Significance of lightning-generated whistlers to inner radiation belt electron lifetimes

Transcription

1 JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 108, NO. A12, 1462, doi: /2003ja009906, 2003 Significance of lightning-generated whistlers to inner radiation belt electron lifetimes Craig J. Rodger Department of Physics, University of Otago, Dunedin, New Zealand Mark A. Clilverd Physical Sciences Division, British Antarctic Survey, Cambridge, UK Robert J. McCormick Department of Physics, University of Otago, Dunedin, New Zealand Received 18 February 2003; revised 27 October 2003; accepted 31 October 2003; published 31 December [1] The behavior of high-energy electrons trapped in the Earth s Van Allen radiation belts has been extensively studied, through both experimental and theoretical techniques. While the evidence for whistler induced electron precipitation (WEP) from the radiation belts is overwhelming, and the mechanisms behind WEP are well understood, the overall significance of WEP on radiation belt loss rates has not been clear. In this paper we investigate the L-shell variation and significance of WEP-driven loss of Van Allen belt electrons by combining in situ measurements of electron precipitation, local WEP rates determined from Trimpi perturbations, and global lightning distributions. Our modeling suggests that long-term WEP driven losses are more significant than all other inner radiation belt loss processes for electron kinetic energies in the range kev in the L-shell range L = These calculated lifetimes are comparable to the observed decay rates of artificially injected high-energy electrons. The upper energy limit of the WEP significance range increases with decreasing L to 225 kev at L = 2. For electron energies above this range manmade VLF transmitters and plasmaspheric hiss should dominate over all other loss processes. However, as our lifetimes are based on rather conservative parameter estimates, these conclusions should represent the lower bounds for the energy ranges over which WEP losses are significant. For lower L-shells the coupling of lightning activity to the production of WEP events rapidly decreases, such that by L 1.7 WEP will be unimportant in the overall loss processes. INDEX TERMS: 2716 Magnetospheric Physics: Energetic particles, precipitating; 2730 Magnetospheric Physics: Magnetosphere inner; 2736 Magnetospheric Physics: Magnetosphere/ionosphere interactions; 2483 Ionosphere: Wave/particle interactions; 3304 Meteorology and Atmospheric Dynamics: Atmospheric electricity; KEYWORDS: whistlers, inner radiation belt, electron precipitation, Trimpi, lightning, wave-particle interaction Citation: Rodger, C. J., M. A. Clilverd, and R. J. McCormick, Significance of lightning-generated whistlers to inner radiation belt electron lifetimes, J. Geophys. Res., 108(A12), 1462, doi: /2003ja009906, Introduction [2] The behavior of high-energy electrons trapped in the Earth s Van Allen radiation belts has been extensively studied, through both experimental and theoretical techniques. During quiet times, energetic radiation belt electrons are distributed into two belts divided by the electron slot at L 2.5, near which there is relatively low energetic electron flux. In the more than four decades since the discovery of the belts [Van Allen, 1997], it has proved difficult to confirm the principal source and loss mechanisms that control radiation belt particles [Walt, 1996]. It has been recognized for some time that the loss of radiation belt Copyright 2003 by the American Geophysical Union /03/2003JA electrons in the inner magnetosphere is probably dominated by both pitch angle scattering in wave-particle interactions with whistler mode waves and Coulomb scattering. Collisions with atmospheric constituents are the dominant loss process for energetic electrons (>100 kev) only in the innermost parts of the radiation belts (L <1.3)[Walt, 1996], as demonstrated by the comparison of calculated decay rates with the observed loss of electrons injected by the 1962 Starfish nuclear weapon test (Figure 7.3 of Walt [1994]). For higher L-shells, radiation belt particle lifetimes are many orders of magnitude shorter than those predicated due to atmospheric collisions, such that other loss processes are clearly dominant. Above L 1.5 Coulomb collision-driven losses are generally less important than those driven by whistler mode waves, including plasmaspheric hiss, lightning-generated whistlers, and manmade transmissions [Abel SMP 22-1

2 SMP 22-2 RODGER ET AL.: INNER RADIATION BELT WEP LOSSES and Thorne, 1998]. The electron slot is believed to result from enhanced electron loss rates occurring in this region. Much attention has been given to the role of plasmaspheric hiss in maintaining the electron slot [Lyons and Williams, 1984], although it has been suggested that lightning generated whistlers may also be significant in this region [e.g., Lauben et al., 2001]. Other calculations suggest that all three types of whistler mode waves may play important roles in the loss of energetic electrons in the inner magnetosphere [Abel and Thorne, 1998]. Here we shall focus upon the radiation belt electron losses due to lightning-generated whistlers. [3] Whistler-induced electron precipitation (WEP) from the Van Allen radiation belts is a known troposphere to magnetosphere coupling mechanism. The energetic electron precipitation arises from lightning produced whistlers interacting with cyclotron resonant radiation belt electrons in the equatorial zone [Tsurutani and Lakhina, 1997]. Pitch angle scattering of energetic radiation belt electrons by whistler mode waves can drive these electrons into the bounce loss cone [Walt, 1994], and result in their precipitation into the atmosphere. At this time, reports on in situ satellite measurements of WEP losses are fairly rare. S81-1 satellite measurements in the energy range from 6 to 950 kev have reported short bursts (0.2 s) of magnetically guided and focused electrons in the bounce loss cone, primarily in the range 75 to 300 kev. A total of 15 WEP events were found to be correlated on a one-to-one basis with single-hop whistlers observed at Palmer, Antarctica [Voss et al., 1998], while the several hundred WEP events observed were correlated with active lightning. These WEP events were found to be globally correlated with regions of high lightning activity, principally in the range 2 < L < 3. A portion of the WEP electrons were observed to backscatter from the atmosphere and bounce repeatedly between the northern and southern hemispheres, leading to a series of decreasing WEP bursts into both hemispheres over a period of 2 3 s. Most recently, SAMPEX and UARS satellite data have revealed hundreds of cases where enhanced losses of kev electrons were associated with individual thunderstorms [Blake et al., 2001]. The latter authors have argued that the extensive amount of observed precipitation suggests that WEP, driven by global thunderstorm activity, may be a significant factor in controlling the lifetime of energetic electrons in the inner belt and slot regions. [4] A complementary technique to study WEP relies upon the ionospheric modifications produced by secondary ionization just below the D-region of the ionosphere. Ionospheric changes alter the propagation of very low frequency (VLF) waves trapped inside the Earth-ionosphere waveguide and lead to perturbations in the amplitude and/or phase of fixed frequency subionospheric VLF transmissions, termed Trimpi perturbations (see the review by Rodger [2003] and references therein). The perturbations begin with a relatively fast (1 s) change in the received amplitude and/or phase, followed by a slower relaxation (<100 s) back to the unperturbed signal level due to the recombination of additional ionization. As classic Trimpi are observed only for VLF propagation under nighttime ionospheric conditions, it is believed that the WEP is not energetic enough to make significant changes to the daytime D-region ionosphere, although the precipitation should still be occurring. Trimpi perturbations permit observers to study WEP and the chemistry of the nighttime lower ionosphere, from locations remote from the actual precipitation region. [5] Until recently there was significant uncertainty as to the typical size of the D-region patch altered by WEP, which complicated the use of Trimpi perturbation observations in radiation-belt studies. Previous estimates had suggested patch sizes of the order of 50 km 200 km, with the major axis lying parallel to lines of constant L shell (see Clilverd et al. [2002] and references therein). More recently, Trimpi perturbations have been used to shown that WEP produced patches are large (at least 600 km 1500 km) [Clilverd et al., 2002]. These sizes are considerably larger than the observed dimensions of the footprint of the field-aligned ionization irregularities, termed whistler ducts, which trap whistlers and extend between the conjugate hemispheres. In situ satellite observations suggest that ducts have latitudinal extents of 25 km at 300 km altitude [Angerami, 1970], and thus one might have expected the ionospheric patch altered by WEP to have similar dimensions. However, large D-region patch dimensions have been suggested through a quasi-trapped whistler propagation theory in which ducted energy spreads at the magnetic equator [Strangeways, 1999], resulting in whistler-mode signals which have leaked outside their whistler duct still contributing to the horizontal lateral extent of WEP. Such leakage produces a significantly larger precipitation footprint than the actual dimensions of the whistler duct. A different mechanism also leading to large WEP patch dimensions comes through the precipitation caused by obliquely (nonducted) propagating whistlers, creating an ionospheric disturbance of 1000 km spatial extent [Lauben et al., 1999; Johnson et al., 1999]. As yet, experimental studies have been unable to draw a definitive conclusion as to whether the whistlers leading to most WEP (and hence Trimpi) are ducted or nonducted [Clilverd et al., 2002]. [6] Estimates of electron lifetimes due to WEP-driven losses using ground-based whistler observations as a proxy for WEP events have assumed that the wave particle interaction takes place in narrow plasmaspheric ducts, such that each whistler influences only a small region of the radiation belts, creating an ionospheric patch that is small (370 km 2 )[Burgess and Inan, 1993]. Due to the significant experimental uncertainties there has been disagreement between the results of such studies. While Burgess and Inan [1993] found that radiation belt losses driven by ducted whistlers might be comparable with those from plasmaspheric hiss, a similar study by Smith et al. [2001] concluded that ducted whistlers were not significant in overall inner-belt losses. However, the recent findings of large WEP-produced D-region patches suggests that the section of radiation belt influenced by each whistler will also be large, and thus WEP may play a more significant role in radiation belt loss processes than previous estimates. Using Trimpi perturbations as a proxy for WEP activity and an approximate WEP flux profile, WEP driven losses were found to be more significant than all other inner radiation belt loss processes at L = 2.23 for electron kinetic energies in the range kev [Rodger and Clilverd, 2002]. [7] While the evidence for whistler induced electron precipitation is overwhelming, and the mechanisms behind WEP are well understood, the overall significance of WEP

3 RODGER ET AL.: INNER RADIATION BELT WEP LOSSES SMP 22-3 on radiation belt loss rates has not been clear. In this paper we investigate the significance of WEP-driven loss of Van Allen inner-belt electrons by combining experimental satellite results, Trimpi observations, and global lightning distributions. 2. WEP Losses From a Single Event [8] One of the most comprehensive studies of the dynamics of an individual WEP burst made use of data from 2 to 1000 kev particle spectrometers in the Stimulated Emissions of Energetic Particles (SEEP) experiment onboard the low-altitude S81-1 satellite. This detailed examination reported on a SEEP-observed WEP event ( Event D ) that occurred at 0333 UT, 9 September 1982, at L = 2.23 [Voss et al., 1998]. It was found that during the WEP burst electrons cm 2 with kinetic energies >45 kev were lost into the atmosphere. Over the WEP burst 0.001% of the total number of >45 kev energetic electrons in the L = 2.23 flux tube were lost through WEP, depositing 10 3 ergs cm 2 into the atmosphere. [9] It is known that the magnitude of the precipitation energy flux for a WEP event is directly proportional to the trapped particle flux level in the radiation belts near the edge of the loss cone [Inan et al., 1985] and is also proportional to the whistler wave equatorial magnetic field intensity, B w, for most realistic wave fields [Inan et al., 1982]. The L-shell variation of WEP losses can therefore be described by including the expected L-variation of the loss cone energy spectra and whistler wave B w. The energetic electrons present in a WEP burst depend strongly upon the L shell of whistler propagation and whistler frequency spectrum [Chang and Inan, 1985]. For cyclotron resonance between an energetic electron trapped in the Van Allen belts and a whistler mode wave of angular frequency w, propagating through the plasmasphere with local electron gyrofrequency w B, the relativistic resonance equation will hold [Chang and Inan, 1985], gw þ gkv // ¼ w B Here g is the relativistic factor for an energetic electron with velocity v, g =(1 v 2 /c 2 ) 1/2, and v // is the velocity parallel to the geomagnetic field line, determined by the electron pitch angle a. For longitudinal whistler mode propagation dominated by the cold plasma component (with plasma frequency w p ), the whistler wave number k, is given by k ¼ w p c rffiffiffiffiffiffiffiffiffiffiffiffiffiffi w : w B w While wave particle interactions can occur well away from the equatorial region, an estimate of the resonant near loss cone electron energies can be obtained by assuming equatorial resonance at the loss cone angle, since typical whistler-induced pitch angle scattering leads to small changes in pitch angle (a 1 [Inan et al., 1989]). Using a dipole magnetic field we may determine the loss cone angle and gyrofrequency, while the plasma frequency is found through a cold plasma model (described below). Thus, given any specific whistler frequency and L-shell the resonance velocity of an energetic electron undergoing ð1þ pitch angle scattering may be found from [Chang and Inan, 1983], 1=2 wk þ w 2 k 2 þ w 2 B w2 k 2 þ w 2 B c 2 cos 2 a v == v R ¼ k 2 þ w 2 B c 2 cos 2 a In order to determine the typical electron energies precipitated in a typical WEP burst, the frequency range of a typical whistler needs to be specified. As this is uncertain, we will consider the effects of whistlers spanning the frequency ranges khz and khz, which should be representative. We acknowledge that this is an important parameter, which would benefit from experimental attention. [10] It has been reported that SEEP Event D was unusually strong, lying in the top 10% of events observed on S81-1 [Burgess and Inan, 1993]. The whistler associated with Event D was observed at a ground station, providing an estimate of its equatorial field strength (34 pt), found to be 3 times larger than average whistlers [Burgess and Inan, 1993]. As noted earlier, scattering is linearly related to B w, and as such this strong whistler would have been expected to produce a non-typical WEP burst. On the basis of these observations we take a typical WEP burst at L = 2.23 to last 0.2 s and have a mean precipitation energy flux of ergs cm 2 s 1. In order to determine the WEP precipitated flux spectrum due to a whistler with given frequency range and L-shell we must determine the equatorial magnetic field and trapped flux population Whistler Wave Magnetic Fields [11] Both the frequency range, and the intensity of whistler frequency components vary with L. Assuming that the power is uniformly distributed across the whistler duct from its entry point, the power present at the geomagnetic equator, P eq, will be dependent upon the geometry of geomagnetic flux tube. This is taken from a reference height of 100 km altitude (where 100 km = kr E ), such that the entry point power is P 100km. Thus after Smith et al. [2001], ð2þ P eq ¼ P 100km ð1 þ kþ 3 pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi L þ ð kþ=l : ð3þ The equatorial whistler wave magnetic field intensity at a given frequency, B w ( f ), is also dependent upon the plasmaspheric refractive index, n eq ( f ), so that B w qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ðf ; LÞ / n eq ðf ÞP eq : ð4þ This proportionality is calculated by taking P 100km in equation (3) to be given by the lightning power spectral density, P lightning / exp[ (log 10 ( f/5.0)) 2 /(0.4) 2 ], where f is given in khz [Pierce, 1977]. As we do not attempt to determine the absolute intensity of P 100km we are limited to determining the relative frequency variation of the whistler wave equatorial magnetic field intensity at a given frequency, B w ( f ). Thus absolute values of B w ( f, L) are

4 SMP 22-4 RODGER ET AL.: INNER RADIATION BELT WEP LOSSES Figure 1. Plasmaspheric number-density of low-energy electrons in electrons per cubic centimeter. The heavy line marked with triangles shows the electron number density adopted for the calculations. The lighter line describes electron lifetimes under Coulomb scattering due to the plasmaspheric number density profiles for 250 kev electrons. not considered, although this has been undertaken previously [e.g., Smith et al., 2001]. Note that the process outlined above neglects any frequency dependent absorption which takes place as the lightning wave propagates through the ionosphere, as discussed further in section 6.1. The plasmaspheric refractive index, n eq ( f ), is calculated following the expressions in the work of Smith et al. [2001], taking the plasmaspheric equatorial thermal electron density as N eq = 1000 (4/L) 4, where N eq is given in electrons per cubic centimetre (heavy line marked with triangles in Figure 1). This plasmaspheric electron density is selected to allow comparison with calculations undertaken by Lyons et al. [1972], as discussed in section 5. [12] In order to determine the relative contribution of differing electron energies to the precipitation energy flux caused by the variation in B w ( f, L) we take the following step-by-step approach: (1) equation (2) is used to determine the electron energy which resonates with a given whistler wave frequency at this L-shell. (2) The intensity of the whistler wave at this frequency in the equatorial plane, B w ( f, L), is found using equation (4) and (3) taking P lightning to be representative of P 100km. B w ( f, L) is then taken relative to the whistler intensity at 5 khz (the peak lightning power), to provide a relative intensity. (3) The relative whistler wave intensity for a given f and L is finally used to weight the electron flux in the precipitated spectrum at the energy determined for this frequency from (2). [13] From this process we include the variation of WEP precipitation flux due to changing whistler wave intensity with frequency, hence altering the relative contribution at each resonating energy. In order to describe a realistic WEP burst, one must also include the large variations with energy in the trapped flux population. This is considered in the section below WEP Energy Spectra [14] At each resonant electron energy the precipitated energy flux is directly proportional to the trapped particle population near the edge of the loss cone [Inan et al., 1985]. If we assumed that B w ( f ) did not vary with L-shell [e.g., Pasko and Inan, 1994], one could determine the relative differential energy and number flux of WEP from the L- and E-variation of the near loss cone trapped energetic particle distribution. Having taken into account the variation in B w ( f, L) as described above, the relative differential energy flux can be determined from the near-loss cone trapped flux, and thus the absolute differential energy flux (and hence number flux) for a given WEP burst can be found from the experimentally observed total precipitation energy flux (section 2). As each WEP burst removes only a small fraction of the total electrons present in a flux tube, the average (undisturbed) trapped energetic particle distribution will probably be the most relevant when estimating WEPdriven lifetimes. This is a similar approach to that taken earlier by Rodger and Clilverd [2002], although these authors did not consider the varying contribution of different electron energy populations due to the frequency varying intensity of their khz whistler waves. [15] In order to determine the significance of WEP-driven losses to the inner-belt, we make use of the empirical AE-5 Inner Zone Electron Model [Teague and Vette, 1972]. This model provides analytic functions for the unidirectional differential energy flux and is based on data collected during solar maximum conditions. The analytic functions in AE-5 describe quiet-day electron fluxes for 1.3 L 2.4 and are based on observations of electrons with E < 690 kev. For our purposes AE-5 is more useful than the current standard trapped electron model for solar max conditions, AE-8MAX [Vette, 1991], as the more modern model does not provide tabular functions for the primary parameters. We note, however, that the two models produce omnidirectional integral fluxes which are within 5% of one another over L =2 3, well within the suggested error estimates for AE-8 of about a factor of 2 [Vette, 1991, pg. 4 2]. A comparison between the AE-5 analytic model and AE-8MAX shows that the analytic expressions provide a reasonable representation of the energy spectra for electron kinetic energies less than 800 kev. At higher electron energies AE-5 seriously underestimates the particle fluxes present. This was not considered by Rodger and Clilverd [2002] who calculated lifetimes up to 1.5 MeV based on the AE-5 analytic model. We note that results presented in their study beyond 800 kev do not represent reality, although their conclusions were restricted to electrons below that kinetic energy. [16] We use the AE-5 analytic model to determine the population of trapped electrons in the pitch angle range from the loss cone angle (a LC )to(a LC + a). Theoretical modelling has shown that most electrons undergoing pitch angle scattering, due to whistler waves, experience a net scattering of While some electrons are scattered by >1, these generally make up a very small component of the overall flux [e.g., Inan et al., 1989]. We therefore take a =0.5, and thus determine from AE-5 the near loss cone trapped particle population at the resonant energies for a given whistler, and L-shell Precipitation Energy Flux Variation With L [17] As outlined above, the absolute differential energy and number flux for a WEP burst can be determined in the

5 RODGER ET AL.: INNER RADIATION BELT WEP LOSSES SMP 22-5 Figure 2. Differential energy flux of precipitated electrons in a WEP event versus energy for different L-shells of whistler-particle interaction and differing frequency ranges of the whistler wave. region over which WEP activity has been experimentally observed (1.7 L 2.4). The differential precipitated energy flux for a single 0.2 s WEP burst at varying L-shells is shown in Figure 2 for a whistler spanning khz (Figure 2a) and khz (Figure 2b). The number flux of the WEP burst (in electrons cm 2 s 1 ) increases with increasing L, although the energy spectra of the precipitation electrons seen in Figure 2 softens with increasing L, as expected and observed [Vampola and Gorney, 1983; Clilverd et al., 1999b]. Increasing the whistlers upper frequency decreases the lowest resonant energy and hence decreases the electron energy at which the peak energy flux lies. Experimentally observed WEP activity occurs primarily in the plasmasphere between L = 2 and L = 3, peaking at L 2.4 [Voss et al., 1998]. While SEEP reported no WEP events below L 1.8, Figure 2 includes the predicted precipitation fluxes at L = 1.7 to allow comparison with other L-shells. [18] Previous studies have estimated the differential energy flux of WEP bursts for differing L-shells and whistler frequency ranges [e.g., Pasko and Inan, 1994, Figure 7] making use of a simplifying set of reasonable assumptions to determine the energy spectrum of the WEP burst in the absence of information on magnetospheric whistler wave intensity [Inan et al., 1988]. The WEP energy spectra in Figure 2 differ from those shown in Figure 7 of Pasko and Inan [1994] as they assume a larger total energy flux, a different plasmaspheric equatorial electron density and different trapped particle flux parameters. In addition, the whistler wave had constant intensity over the specified frequency range instead of one that varies with f, as in this study. However, we note that if we make use of the same parameter set (except those for the trapped flux, which we take from AE-5), we can essentially reproduce Figures 6 and 7 of Pasko and Inan [1994]. 3. Case Study: SEEP Event D [19] In order to test the validity of our assumptions in section 2, we examine the SEEP-observed Event D. A detailed analysis of this event has been previously undertaken using test-particle modeling of the gyroresonant scattering process [Inan et al., 1989], using a whistler spanning khz, an equatorial loss cone angle of a LC 14.15, and a trapped particle population with e-folding energy E 0 = 120 kev. Test-particle modeling predicted a precipitating electron spectra distributed between 90 and 300 kev. The differential electron energy spectra for three WEP events (including event D) were examined in the SEEP experimental data, showing a broad distribution from kev, with a maxima at approximately 150 kev [Voss et al., 1998]. Our estimate of the differential electron number flux precipitating in event D is shown in Figure 3. Note that the e-folding energy determined by Inan et al. [1989] is roughly two and half times bigger than that found from the spectra of the near-loss cone trapped particle population given by AE-5, leading to the WEP burst (Figure 3) with a greater high-energy electron contribution than would be predicted by a direct application of the AE-5 spectra (outlined in section 2, leading to the fluxes shown in Figure 3. Differential electron number flux (electrons cm 2 s 1 kev 1 ) estimated for the S81-1 SEEP observed WEP burst Event D due to a whistler spanning khz.

6 SMP 22-6 RODGER ET AL.: INNER RADIATION BELT WEP LOSSES Figure 4. Estimated diurnal variation of lightning activity in the region which causes Trimpi perturbations observed at Faraday. Taken from NLDN data for June August 1996, the dashed line shows the daily mean flash rate. Figure 2). The lowest electron energy component present in Figure 3 is 90 kev, due to the upper whistler wave frequency and equatorial cold plasma density. Increasing the upper whistler wave frequency to 7 khz would lead to the lowest energy electrons present in the burst decreasing to 75 kev. The precipitating number flux shown in Figure 3 peaks at 140 kev, and is dominated by electrons with energies from kev, which appears rather similar to the precipitation spectra shown in Plate 1 of Voss et al. [1998]. Over a 0.2 s burst with the differential electron number flux shown in Figure 3, electrons cm 2 would be lost from the radiation belts, 70% of that experimentally reported ( electrons cm 2 ). For comparison purposes, we estimate that a whistler spanning khz would precipitate electrons cm 2.On this basis we conclude that we can adequately describe the loss of energetic electrons from the radiation belts in WEP events and may be somewhat underestimating the total magnitude of WEP events. 4. Lightning Driven WEP Rates [20] Earlier studies have used ground based whistler occurrence rate observations as a proxy for WEP events leading to energetic electron losses [e.g., Burgess and Inan, 1993; Smith et al., 2001]. This approach may not be particularly reliable, given the suggestion that nonducted whistlers, which are unlikely to be observed on the ground in the conjugate hemisphere, may play an important role [Lauben et al., 1999]. In addition, these studies made use of much smaller ionospheric patches modified by WEP than is indicated by recent reports. We instead make use of Trimpi observations as a more direct proxy for WEP activity leading to ionospheric modifications. The uncertainties in the use of Trimpi observations as a WEP proxy are discussed in section Average Trimpi Rates in the Antarctic Peninsula [21] An indication of the long-term average WEP rate can be taken from Trimpi rate observations at Faraday, Antarctica (65.3 S, 64.3 W, L = 2.5) made over 115 days from 1993 and 1994 [Rodger et al., 2002]. As Trimpi are not observed for daytime ionospheric conditions, only days in March through to September were included, avoiding the Antarctic summer. Optimal experimental conditions for VLF subionospheric observations at Faraday occur at UT, at which time the influence of lightning noise levels is lowest [Clilverd et al., 1999a]. In this time window the most likely rate was one Trimpi perturbation per min, while on 30% of days the rate was greater than 2 min 1, and on only 10% of the days was the rate higher than 3 min 1 [Rodger et al., 2002]. Trimpi perturbations observed in the Antarctic Peninsula are known to be strongly associated with high-current cloud to ground lightning occurring around 34 N, 76 W [Clilverd et al., 2002], close to the footprint of L 2 flux tubes. We thus argue that the WEP occurrence rate in the Antarctic Peninsula sector will vary across the day in a similar manner to lightning activity in the Trimpi perturbation source region Diurnal Variation of Trimpi Source Lightning [22] To examine the strong diurnal variation of lightning activity in the Trimpi perturbation source region is examined using lightning data from the coastal region of eastern United States. The U.S. National Lightning Detection Network (NLDN) has operated since A network of 106 receiving stations is connected to a central processor that records the time, polarity, signal strength (proportional to peak current), and number of strokes of each cloud-toground lightning flash detected over the continental United States. In 1996 the NLDN had a typical accuracy of 0.5 km, with a detection probability of between 80 and 90% (for return stroke peak currents >5 ka), varying slightly by region [Cummins et al., 1998]. NLDN observations indicate that lightning activity occurring over land peaks during the afternoon and early evening ( local time (LT)), while over water the peak in this dataset occurs at night and in the early morning hours (0400 to 1200 LT) [Orville and Huffines, 2001]. [23] The diurnal variation of lightning activity in the Faraday Trimpi perturbation source region was estimated from representative diurnal density rates (i.e., per km 2 per min) in east coast U.S. above land and above water regions using June August 1996 NLDN data. These ocean and land flash densities are similar to the NLDN mean annual flash densities, taking into account that 65% of NLDN-observed lightning occurs during the months of June August [Orville and Huffines, 2001]. The diurnal variation of lightning which may lead to Faraday-observed WEP is found by taking a 10 6 km 2 zone around the source location reported by Clilverd et al. [2002]. The results are shown in Figure 4. The diurnal variation is broadly peaked, with the overall daily mean being 15.6 flashes/min. The mean flash rate in the time period UT is 16.3 flashes/min, only 4% greater than the daily mean Mean WEP Rate From Faraday Trimpi [24] Previously, a constant 1/min average WEP rate throughout the day was assumed from the Faraday Trimpi observations [Rodger and Clilverd, 2002]. However, we note that this 1/min Trimpi rate was based on observations in months that have high lightning activity in this region

7 RODGER ET AL.: INNER RADIATION BELT WEP LOSSES SMP 22-7 Figure 5. The annualized geographical distribution of total lightning activity determined from 5-years of OTD data in units of flashes km 2 yr 1, after Christian et al. [2003]. Superimposed are the 100 km altitude footprints of the L-shells L = 1.7, 2, and 2.4, moving outwards from the equator. [Orville and Huffines, 2001]. Strictly, Faraday Trimpi rates should be higher in the northern summer months, showing strong modulation with seasonal changes in the source lightning activity. This is a valid experimental problem, but due to the large number of factors involved with Trimpi production, appears to be experimentally difficult to confirm. [25] The seasonality of global lightning activity has been examined using Optical Transient Detector observations, described in greater detail below. These observations suggest that on average, the lightning activity levels from March September in the Faraday Trimpi producing region are 30% higher than the annual mean activity level. Therefore we take 0.79 WEP/min as the representative rate for mean WEP activity affecting Faraday flux tubes at all times throughout the year Global Average WEP Rates [26] As the energetic electron lifetime is likely to be considerably longer than the azimuthal drift rates for our kinetic energies, any given flux tube will have drifted round the Earth many times during an electron lifetime. Therefore we may use a global average WEP rate to characterize the loss process. The large size of observed WEP-modified ionospheric patches indicate that WEP events produced by a single lightning stroke affect a range of L-shells. Trimpi observed at Faraday are caused by WEP-modified ionospheric patches stretching from L 2.1 to L 2.6, linked to lightning at L 2[Clilverd et al., 2002]. [27] Recently, dedicated satellite observations have been undertaken to detect and locate lightning discharges from low-earth orbit. Five years of Optical Transient Detector (OTD) observations have been combined to produce average geographical flash density distributions, both annually and seasonally [Christian et al., 2003]. Figure 5 shows annualized geographical distribution of total lightning activity (in units of flashes km 2 yr 1 ) taken from the OTD Low Resolution Full Climatology dataset. Superimposed upon this plot are the L-shell footprints at 100 km, for L = 1.7, 2, and 2.4, determined for eccentric geomagnetic dipole coordinates [Fraser-Smith, 1987]. From this figure we have determined the longitudinally varying mean lightning activity levels at 100 km altitude in a 2.5 geomagnetic latitude band centered on the footprints of the field lines of L = 1.7, 2, and 2.4 (Figure 6). The size of the band is taken from Clilverd et al. [2001] from their observations of welldefined Trimpi correlated against source lightning location. In Figure 6 the total activity (heavy line), is shown, along with that for only the northern (light) and southern (dashed) hemispheres, for each of the 3 L-shell contours considered. The longitude of the Antarctic Peninsula is marked by an arrow. Clearly, lightning in the North American sector is the dominant region of lightning activity for L = 2 and L = 2.4, with southern hemisphere activity making small contributions. The situation is less extreme for the lowest L-shell considered. Here, Australia dominates over northern hemisphere sources in the longitudes 180 E eastwards through to 90 E, Southern Africa is an equal contributor to northern hemisphere sources ( E geomagnetic longitude), while North America dominates in the American longitudes. Note that lightning activity levels increase for more equatorial locations, as expected from the OTD observations [Christian et al., 2003]. [28] Making use of the lightning activity across these L-shells, we can estimate the global mean daily WEP rates, assuming that the WEP rate is directly linked to lightning activity around the base of the field line. This assumption is discussed further in section 5.2. The global mean daily WEP rates found are given in Table 1. Typically global flash rates at these latitudes are about one-third to one-half of those of North American longitudes, and thus we estimate that the global WEP rates will have a similar ratio to that of lightning activity. For example, the lightning activity levels occurring at L = 2 in American Longitudes (10.5 fl.km 2 yr 1 ) leads to the mean WEP activity affecting Faraday flux tubes found in subsection 4.3. As the global average

8 SMP 22-8 RODGER ET AL.: INNER RADIATION BELT WEP LOSSES lightning activity level at L =2is36% of that in American Longitudes at L = 2, we expect the global mean WEP rate to be 36% of the mean WEP activity affecting Faraday flux tubes, as shown in Table Determination of Lifetimes From Loss Rates [29] We follow previous authors and define the energetic electron lifetime, t, as the time in which the flux tube electron population at a given L and energy would drop to 1/e of its original density, assuming that pitch angle diffusion near the bounce loss cone is adequate to maintain the percentage flux losses at a constant rate [e.g., Burgess and Inan, 1993]. Other source or loss processes are not included in our estimate for t. The undisturbed flux tube electron population at a given L and energy is found by first determining the differential number of electrons in a magnetic flux tube of 1 square centimeter in area at the equator plane, N(E, L), given by NðE; LÞ ¼ Z p=2 0 j eq a eq ; E tb a eq ; E 2p cos aeq sin a eq da eq ; ð5þ where j eq is the differential directional electron flux in the equatorial plane determined from AE-5 and t b is the full bounce period [Voss et al., 1998]. The differential number of electrons in a tube having unit area perpendicular to B at the top of the atmosphere is obtained by multiplying the equatorial density from equation (5) by the ratio of the magnetic field values at 100 km altitude to that at the equator. This provides the undisturbed flux tube electron population at a given energy in a magnetic tube having one square centimeter cross section perpendicular to B at 100 km. For each resonating energy the differential electron number flux due to a 0.2 s WEP burst found for a specified L-shell and whistler frequency range as described in section 2 is removed from the trapped flux tube electron population at the rate determined in section 4.4 (shown in Table 1) until the population has decreased to 1/e of the original density, thus determining t for this L and electron kinetic energy. This is equivalent to evaluating t = N(E, L)/(dN(E, L)/dt), clearly a more elegant approach. Figure 6. Longitudinal variation of lightning activity determined from the OTD observations for the L-shells of L = 2.4 (a), L = 2 (b), and L = 1.7 (c). The total activity (heavy line), is shown, along with that for only the northern (light) and southern (dashed) hemispheres. The arrow marks the longitude of the Antarctic Peninsula WEP Driven Lifetimes at L =2 [30] The top panel in Figure 7 shows the energetic electron lifetime, t, forl = 2. The solid lines in this plot show the estimated lifetimes due to whistlers spanning khz (heavy line) and khz (light line), respectively. Also shown in this figure is an estimate of the electron lifetime due to Coulomb collisions, t c (dashed line), between energetic radiation belt electrons and low-energy plasmaspheric electrons, given by (after Lyons and Thorne [1973]), t c ¼ E 3=2 N 1 eq ; where in this equation t c has units of seconds, E is in kev, and N eq is in electrons per cubic centimeter. The L variation of t c for 250 kev electrons is shown as the light line marked with circles in Figure 1. Figure 7 also shows the calculated ð6þ

9 RODGER ET AL.: INNER RADIATION BELT WEP LOSSES SMP 22-9 Table 1. Global Average Values of WEP Event Rates for Varying L-Shells, Determined From Varying Lightning Activity With Longitude a L-Shell Lightning Activity, fl km 2 yr 1 American Longitudes Global Average Global Mean WEP Rate, per min a The absolute global rates are found using the experimentally observed L = 2 WEP rate from the Antarctic Peninsula due to lightning at American longitudes (section 4.3). values of t taken from Lyons et al. [1972, Figure 7] due solely to plasmaspheric hiss (shown in Figure 7 as diamonds). Note these lifetimes are somewhat approximate, having been extrapolated from the curves shown in Figure 7 of Lyons et al. [1972], in some cases beyond the limits of the figure axes. A more recent set of papers have used different, and probably updated, representative wavefields to calculate typical t values, which are generally lower than those of Lyons et al. [1972]. The diamonds shown in this figure are lifetimes reported for a combination of plasmaspheric hiss, lightning generated whistlers, manmade VLF transmissions, and Coulomb scattering [Abel and Thorne, 1998, Figure 10; Abel and Thorne, 1999, Figure 9]. While the Abel and Thorne studies did include losses generated by lightning generated whistlers a rather low occurrence rate was used in comparison with that employed in our study. For this reason our WEP-driven lifetimes are substantially shorter from those reported by Abel and Thorne [1998, 1999]. [31] As shown by Figure 7a, at L = 2 plasmaspheric hiss will be a more important loss process than Coulomb collisions for electrons with energies greater than 275 kev. However, as shown by the triangles, when considering a larger range of loss mechanisms (and particularly VLF transmitters [Abel and Thorne, 1998]), plasmaspheric hiss is generally less important than other mechanisms at this L-shell over this energy range. We find that WEP is dominant over the other loss mechanisms considered by Abel and Thorne [1998] for electrons with energies spanning kev. This conclusion is largely independent of the whistler s maximum frequency (5 khz or 10 khz), only slightly altering the limits of the energy range over which WEP dominates over the other loss processes considered Lifetimes at Other L-Shells [32] The WEP rates determined at L = 2 were found by comparing the experimentally observed Trimpi rate with lightning density levels at the foot of these field lines. Estimated WEP rates have been determined for different L-shells (section 4) through relative lightning levels and can thus be used to find WEP driven lifetimes at these L-shells. These lifetimes are shown in Figures 7b (L = 1.7) and 7c (L = 2.4), based on the WEP rates in Table 1. We note that this is equivalent to assuming that lightning activity will couple to WEP production at different L-shells in the same way as at L = 2, e.g., through the same availability of whistler ducts. The description of the L-shell variation in coupling is highly uncertain. In situ observations indicate that WEP is rare at low L-shells [Voss et al., 1998], despite high lightning activity (Figure 5), due to increasingly unfavorable gyroresonance conditions [Friedel and Hughes, 1992]. Low-latitude Trimpi observations are rare but may be used to estimate the coupling parameter for L = 1.7. VLF perturbation observations undertaken in July 1991 from Durban, South Africa, found that the Trimpi rate along an approximately L = 1.7 east west path was 2.5/day [Friedel et al., 1993]. We caution that these observations may not include all Trimpi events, as the authors note the noise levels were very high at the Durban site but may also include Trimpi not produced by WEP [e.g., Rodger, 2003]. Nonetheless, the Durban observations suggest that the WEP rate at L 1.7 is 850 times lower than predicted in Table 1 (taking into account seasonal OTD activity levels). The lifetimes for a WEP rate 850 times lower than that given in Table 1 is not shown as in Figure 7 as it 2 orders of magnitude greater than the lifetimes due to Coulomb collisions. As such we conclude that lightning-generated whistlers will play an insignificant role at this L-shell (and for all smaller L-shells). [33] In contrast, at L = 2.4 SEEP measurements suggest that lightning activity (in flashes per year per square kilometer) may be 5.5 times more effective at generating WEP events than lightning activity at L =2[Voss et al., 1998, Figure 11]. This would lead to lifetimes which are 5.5 times lower than shown in Figure 7c (line marked with crosses in this figure). However, at this L-shell the energy range over which WEP losses are more important than other loss processes considered by previous authors and shown by the diamonds and triangles ( kev for the Table 1 WEP rates) is primarily controlled by the range of resonating energies rather than the absolute WEP rate. Thus while energy range over which WEP losses dominates will increase to as much as 180 kev, it cannot extend beyond the range of resonant electron energies, determined by the whistler spectra. We argue that the lifetimes at L = 2.4 will lie closer to the lower figures, and that a reasonable estimate for the energy range over which WEP should dominate at this L-shell will be kev. [34] A key assumption in these calculations has been that the complex geographical distribution of lightning activity can be represented by a global average WEP rate, as the electron populations will drift around the Earth many times over their lifetime. The ratio of the WEP determined electron lifetimes to the azimuthal drift period for near-loss cone electrons trapped in Earth s radiation belts [Walt, 1994, p. 49] is shown in Figure 8. For this figure the whistler frequency span is taken as khz, so these ratios are generally larger for khz whistlers. Even for the lowest energy near-loss cone electrons located at L = 2.4 the smallest electron lifetime due to WEP is 30 drift periods, and hence this assumption is reasonable. 6. Uncertainties in WEP Driven Lifetimes [35] The variation of WEP-driven t with electron energy is strongly determined by the spectra of the WEP event relative to the trapped electron spectrum and the number of precipitated electrons in a WEP burst, as well as the global WEP rate. In the calculations presented in this paper we

10 SMP RODGER ET AL.: INNER RADIATION BELT WEP LOSSES have made use of empirical, or directly experimental, measurements wherever possible to quantify these parameters. There is, however, significant uncertainty in all of these factors, which leads to significant uncertainty as to the importance of WEP over other whistler-mode processes. The prime sources of uncertainty in our calculations are detailed below. Figure 7. Lifetime of energetic electrons in flux tubes at the selected L-shells due to the global mean WEP rates given in Table 1. Lifetimes due to whistlers with differing frequency ranges are shown by heavy (0.5 5 khz) and light lines ( khz). The dashed line shows the estimated lifetime due to Coulomb scattering driven losses, the diamonds indicate the lifetime due to plasmaspheric hiss losses taken from Lyons et al. [1972], while the triangles indicate lifetimes due to multiple whistler mode wave sources taken from Abel and Thorne [1998, 1999]. The line marked with crosses in the lower panel uses a different estimate for the WEP rate, as described in the text Which WEP Spectra? [36] The most significant uncertainties in the WEP-driven lifetimes come from the characterization of the WEP losses, as described in section 2. Detailed analysis of in situ observed WEP events are rare, and it is as yet unclear how representative the SEEP observations are of typical WEP events. This would be a worthy area of further consideration by experimentalists, particularly given the new datasets becoming available (e.g., SAMPEX). [37] In order to estimate the lifetimes we have made use of a trapped electron energy spectrum taken from AE-5. However, the particles fluxes in AE-5 are forced to drop with decreasing pitch angle with a sinusoidal dependence such that the fluxes are zero at the loss cone. Undertaking calculations using AE-5 near the loss cone may introduce additional errors in the modeling. While the calculations described in sections 2.3 and 3 provide confidence in our fluxes, we have also examined our conclusions using an alternative experimentally measured WEP energy spectra. As noted previously, experimental observations immediately prior to SEEP Event D that showed that the differential energy spectrum of trapped electrons could be best described by an e-folding energy of E 0 = 120. Radiation belt electron lifetimes have been calculated at L = 2.23 using E 0 = 120 kev for a 0.2 s WEP burst depositing ergs cm 2 s 1, caused by a whistler spanning khz, using the same whistler-wave spectrum as derived in section 2.1. These lifetimes are shown as the dash-dot line in Figure 9. In the energy ranges of greatest interest, where WEP lifetimes dominate over plasmaspheric hiss ( kev), lifetimes determined using the e-folding spectra are either similar to (at low energies) or lower than those determined using the spectra from the AE-5 loss cone (line marked as Normal in Figure 9) due to the large high-energy component to the WEP spectra caused by this e-folding energy. While the absolute lifetimes are somewhat different, the range of energies over which WEP should be the dominant loss process increases only by kev and so should not affect our general conclusions. As the alternative energy spectrum is based on a single measurement, we favor the use of the trapped spectra derived from AE-5, which involves the direct comparison of the AE-5 trapped population with the AE-5 derived spectra (i.e., like with like). Nonetheless, the selection of spectra and the value of typical precipitation magnitude clearly lead to a significant source of uncertainty in the calculated lifetimes. [38] In our determination of the energy varying electron precipitation, we made use of an experimentally based lightning power spectral density, neglecting any frequency dependent absorption which takes place as the lightning wave propagates through the ionosphere. This absorption will tend to decrease the higher frequency component of the whistler [Helliwell, 1965], making the spectra of a 0.5