[Rycroft, M.J.] Introduction to the Physics of Sprites, Elves and Intense Lightning Discharge

INTRODUCTION TO THE PHYSICS OF SPRITES,ELVES AND INTENSE LIGHTNING DISCHARGES

Michael J. RycroftCAESAR Consultancy, 35 Millington Road, Cambridge CB3 9HW, U.K.

Abstract This chapter introduces the fundamentals of the subject, the laboratory for whichis the Earth’s atmosphere. All of its important physical properties vary signif-icantly with altitude; its electrical conductivity varies greatly with altitude andalso with latitude. The modus operandi of the global atmospheric electric circuit,in part powered by thunderstorms, is outlined. Some observations of transientluminous events, which occur above certain energetic thunderstorm systems justafter a strong lightning discharge (the effect of which is usually to take positivecharge to the ground), are introduced and their characteristics mentioned. Dif-ferent theoretical ideas that have been put forward to explain crucial aspects ofthese phenomena are introduced, and some relevant numerical simulations arebriefly discussed.

1.1 Basic Properties of the Atmosphere

1.1.1 Global Scale Variations (Horizontal Scale greaterthan 104 km)

The Earth’s atmosphere is bound gravitationally to our home planet. Thepressure and density of the air decrease exponentially upwards from the sur-face, the scale height being ∼7 km (Rycroft, 2003). This scale height variesslightly through the atmosphere because it is not isothermal. Relatively, thehottest regions of the Earth’s neutral atmosphere are at its surface (globalaverage temperature T=288 K, pressure p=1013 hPa, density �=1.2 kg/m3),at the stratopause (∼250 K, near 50 km altitude) and in the thermosphere(above ∼110 km, from where the temperature rises rapidly up to ∼2000 K at∼300 km altitude), depending on the phase of the cycle of solar activity, withsuccessive maxima ∼11 years apart. About half of the atmosphere resides atand below an altitude of 5 km; 90% of the atmosphere lies below an altitude of∼15 km. The pressure of the air at 32 km altitude is ∼1% of its surface valueand, at 100 km altitude, it is about one millionth of its surface value. The cold-est regions are at the top of the troposphere, termed the tropopause (at 18 km

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2 SPRITES, ELVES AND INTENSE LIGHTNING DISCHARGES

altitude over the tropics, 14 km at middle latitudes, and only 9 km at high lati-tudes), and at the top of the mesosphere, termed the mesopause (∼140 K near85 km altitude in summer, and ∼210 K in winter). Above the rotating Earth,winds blow away from the hotter regions, essentially horizontally – zonally(at constant latitude) or meridionally (at constant longitude). The winds carryheat through the atmosphere, in an attempt to bring the atmosphere into ther-mal equilibrium.

The atmosphere near the Earth’s land surface is an electrically charged gas;∼2·106/m3s−1 molecular ion pairs are formed by radon emanating from theland but, since recombination is rapid, the electron density is only ∼1 m−3.Bursts of gamma-radiation and galactic cosmic rays, which are extremely en-ergetic (GeV) charged particles (electrons, protons and helium nuclei) fromoutside our galaxy, come down into the atmosphere, ionising atmosphericmolecules by collision. The maximum ionisation production rate is reachednear 20 km altitude. Thus, from the Earth’s surface up to ∼20 km, the electri-cal conductivity (the reciprocal of the electrical resistivity of the atmosphere)increases from ∼10−14 Sm−1 with a scale height ∼5 km; above 20 km, it in-creases with an ever increasing scale height. The concentration of molecularion pairs has a maximum value ∼109m−3 at 15-20 km altitude (Harrison andCarslaw, 2003). The electrical conductivity of the stratosphere varies some-what, and that of the mesosphere varies enormously, according to the prevail-ing geophysical conditions.

Near solar minimum, the solar wind flowing outwards from the Sun is“quiet”, with few irregularities whereas, at solar maximum, it is disturbed, withmany large amplitude fluctuations. These fluctuations scatter galactic cosmicrays coming into the solar system so that their flux is smaller at solar maxi-mum than at solar minimum. Because of the dipolar character of the Earth’smagnetic field, cosmic rays preferentially enter the Earth’s environment at po-lar and high latitudes. These two considerations explain the interesting resultsof Ney (1959), that there is a significant variation of atmospheric ionisationthrough the 11 year cycle, and that this is especially marked at higher latitudes(∼50◦-60◦ geomagnetic latitude).

A complicating effect is that the Sun is more prone to generate very ener-getic charged particles (termed solar particle events, SPEs) at, and after, solarmaximum than at solar minimum. These enter the Earth’s environs preferen-tially in the polar regions, polewards of the auroral oval, at ∼67◦ magneticlatitude.

The ionosphere is formed in the thermosphere by the ionising action of theSun’s extreme ultraviolet radiation and X-rays; both of these are ∼100 timesstronger at solar maximum than at solar minimum. The lowest region of theionosphere, the D-region, is formed at and above 80 km, primarily by the ac-tion of solar Lyman-alpha radiation on nitric oxide. At night, the ionospheric

INTRODUCTION TO SPRITES 3

plasma density decreases most rapidly at the lowest altitudes (decreasing from1011 to 108m−3 at 90 km altitude), and less rapidly higher up where the effec-tive recombination process takes much longer (Schunk and Nagy, 2000).

The ionosphere and the magnetosphere above it respond rapidly to solarwind disturbances, nowadays termed space weather events. Often associatedwith solar flares, coronal mass ejections (CMEs) or shocks in interplanetaryspace, these can manifest themselves as geomagnetic storms or magnetosphericsubstorms (Baker, 2000).

1.1.2 Regional Variations (Horizontal Scale between 30and 300 km)

For our purposes, the most important phenomena in this category are thun-derstorms (Rakov and Uman, 2003). Thunderstorms form under strongly con-vective meteorological conditions, where cumulus clouds become cumulonim-bus clouds, and reach up to the tropopause. In the simplest case, the bottom ofa thundercloud is negatively charged, and the top (which may evolve into an“anvil”) is positively charged. More complex arrangements of charge generallyoccur; there can be a region of positive charge below the negatively chargedregion. Several different electrification mechanisms have been proposed.

Within a thundercloud, the vertical electric field ranges within±100 kVm−1,and varies considerably over a fraction of 1 km due to the presence of narrowcharged layers. Directly above a thundercloud, this field deviates from themean field by a few kVm−1; it changes between such values when a lightningdischarge occurs. Just after the stroke, even larger fields can be reached.

Individual convective cells are typically >1 km in radius, and may consti-tute individual thunderstorms. Alternatively, they may develop into mesoscaleconvective systems (MCSs), large scale thunderstorms; their radius is typicallyup to 100 km, or even more.

There exist regional scale variations of the troposphere and the stratosphere,due to meteorological processes, and of the mesosphere, the thermosphere andthe ionosphere, some of which are due to various different effects of spatiallystructured charged particle precipitation from the magnetosphere.

1.2 Basic Theory of Electrical Phenomena Occurring inthe Atmosphere

1.2.1 Introduction

Throughout the atmosphere, the electric (E) and magnetic (B) fields, chargedensity q(Ni - Ne) and total electric current density J are related by the fourequations of electromagnetism known as Maxwell’s equations. (Here the mag-nitude of q is the charge of an electron, the number density of positive ions is


Ni, and the number density of electrons and/or negative ions is Ne.) Togetherwith laws expressing the continuity of mass, momentum and energy, an ap-propriate equation of state p(N,T), an appropriate constitutive relation betweenJ and E, and appropriate parameterisation schemes, all these equations can,in principle, be solved to determine the overall behaviour of the atmosphere.However, this goal may never be fully achieved because many of the physicalprocesses occurring are nonlinear, and because of the extremely broad rangeof scales involved. Spatially, these range from turbulence to the global scaleand, temporally, from microseconds to centuries.

1.2.2 The DC Global Atmospheric Electric Circuit

One important generator for the global circuit (for reviews see Rycroft etal., 2000; Williams, 2002, pp. 9; Harrison, 2004; Rycroft, 2005) is linkedto thunderstorms and electrified shower clouds. Wilson (1920) suggested thata current should flow up from the top of a thunderstorm to the upper atmo-sphere. Upward (or Wilson) current passes through a charging resistor (R1 inFigure 1) to the ionosphere which is almost an equipotential. Electric currentsflow to different latitudes, mostly through the highly conducting ionosphere asindicated in Figure 1, but partly through the mesosphere. Currents flow alonggeomagnetic flux tubes into and out of the magnetosphere, especially at highlatitudes. Currents flow downward in the fair weather regions of the Earth,remote from thunderstorms; in these regions, most of the electrical resistance(r in Figure 1) is within a few km of the surface. This current closes throughthe land and sea portions of the Earth’s surface and through the atmosphere be-low the thunderclouds. To a first approximation, the region between the goodconducting Earth and ionosphere acts as a spherical capacitor, the atmospherebeing an insulator. This capacitor is charged up by the upward currents associ-ated with thunderstorms, and by other generators of potential difference. Theseother sources of upward currents include processes linked to thermal convec-tion currents and to point discharge (or corona) currents (Wormell, 1953).

Cloud-to-ground discharges transferring negative charge-to- ground (termed-CG) are effectively another source of upward currents. Also to be consideredis the displacement current (Roble, 1991), but this cannot charge up the ca-pacitor, neither can this discharge it. Chauzy (personal communication, 2003)has measured upward currents due to precipitation (rain) below thundercloudsand shower clouds, as postulated by Wilson (1920) – see also Williams andSatori (2004). However, the electric current from rain clouds can be down-wards rather than upwards, as mentioned by Williams and Heckman (1993).Boundary layer aerosol particles due to the burning of fossil fuels (Adlermanand Williams, 1996) complicate the situation over land areas, especially inwinter.


Figure 1. In this schematic equivalent circuit for the global atmospheric electric circuit, thecurrent generators shown to the left of the vertical dashed line act over <1 % of the Earth’ssurface. The load on this circuit is the fair weather region, shown to the right of the dashedline, ∼99 % of the Earth’s surface. The total current flowing is ∼1 kA. The time constant ofthe circuit is rC, a few minutes. When a +CG discharge occurs, the S2 for that storm closes for∼1 ms and then reopens; when a sprite occurs, its S1 closes for a few ms, and then reopens.

1.2.3 The AC Circuit

The AC circuit operates on time scales smaller than the relaxation time,which is defined as the permittivity of free space divided by the conductivity, σ,at the point under consideration. It is a strong function of altitude. For example,from 60 to 80 km on a typical night, the relaxation time is 10 ms (Hale, 1984).Atmospherics (or “sferics”) are radio signals of∼1 ms duration and which con-tain frequencies from a few kHz to 30 kHz (in the Very Low Frequency (VLF)band) radiated as an ElectroMagnetic Pulse (EMP) by a lightning discharge;these propagate up to 104 km or further in the Earth-ionosphere waveguide.Also excited by lightning are Schumann resonances (at 8, 14, 20, 26, . . . Hz)of the insulating spherical shell between the Earth and the ionosphere. Theseare in the ELF (Extremely Low Frequency) part of the spectrum, at <3 kHz,down to 3 Hz. The properties and uses of these ELF/VLF radio waves arediscussed in considerable detail in Chapters 8 and 10 by Rodger and Hobara,respectively. Temporal changes (occurring on time scales longer than minutes)to the current sources for, and the properties of, the DC circuit are not consid-ered as contributing to the AC circuit discussed here.


1.2.4 Thundercloud Charges and their Screening

As is evident from Figure 2, there should be a large electrostatic field abovethe large positive electric charge (∼100 C) at the top of a thundercloud. How-

trons screen the Coulomb field produced by a single positive charge at dis-tances > the Debye length. In the atmosphere, which is a weakly ionised gas,where the electron-neutral collision frequency is very large, the conductivity isfinite. In the real atmosphere, screening from the positive charge at the top ofa thundercloud takes place first at ∼60 km altitude, where the relaxation timeis ∼10 ms; at 40 km, the relaxation time is ∼100 ms, and it is a few s abovethe cloud top. Only on these time scales does there exist a downwards quasi-static electric field, from the ionosphere to the cloud top. Screening reduces theelectric field above a thundercloud to a value which is almost comparable withthe fair weather electric field, i.e. the field shown in Figure 2, with horizontalequipotentials.

Figure 2. Schematic diagram showing the distribution of equipotential surfaces between theEarth and the ionosphere near an idealised thundercloud, having +100 C at 15 km altitude and-100 C at 5 km, at +100 MV and -100 MV, respectively, before a lightning discharge occurs(with acknowledgements for valuable discussions to L.Sorokin).

ever, such large fields do not always exist in practice due to screening. Screeningis a well known concept in plasma physics; in a highly ionised gas, elec-


1.2.5 Spatial and Temporal Variations of the GlobalCircuit

Both in the charging (where J·E is negative) and the load (positive J·E) partsof the circuit, Ohm’s law can be applied; the conduction current J=σ·E. Fourdifferent types of variability may occur:

i) if σ is constant, J and E are linearly related

ii) if J is constant and σ is increased, E decreases

iii) if E is constant and σ is increased, J increases in proportion to σ

iv) J, σ and E may vary independently.

Thus, the interpretation of the apparently simple Ohm’s law is not straight-forward.

Regarding spatial variability, different processes can dominate depending ongeographic location (e.g., latitude, land or ocean, type of weather, the presenceor absence of pollution). Temporal variability occurs over a huge period range,from ∼ µs (lightning discharge) to ∼ ms (VLF/ELF radio phenomena), ∼0.1 s(Schumann resonance phenomena), and minutes to hours (evolution of thun-derstorm cells and thunderstorms) to diurnal (both with local time and withUniversal Time) and 27 day (solar rotation). Changes of tropospheric currentsources and solar/geomagnetic activity effects exhibit seasonal, semi-annualand annual variations. Quasi-biennial oscillations (of the stratosphere), solarcycle and longer term climatic variations also exist.

Consider, for example, possible changes as solar activity increases fromsolar minimum to solar maximum:

i) the height of the lower ionosphere decreases slightly

ii) the electrical conductivity of the stratosphere is reduced appreciably.

If the current generator does not vary with the solar cycle, the charging resis-tor R1 in the generator part of the circuit will increase, raising the ionosphericpotential. In the fair weather part of the circuit the current will be unchanged,and the electric field will be increased on all three counts. These qualitativestatements need to be made more quantitative. Markson (1981) has reportedsome interesting observations in this regard.

1.3 The Properties of Sprites, Elves and IntenseLightning Discharges

Having outlined some of the relevant properties of the laboratory in whichthe phenomena of our interest are observed, and also some basic theoretical


concepts, attention is now focused on observations, i.e., on what theory has toexplain. An overview of what is observed, and how, is presented; this includesa discussion of where and when sprites, elves and the intense discharges, whichproduce them, occur. Their signatures across the electromagnetic spectrum,from radio waves of the lowest to highest frequencies and into the visible partof the spectrum are mentioned, including typical intensities. Attention is paidto both spatial structure and temporal structure, i.e. their evolution. Many moredetails are given in subsequent chapters of this book.

1.3.1 Observations and their Interpretation – AnOverview

Intense Lightning Towards the end of an intense Mesoscale Convective Com-plex ahead of a cold front observed near local midnight over the High Plainsof the mid West of the U.S.A., strong lightning discharges that produce spritesare often observed to carry positive charge from the stratiform region of a thun-dercloud at ∼5 km height to ground (termed a +CG discharge). The largecharge moment formed by the charge in the cloud (∼100 C) and its image inthe ground, ∼1000 C·km, is destroyed (Lyons et al., 2003). That is equiva-lent to a current of 100 kA flowing over a horizontal distance of, 15 km at aheight of 5 km, and then flowing to ground (a current moment of 1000 kA·km),in a discharge lasting ∼1 ms. These values correspond closely to the modelvalues used by Cho and Rycroft (2001), to be discussed later. Huang et al.(1999) measured the charge moment change for the entire lightning dischargewhich initiates a sprite, and found it to exceed 300 C·km. Hu et al. (2002)reported that sprites are triggered by intense CG discharges, with charge mo-ments >100 C·km.

Elves A +CG discharge radiates a strong electromagnetic pulse which heatsthe atmosphere at ∼90 km altitude. The heated electrons excite nitrogenmolecules which then radiate in the N2 first positive band (red). Geometrydetermines that this light appears as a ring (at 90 km altitude) which expandsat the speed of light (e.g., Inan et al., 1997; Cho and Rycroft, 1998; Rycroftand Cho, 1998; Nagano et al., 2003). This is termed an “ELVE”, which standsfor Emission of Light and VLF perturbation from an EMP source (Fukunishiet al., 1996). It occurs ∼0.3 ms after the onset of the discharge.

Sprites From about 1 ms up to 10 ms after the lightning discharge, a brightspot of red light can typically appear at ∼70 km altitude. Within the next 1 ms,discharges moving both upwards and downwards are generated, with lengths ofseveral (up to 10) km and widths ∼0.1 km, or even less; these evolve for up to100 ms. Many similar discharges can appear simultaneously over a horizontaldistance of several km, up to 30 km. Such spectacular “transient luminous


events” (TLEs), which last for a few ms, and which may be reignited, aretermed sprites. On a frame from a video camera observation, sprites look like“celestial fireworks”.

Sprites may develop other interesting and notable features, such as halos attheir tops and tendrils at their bottoms, down to ∼50 km typically. Differentsprites may exhibit different features (termed, e.g., “carrot” sprites, or “colum-niform” sprites), and may evolve differently on time scales of ∼>1 ms. Somesprites may last for ∼> 100 ms.

These properties are known from video images (generally taken at a repe-tition period of 33 ms) or from photometer traces (which can have 1 ms res-olution, or even better). For example, Gerken et al. (2000) have presented atelescopic image of a sprite observed on 13 July 1998 over the North of Mex-ico which exhibits considerable structure on the 0.1 km scale, and a bright-ness up to 650 kR (kiloRayleighs), caused by a 128 kA peak current +CGdischarge. Neubert et al. (2001) observed sprites over Europe which evolvedmarkedly during 33 ms, and which were caused by +CG discharges between 7and 124 kA. Hardman et al. (2000) observed “dancing” sprites on a time scaleof 20 ms over active summer thunderstorms, having unusually high cloud tops,in Australia; their duration was up to 1 s. And Stenbaek-Nielsen et al. (2000)reported a considerable evolution of a large sprite over Nebraska, U.S.A., on atime scale of only 1 ms.

Sprites observed over the oceans around Taiwan in the summer of 2001were brighter than those seen over land; “the brightness of some of the oceanicsprites was estimated to exceed 5 MegaRayleighs” (Hsu et al., 2003). Duringthree winter seasons, sprites were recorded photometrically (with ∼1 ms reso-lution) off the coast of Japan (Takahashi et al., 2003). On 27 January 1999 thecausative discharge was identified as being in the cloud band of a cold front,the top of which was at a height of 5 km.

Besides being observed from the ground, sprites have also been studiedusing various instrumental techniques from aircraft, from balloons and fromspace, e.g., from the International Space Station (Blanc et al., 2004) and fromthe ill-fated Columbia Space Shuttle mission (Yair et al., 2003; Price et al.,2004).

Sprite spectra were studied by Hampton et al. (1996) and Wescott et al.(2001); theoretical spectra were computed by Milikh et al. (1998). They arestrong in the first positive band of nitrogen (red) and also in the N+

2 first nega-tive band and in the second positive band of nitrogen (blue).


1.3.2 ELF Radiation by Sprites

It has been reported (Cummer et al., 1998; Cummer, 2003) that sprites canradiate signals at up to 1 kHz (ELF). The sprite discharge enhances the localconductivity appreciably, allowing currents of up to 5 kA to flow for ∼2 msover a height interval of, say, 25 km. With its image in the ionosphere, this cur-rent moment amplitude of 250 kA·km is equivalent to a charge moment changeof 500 C·km, which is about half of the charge moment of the causative dis-charge (in the ELF band). Bering et al. (2002) discuss comparable numericalvalues of these parameters in terms of their sprite observations made from aballoon at 32 km altitude. Destroying this charge moment of 500 C·km ex-tracts ∼10 C from the reservoir of 2·105 C stored in the spherical capacitorwhich represents the global atmospheric electric circuit (Rycroft et al., 2000).Thus, one sprite removes up to 0.5·10−4 of the charge stored in the globalcircuit.

Price et al. (2004) reported 7 sprites and 7 elves observed from the SpaceShuttle; they detected “ELF transients, with accurate geolocation, for 5 out of7 elves, but for no sprite events.” This result may be “contrary to the presenttheories of TLE formation, and may require some new thinking into the mech-anisms that produce sprites and elves.” “Is it possible that, if CG dischargesdid produce the sprites, they were too weak to produce ELF transients?” “Ifthis is the case, the discharges had charge moments less than 100 C·km.” “Arethe lightning discharges that produce sprites in the tropics different from thosestudied in mid-latitude storms? Is the conductivity of the mesosphere in thetropics significantly different from that in mid-latitudes, allowing for weakerdischarges to initiate sprites?” Further research is clearly needed.

The electric field between the Earth and ionosphere is positive in the down-ward direction in the fair weather region. For a downward flowing current, ineither a +CG discharge or a sprite, J·E is positive. Thus, both represent dissipa-tion in the global electric circuit. Davydenko et al. (2004) have found that, fora MCS, the quasi- stationary vertical current is ∼25 A, downwards. If there isone such positively charged cloud created somewhere in the world each 15 s,this is equivalent to a charge transfer to ground of +100 C per minute. (This isequivalent to a current of <2 A, which is small compared with the DC currentof ∼1 kA flowing in the global circuit.) Füllekrug (2004) has recently shownthat intense positive discharges removing ∼100 C on the ∼1 minute time scaleshould decrease the geoelectric field near the Earth’s surface by ∼10−4 on the1 minute time scale, which could be measurable. Two sprites occurring in oneminute would remove this same amount of charge.

It is not yet evident whether sprites radiate elsewhere in the electromagneticspectrum. In particular, it is not known whether photons more energetic thanthose in the ultraviolet part of the spectrum (wavelength ∼100 nm) that are


required to photoionise molecules at the head of a sprite streamer discharge(Liu and Pasko, 2004) could be generated and, if so, by what process.

1.3.3 Summary of Observations

The main features of the observations discussed in this section may be sum-marised as follows.

• Elves may occur at 90 km altitude 0.3 ms after an intense discharge inthe tropics or at middle latitudes; after 1 ms, their radius is ∼300 km.

• Sprites may be generated at 70 (±15) km altitude, above intense thun-derstorms which have discharges bringing positive charge to ground.

• The spatial structure of sprites in the mesosphere ranges from ∼< 0.1 to30 km.

• The temporal evolution of sprites occurs on time scales ranging from

∼<1 ms to ∼100 ms.

• Sprites radiate up to ∼1 MR (MegaRayleigh) of light, primarily in thefirst positive band of molecular nitrogen (red) and in the second positiveband (blue), in the first ms of their life.

• Considering their electrostatic image in the ground, +CG dischargeswhich generate sprites have a charge moment ∼>100 C·km, and a cur-rent moment ∼> 100 kA·km.

• A 1000 C·km charge moment change is equivalent to a lightning dis-charge current of 100 kA flowing horizontally for ∼15 km at a height of5 km, and then flowing to ground, for ∼1 ms.

• Sprites can radiate a burst of ELF radio energy lasting ∼2 ms; consider-ing their image in the ionosphere, a charge moment change of 500 C·kmis equivalent to a current of ∼5 kA flowing over a distance of 25 km,which corresponds to a current moment change of 250 kA·km.

• Four intense mesoscale convective systems (MCSs), having positivecharges, remove ∼10−4 of the potential difference stored in the globalcircuit on a time scale of one minute.

• Sprites also represent dissipation in the global circuit; two sprites occur-ring in one minute also remove ∼10−4 of the potential difference acrossthe global electric circuit.


1.4 Introduction to Theories and Numerical Modelling ofSprites

1.4.1 Basic Physical Concepts

The energy source for sprites and elves is electric field energy associatedwith lightning. This can be in the form of the quasi-static field due to thedistribution of charge in a thunderstorm, or the EMP pulse from a lightningdischarge. There are two basic theories for the formation of sprites above en-ergetic thunderstorms; these are:

i) conventional (thermal) discharge physics, and

ii) runaway (relativistic) electron discharge physics.

These theories have been outlined by Rowland (1998) and Rycroft (2005),amongst others. The latter theory is more complex than the former (although,when considering details, both are complex). By Occam’s razor, the formeris preferred until it has been demonstrated that it fails to explain a significantobservation.

1.4.2 Computer Modelling Results

Computer codes, both electrostatic and electromagnetic, have been devel-oped by a number of groups to model the response of the upper atmosphereto thunderstorm fields and to lightning discharge currents (the electrostaticcode results are included within the predictions of an electromagnetic model).Maxwell’s equations are solved self consistently through the atmosphere whichhas a modelled conductivity profile. When the transient electric field becomeslarge, the accelerated electrons heat atmospheric molecules by collision; whenit becomes even larger, the greatly accelerated electrons create additional ioni-sation via collisions with neutral molecules.

In the conventional discharge picture, the crucial parameter is the transient(either quasi-static or EMP pulse) electric field at a certain altitude in the meso-sphere divided by the neutral gas density there; this parameter is termed the “re-duced” electric field. When this parameter exceeds a certain value, a dischargespontaneously occurs. Examining the spatial and temporal development of this“reduced” electric field parameter, Figures 7 and 9 of Cho and Rycroft (1998)show clearly how an elve is launched and travels horizontally at ∼90 km al-titude. By having a +CG discharge transferring 100, 200 or 300 C, Cho andRycroft (1998) also show that the process by which the optical emissions aregenerated is very nonlinear. Rycroft and Cho (1998) modelled the ELF/VLFspectrum radiated by a +CG discharge, and found it to be rich near ∼10 Hz(about the fundamental Schumann resonance frequency) and also from 0.1 to0.3 kHz.


Currents ∼100 kA flowing in a strong horizontal lightning discharge (whichcreate large oscillatory vertical electric fields above it) were considered in anelectromagnetic code model by Cho and Rycroft (2001). They emphasised theimportance of the interference at VLF/LF between electromagnetic waves ra-diated directly by the lightning, waves reflected from the ground, and wavesreflected by the ionosphere as a means of creating a spatially structured regionof enhanced “reduced” electric field, the position of which changes apprecia-bly on a time scale of ∼< 0.03 ms. These could generate propagating streamers,see Figure 26 of Cho and Rycroft (2001), and so account for the multiplic-ity of sprites in a region of ∼30 km horizontal extent above an active MCSthundercloud (Lyons et al., 2003).

Liu and Pasko (2004) have modelled in detail the photoionisation phenom-ena occurring at the head of the sprite, where the electric field is very large,and the spatial and temporal structure so caused; these topics are considered inChapter 12 by Pasko.

1.5 Conclusions

The purpose of this chapter has been to introduce the reader to the atmo-sphere, and its spatially and temporally varying properties over a wide rangeof scales, to thunderstorms, to lightning discharges and their ELF/VLF radia-tion, to optical emissions termed elves lasting <1 ms at ∼90 km altitude, andto sprites with a time scale from ∼1 ms up to 0.1 s at altitudes ∼70 (±15) km.Further, the chapter has presented in outline some important published results;it gives some key references.

Acknowledgments

The author appreciates the comments expressed by both the formal and theinformal referees, which have led to significant improvements in the content ofthis chapter.

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[Rycroft, M.J.] Introduction to the Physics of Sprites, Elves and Intense Lightning Discharge

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