Ragheb, M. M. PAS-95, 1019-1027


Badaloni, S. and Gallimberti, I.

Bondiou, A. and Gallimberti, I.

Castellani, A., Bondiou, A., Bonamy, A., Lalande, P. and Gallimberti, I.

Crabb, J. and Latham, J.

Dawson, G.

Dawson, G. and Winn, W. Gallimberti, I.

Griffiths, R. F. and Latham, J.

Griffiths, R. and Phelps, C .

Harrison, M. A. and Geballe, R.

Healey, R. H. and Reed, J. W.

Ibrahim, A. A. and Singer, H.

Krehbiel, P. R.

h b , L. B.

Marshall, T., McCarthy, M. and

Penney, G. W. and Hummert, G. T.

Rayleigh, Lord

Shao, X. M. and Krehbiel, P. R.

Taylor, G. I.

Winn, W. P., Schwede, G. W. and

Rust, W. D.

Moore, C. B.

1912

1994

I994

1974

1969

1965 1979

1974

1976a

1976b

1953

1941

1982

1986

1965

1995

1910

1882

1996

1964

1974

‘The inception mechanism of the first corona in non-uniform gaps’. UP Report no. 72/05, University of Padua, Italy

Theoretical modelling of the development of the positive spark in long gaps. J. Phys. D., 27, 1252-1266

‘Laboratory simulation of the bi-leader process on an electrically floating conductor’. International conference on lightning and static electricity, Mannheim, Germany, May 1994

Corona from colliding drops as a possible mechanism for the triggering of lightning. Q. J. R. Meteoml. Soc., 100,191-202

Pressure dependence of water-drop corona onset and its atmos- pheric importance. J. Geophys. Rex, 74,6859-6868

A model for streamer propagation. Z. Phys., 183, 159-171 The mechanism of the long spark formation. J. de Physique, 40,

Electrical corona from ice hydrometeors. Q. J. R. Meteorol. Soc.,

A model for lightning initiation arising from positive corona streamer development. J. Geophys. Res., 31, 3671-3676

The effects of air pressure and water vapour content on the propagation of positive corona streamers. Q. J. R. Meteorol. SOC., 102,4 19-426

Simultaneous measurements of ionization and attachment coefficients. Phys. Rev., 91, 1

The behavior of slow electrons in gases. Wireless Press, Sidney, Australia

‘Calculation of corona discharge in positive point to plane gaps’. Pp. 128-131 in Proceedings of the seventh international conference on gas discharges and their applications. London. Published by Peter Peregrinus

The electrical structure of thunderstorms. Pp. 90-1 13 in The earth ’s electrical environment. National Academy Press, Washington DC, USA

Electrical coronas-their basic physical mechanisms. University of California Press, Berkeley, USA

Electric field magnitudes and lightning initiation in thunderstorms. J. Geophys. Rex, 100,7097-1103

Photoionization measurements in air, oxygen, and nitrogen.

On the equilibrium of liquid conducting masses charged with

The spatial and temporary development of intracloud lightning.

Disintegration of water drops in an electric field. Proc. R. SOC.

Measurements of electric fields in thunderclouds. J. Geophys.

Colloque 7, 193-250

100,163-180

J. A@. Phys., 41,512-517

electricity. Phil. Mag., 14, 186185

J. Geophys. Res., 101,26641-26668

London, 280,383-397

Res., 79,1761-1767

a model study of corona emission from hydrometeors

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