Influence of a ground-based VLF radio transmitter on the inner electron radiation belt

Transcription

1 JOURNAL OF GEOPHYSICAL RESEARCH: SPACE PHYSICS, VOL. 8, , doi:.02/jgra.50095, 203 Influence of a ground-based VLF radio transmitter on the inner electron radiation belt R. S. Selesnick, J. M. Albert, and M. J. Starks Received 2 October 202; revised 9 December 202; accepted 2 December 202; published 28 February 203. [] Observed signatures of electron precipitation from the inner radiation belt are shown to be consistent with the theory of resonant scattering by whistler-mode plasma waves, assuming the waves originate in VLF radio transmissions from the ground station NWC. The conclusion is based on a stochastic model of electron transport that includes pitch angle diffusion, radial diffusion, energy loss, and azimuthal drift. The wave scattering causes an increase in quasi-trapped electron intensity, forming the wisp signature, and a corresponding decrease in stably trapped intensity at low altitude. A smaller decrease at high altitude is expected to be obscured by inward radial diffusion. If NWC were shut down, the resulting increase in stably trapped electron intensity would be minimal. Citation: Selesnick, R. S., J. M. Albert, and M. J. Starks (203), Influence of a ground-based VLF radio transmitter on the inner electron radiation belt, J. Geophys. Res. Space Physics, 8, , doi:.02/jgra Introduction [2] Radiation from powerful ground-based VLF radio transmitters is confined mostly within the Earth-ionosphere waveguide, but some escapes into space and propagates through the magnetosphere in the form of whistler-mode plasma waves. Precipitation of radiation belt electrons caused by resonant scattering from these waves has long been inferred [Vampola and Kuck, 978; Koons et al., 98; Imhof et al., 983]. Radiation from the Naval Communication Station Harold E. Holt (call sign NWC) in western Australia is the most effective at electron scattering, because of the station s location (22 S, 4 E, L =.4), transmission frequency (9.8 khz), and high radiated power ( MW) [Kulkarni et al., 2008]. Convincing evidence of precipitation caused by NWC has been obtained by the Instrument Détecteur de Particules (IDP) onboard the DEMETER satellite [Sauvaud et al., 2008; Gamble et al., 2008]. Enhanced precipitating electron intensity as a function of energy and forms a characteristic signature, resulting from the dependence of the resonant energy on local plasma density, which is known as a wisp and is clearly seen in the data. [3] Such precipitation is thought to cause significant loss of inner belt electrons, thus substantially modifying the natural radiation belt [Abel and Thorne, 998]. The NWC station has been in nearly continuous operation since 968, and a detailed understanding of its influence would therefore have some practical value. Much work on losses of inner belt electrons followed measurements of the artificial radiation belt formed from the Starfish nuclear detonation of 962. Ground Space Vehicles Directorate, Air Force Research Laboratory, Kirtland AFB, New Mexico, USA. Corresponding author: R. S. Selesnick, Air Force Research Laboratory, 3550 Aberdeen Ave. SE, Kirtland AFB, NM 877, USA. (richard.selesnick@kirtland.af.mil) 203. American Geophysical Union. All Rights Reserved /3/.02/jgra stations other than NWC were then in operation, but were not thought to be influential in the decay of Starfish electrons [Walt, 964]. In principle, the influence of NWC on the natural radiation belt could be determined by an extended period of nonoperation, as has occurred for maintenance reasons [Li et al., 202], but limited trapped electron data and natural intensity variations complicate the analysis. However, with the theory of resonant wave-particle interactions, it is possible to predict the outcome. The goal of this work is to find a model of radiation belt electron transport, including scattering by waves from NWC, that can reproduce the wisp signature and is generally consistent with inner belt electron data. Then the model can be used to determine the influence of NWC on the trapped electron intensity. 2. Data [4] A typical wisp signature of electron scattering, observed by IDP in March 20, is shown in Figure a (for a description of IDP, see Sauvaud et al., [2006]). Enhanced electron intensity is observed in a narrow range of L values, between ~.6 and 2, for each kinetic energy from ~0 to 375 kev. The scattering is presumed to have occurred near the NWC longitude of 4 E, and the electrons then drifted eastward to the observation longitude near 250 E. At this time IDP was observing electrons exclusively within the drift loss cone (DLC), so all of the observed electrons were destined to soon reach the dense atmosphere on the western side of the South Atlantic Anomaly (SAA). Barring additional scattering, they would then rapidly lose energy and be lost from the radiation belt by precipitation into the atmosphere. [5] Waves from NWC propagate through the ionosphere primarily at night [e.g., Starks et al., 2008]. The effect of this in creating the wisp is seen in Figure 2, where electron intensity at a fixed kinetic energy of 62 kev is shown as a function of L and dipole longitude. ( is measured relative to the geomagnetic dipole axis, but uses the same prime meridian and is nearly the same as geographic 628

2 E (kev) IDP 20/ 3/ 3, log[electrons (cm 2 sr s kev) - ] (a) Data (b) Model effect of NWC-induced precipitation losses, as will be shown below. Similar minima are also evident upon close inspection of the SAA data in Figure 2. (Electrons observed in the SAA generally are stably trapped because their mirror points have higher altitudes at all other longitudes.) [8] The data in Figures a and 3 will be compared to model simulations described in the following sections. The model requires initial condition data, examples of which are shown in Figure 4. They are energy spectra of stably trapped electrons at selected L values from ~ year prior to the data of the previous figures, observed by IDP in the SAA. 3. Model 3.. Pitch Angle Diffusion [9] Whistler-mode waves from NWC are assumed to be at a fixed frequency o with index of refraction m = kc/o given by E (kev) Figure. (a) A wisp in DEMETER/IDP data, taken in the Southern Hemisphere near longitude 250 E, and (b) a model simulation. Electron intensity is shown as a function of kinetic energy E and satellite. longitude.) Data from many satellite orbits during 4 March 20 are included. Electrons scattered by NWC are seen near L =.8, in both the Northern and Southern Hemispheres, when the scattering would have occurred over NWC during the night (Figure 2, left). When it would have been during the day, scattered electrons generally are not seen (Figure 2, right). The rate of eastward electron drift is accounted for in the separation of data by night and day at NWC. The nighttime scattered electrons are seen at longitudes east of NWC up to the SAA region near 300. [6] The data show no other strong signatures of electron scattering for L 2.3, supporting the conclusion that NWC is the primary source of VLF waves that cause electron precipitation in this region [Kulkarni et al., 2008]. For 2.3 L 3., there is a broad band of precipitation that occurs day and night, north and south. This represents slot-region scattering by lightning-generated whistlers and plasmaspheric hiss [Meredith et al., 2007]. Similar results are obtained for other electron energies, with the expected energy dependence in the L values of the precipitation regions. [7] Data from a few satellite passes through a region in and west of the SAA are shown in Figure 3, now for 250 kev electrons. The scattering by NWC at night but not during the day is again clearly shown by the intensity maxima near L =.7 for the more westerly longitudes (blue curves). Generally higher intensities at the more easterly longitudes (red/yellow curves) represent stably trapped electrons. Here there are shallow intensity minima near L =.7 that represent the long-term o 2 p m 2 ¼ þ oðωjcosθj oþ for wave number k, wave normal angle θ, plasma frequency o p, and electron cyclotron frequency Ω. The condition for electron-wave resonance is o k k v k ¼ nω g where n is a positive or negative integer or zero, k k = kcos θ, v k = vcos a, v is the electron speed, g is the corresponding Lorentz factor, and a is the local pitch angle. It can be satisfied at discrete locations along a given magnetic field line. Then the waves cause electron pitch angle diffusion with a bounce-averaged coefficient [Albert, 202, equation 4] ¼ py2 c 2 B 0 X t b x 2 g 2 v 3 n;r B 2 w Ω2 Φ 2 n B 3 m 2 sin 2 a þ nω go k k v k nω g where x =cosa 0 for equatorial pitch angle a 0, y 2 = x 2, B w is the wave magnetic field, B is the background magnetic field, B 0 is the equatorial background magnetic field, s is the distance along the background field, t b is the bounce period, Φ 2 n is a standard combination of Bessel functions with argument gk v /Ω [e.g., Albert, 202, equation 3], k = ksin θ,andv = vsin a. Everything in the summation is evaluated at each of the resonance locations r, along the full length of the field line between mirror points and for < x <, derived from equation (2) for each n. Typically there are 0 or resonances in each hemisphere for each n. Only values of n = 0 and are included in the model; other values were found to not make significant contributions. [] Model parameter values relevant to the computation of from equation (3) have been chosen as follows:. Wave frequency o/(2p) = 9.8 khz. 2. Wave normal angle θ is derived from the assumption that the k vector is vertical at the southern magnetic foot point, taken at 200 km altitude where θ 30, then rotates linearly with distance s along the magnetic field through θ =60 at the magnetic equator, reaching θ 90 at the northern foot point. This is roughly consistent with ray-tracing results [Kulkarni et al., 2008; Starks et al., () (2) (3) 629

3 IDP 20/ 3/ -4, E = 62 kev, log[electrons (cm 2 sr s kev) - ] North, NWC night North, NWC day South, NWC night South, NWC day Figure 2. Measured electron intensity, in March 20, versus L and longitude from the Northern and Southern Hemispheres (top and bottom) and from times when drifting electrons would have previously passed the longitude of NWC at night and day (left and right). Several data gaps result from the separation into day and night. 2008]. (A small range of θ values at each location, which may result from fluctuating plasma conditions, should not significantly change the results.) 3. The wave power is nonzero only when NWC is at night, and is then ( " #) B ð S w ¼ S 0 exp L L wþ 2 ð þ ϕ ϕ wþ 2 B 0 2s 2 L 2s 2 ϕ where the maximum equatorial value is S 0 = 5 nw/m 2 (except as noted below), L w =.6,ϕ w =4 (the longitude of NWC), s L = 0.6, and s ϕ =5. The Gaussian dependences on L and ϕ roughly match the spatial distribution of wave power observed by a receiver on DEMETER, averaged over north and south [Sauvaud et al., 2008; Gamble et al., 2008, Figure in each]. The factor B/B 0 accounts for changing flux tube area with distance along the magnetic field. Wave magnetic field B w and electric field E w are derived from S w, using the wave and plasma properties [Albert, 202, equations 7 and 8]. 4. For evaluation of the plasma frequency, the plasma density n p =9 3 L exp( h/350) cm 3 where h is altitude (km). The choice is justified below (see section 4). The two terms represent the plasmasphere and ionosphere, the ionosphere being important only for comparing wave fields to those observed at DEMETER (see section 5). (4) 5. The background magnetic field B for equation (3) is a dipole with moment GR 3 E (in all other uses, it is from the IGRF- model for 20 [Finlay et al., 20]). [] Sample values of =y 2 ¼ D a0 a 0 from the NWC wave model are shown in Figure 5. Maxima near a 0 =80 are from equatorial n = 0 Landau resonance and those at lower a 0 from equatorial n = cyclotron resonances. Offequatorial resonances contribute to values below the maxima. A wisp is expected at L values for which has a high value in and near the DLC, that is, near L =.7 for E = 250 kev and.8 for E = 50 kev (compare Figure a) Stochastic Transport [2] Apart from the NWC wave scattering, other components of the electron transport model have been described in detail previously [Selesnick, 202]. Only a brief outline is presented here. [3] Additional pitch angle diffusion is caused by Coulomb scattering in the atmosphere and plasmasphere; a diffusion description of Coulomb scattering is adequate in place of the more accurate, but complex, jump-process scattering. This is calculated from standard neutral and plasma density models [Selesnick, 202, and references therein]. (The simplified plasma density model described above was used only in equation (3).) Sample D a0 a 0 values from Coulomb scattering are shown in Figure 6. Similar calculations provide an energy diffusion coefficient D EE andsteadylossrate 630

4 -5 E = 250 kev, φ = 4, L = IDP E = 250 kev 20/3/4-6 NWC night /y 2 (s - ) IDP E = 250 kev 20/3/5-7 NWC day /y 2 (s - ) -5 E = 50 kev,φ = 4, L = Figure 3. Measured electron intensity versus L from selected passes through the western SAA for 3 day intervals in March 20, color coded by dipole longitude, from times when drifting electrons would have previously passed the longitude of NWC at night and day (top and bottom) Figure 5. Model D a0 a 0 = /y 2 from NWC wave scattering versus a 0, for selected L values. Thick line segments are for a 0 ranges in the DLC / 3/ 5, L = E = 250 kev, F.7 = 70, φ = 0 L = Electrons/(cm 2 sr s kev) 0 /y 2 (s - ) E (kev) Figure 4. Sample electron energy spectra taken by IDP in the SAA on 5 March These and similar data are used for the model initial conditions Figure 6. Model D a0 a 0 = /y 2 from atmospheric Coulomb scattering versus a 0, for selected L values at longitude ϕ =0. The solar F.7 paramaterizes atmospheric density, and the value of 70 is suitable for 2009 and early

5 hde/dti c caused by collisions with neutral atoms, plasma ions, and free electrons. [4] To describe the wisp, which is observed in the DLC, it is necessary to retain a dependence in the electron distribution function f on longitude, or drift phase ϕ. Other required dependencies are on x = cos a 0, L, kinetic energy E, and time t. With four phase-space dimensions plus time, a stochastic description of electron transport is convenient. Stochastic differential equations (SDEs) describing electron diffusion in L, x, and E, with steady energy loss and azimuthal drift at a rate o d, are dl ¼ D LL L 2 dt þ ð2d LL Þ =2 dw (5) dx ð t b t bx Þdt þ ð2 Þ =2 dw þ dx a (6) de ¼ de dt þ ð2d EE Þ =2 dw þ de a dt c (7) df ¼ o d dt (8) Relative f Stochastic Finite-difference where D LL is the radial diffusion coefficient and dw represents a Brownian motion (or Wiener process). The a subscript indicates adiabatic changes in x or E due to conservation of the first and second adiabatic invariants during radial diffusion, calculated from the magnetic field model. [5] The SDEs (5) to (8) describe possible stochastic electron paths. The electron distribution function f is obtained by averaging over many such paths using the Feynman-Kac formula fðþ¼e t " fðt 0 Þe Z t # CðÞ t 0 dt 0 t 0 where E is an expectation or mean value and C de gp dt c (9) () [6] To compare the model to a given data point, electron arrival directions are sampled from the aperture of IDP, then sample paths are obtained by backward Monte Carlo integration of the SDEs to the initial time t 0, the initial condition is evaluated for each, averaged according to equation (9), and finally converted to intensity j = p 2 f. For paths that do not reach t 0, because they enter the dense atmosphere or reach the upper boundary in L, the initial condition is f(t 0 )=0. [7] Discontinuous changes in (Figure 5) can cause errors in numerical integration of the SDEs, because changes during a single step dx should be small. However, with adaptive step sizes, and by evaluating x term in equation (6) with finite differencing across the whole dx interval, it is possible to achieve reasonably accurate results, as illustrated in Figure 7. Stochastic solutions of a simplified one-dimensional x-diffusion model are compared to solutions of the corresponding diffusion equation by a finite difference method. They should not be considered as realistic because transport in ϕ, L, ande have been neglected, but are simply Figure 7. (top) Artificial diffusion coefficients for testing the stochastic numerical method and (bottom) corresponding solutions of a simplified one-dimensional pitch angle diffusion equation. Colors distinguish values and model solutions corresponding to relatively high (blue) or low (red) VLF wave power. Stochastic solutions are compared to those from a finite difference method. The initial condition was f = and, for in units of s, the simulation time was year. to test the numerical method. Solutions for two versions of are included, corresponding roughly to drift-averaged model values with wave power S 0 = 5 and 50 nw/m 2.The accuracy of the stochastic method is seen to decrease for the higher S 0 value because of larger jumps in Sample Solutions [8] Sample electron stochastic paths in a 0 and ϕ, ending at a similar location in the DLC to the wisp observation of Figure a, are shown in Figure 8. Values of at the ending time, from wave and Coulomb scattering combined, are indicated by shading. When NWC is in daytime, it does not contribute to and all paths begin in the dense atmosphere, where is high, with only a slight spread due to Coulomb scattering. Such paths contribute nothing to simulated electron intensity. When NWC is in nighttime, there is additional scattering near its longitude of ϕ = 4. One of the sample paths shown was scattered from the stable trapping region outside the DLC, where it completed several drifts around the Earth, to the observation point inside the DLC. Such a path, if it reaches back to the initial time t 0, contributes to the wisp. 632

6 Results (a) NWC night (b) NWC day log /y 2 (s - ), E = 250 kev, L = Figure 8. Sample stochastic electron paths in longitude ϕ and equatorial pitch angle a 0, ending at ϕ = 250 in the DLC when NWC was at (a) night and (b) day. Independent paths are distinguished by color. Shading indicates values of the combined diffusion coefficient /y 2 at the ending time, energy, and L. 4.. Wisp [9] A model simulation of the observed wisp of Figure a is shown, for comparison with the data, in Figure b. The plasmasphere component of the plasma density n p (parameterized as a power law in L as described above) and the wave power normalization S 0 were adjusted for near agreement between model and data. Of these, n p determines the shape and location of the wisp (i.e., the dependence on L of the electron energies in the wisp), through the resonance condition, and S 0 determines the intensity. The value S 0 = 7.5 nw/ m 2 was used for this case; S 0 = 5 nw/m 2 was used for all other simulations to better match the data in Figure 3, as described below. Changing model parameter values is justified because the observed intensity and location of the wisp both show some variability, as seen in the data of Figure 2, probably as a result of changing plasma conditions in the ionosphere and plasmasphere, respectively. [20] The wisp is observed in the DLC and so must be replenished within the electron drift period (t d 5 h for E > 0 kev). Therefore, the initial conditions of the wisp simulation need to be chosen from only one or more drift periods prior to the observation time. In this case the initial conditions are from the IDP data taken on 2 March 20 and the wisp data were taken late on 3 March. The wisp intensity depends strongly on the intensity of stably trapped electrons available for scattering into the DLC from just outside it. This comes from the initial condition data, so, for accuracy, it is beneficial to use a relatively short simulation time. Such a short simulation does not require radial diffusion, which is effective only over longer periods Radial Profiles [2] Simulations of the Figure 3 data, for 250 kev electron intensity versus L, are shown in Figures 9 and. For Figure 9, as for Figure b, the model includes all of the x and E transport terms, from atmospheric scattering and NWC wave scattering, but no L transport. Radial diffusion is 9.5 added for Figure, with diffusion coefficient D LL = s for L <.75 and D LL = (L.75) s for L >.75. These D LL values were chosen to fit the model to the data, as described below [see also Selesnick, 202], and are near the upper limit of the range of estimated values [e.g., Holzworth and Mozer, 979, Figure 5]. [22] The outer boundary condition for radial diffusion is f =0 at L = 2.5, to approximate slot region losses. No inner boundary is required because all electron paths enter the dense atmosphere near L =.5. The initial time t 0 is 5 March 2009, and the initial conditions are from IDP data taken on that date (Figure 4). The initial equatorial pitch angle dependence, for this and other simulations, is y 8, similar to that reached in steady decay [Selesnick, 202]. The ~ year simulation time is long enough for the stably 0 0 Model(no radial diffusion) 20/3/4-6 NWC night E = 250 kev Model(no radial diffusion) 20/3/5-7 NWC day E = 250 kev Figure 9. Simulated electron intensity versus L for comparison with the data in Figure 3. Radial diffusion was not included in the model. Light gray lines reproduce the data. 633

7 DLC 0 Model 20/3/4-6 NWC night E = 250 kev year simulation, L =.7, E = 250 kev, φ = 250 Initial condition NWC off (no radial diffusion) NWC off NWC on (no radial diffusion) - NWC on 0 Model 20/3/5-7 NWC day E = 250 kev Figure. Simulations similar to Figure 9, but radial diffusion was included. trapped electron distribution to evolve in L and x, allowing the roles of radial and pitch angle diffusion to be evaluated. [23] Without radial diffusion the simulation results are as expected (Figure 9): there is a significant dip in the stably trapped electrons seen near the wisp location, L =.7 at more easterly longitudes (red/yellow curves), caused by NWC scattering losses; there is a higher intensity of quasi-trapped electrons, seen at more westerly longitudes (blue curves), for L.7 when NWC is at night relative to day. Compared to the data (Figure 3 and reproduced in Figures 9 and ), the simulated intensities at the lower L values are too low and the dip in the stably trapped intensity is too deep. These problems are addressed by including radial diffusion (Figure ): now the simulated intensities at low L are similar to those observed, confirming earlier conclusions that inward diffusion is required to replenish atmospheric scattering losses there [Farley, 969; Selesnick, 202]; the dip near L =.7, due to NWC, is also similar to that observed, having being partially filled by diffusion from nearby L values. [24] An increasing D LL with L is required, at the higher L values, to sufficiently modify the NWC signatures. With the long integration time, this causes a large spread in L values at which the initial conditions must be evaluated and a corresponding large spread in the initial energies due to conservation of the adiabatic invariants. Consequently, there are large fluctuations in the simulated data, relative to the simulations without radial diffusion, due to statistics of the stochastic solution and the soft initial condition spectra (Figure 4). This is a limitation of the stochastic method that could be remedied by including a larger number of sample paths, but it is computationally intensive Figure. Model equatorial pitch angle distributions after evolving from the initial condition for year, with NWC turned on or off, and with or without radial diffusion. The shaded region represents the drift loss cone. [25] There are still some clear differences between the data and model, even with radial diffusion. The nighttime quasitrapped electron enhancement is too broad in L and at a slightly higher L than observed; the daytime intensities decrease with L more rapidly than observed. These shortcomings may result from an inaccurate model wave field, inaccurate D LL values, or from some other process that is unmodeled Pitch Angle Distributions [26] The IDP data taken at DEMETER s ~700 km altitude include only a limited x range, or a 0 range, near the DLC. Most of the stably trapped electrons have mirror points above the satellite and are not observable. The model can be used to predict the influence of NWC on these electrons. Simulations of equatorial pitch angle distributions for E = 250 kev, ϕ =250, and at L =.7 where the effects of NWC are strongest, are shown in Figure. Initial conditions were the same as in the previous cases with a simulation time of year. The influence of NWC is shown by including separate simulations with the transmitter turned on or off for the entire period. The main difference is in the DLC, which is partially filled by the wisp when NWC is on but empty when it is off. Without radial diffusion, the stably trapped electron intensity outside the DLC is lower when NWC is on, due to precipitation, but the difference decreases with increasing a 0 and the reduction is a factor ~2 overall. Separate simulations with radial diffusion are also included in the figure. The main effect of radial diffusion is to increase the electron intensity at all a 0 values. This is a result of inward diffusion from higher L and lower E, where the initial intensity was higher. It obscures electron losses caused by NWC, and no clear intensity reduction, relative to the case with NWC turned off, is evident at the higher a 0 values. 5. Summary and Conclusions [27] A model of the whistler-mode wave distribution escaping into space through the ionosphere from the ground-based NWC radio transmitter was constructed. It was used to calculate pitch angle diffusion coefficients for resonant scattering of 634

8 radiation belt electrons. These were incorporated into a stochastic electron transport model to determine the influence of waves from NWC on the inner belt electron intensity. The density of the plasmasphere and a normalization of the wave power were adjusted to give approximate agreement between model simulations and the wisp signature observed from the DEMETER satellite. With the inclusion of radial diffusion, it was also possible to obtain approximate agreement with radial profiles of quasi-trapped (DLC) and stably trapped electron intensity. [28] The model contains several simplifying assumptions, and the values of the adjusted parameters may be inaccurate in partial compensation. For example, a shift in peak wave intensity to higher L as the waves propagate from south to north is excluded from the model; instead, the wave power was assumed to maximize at an average L =.6. However, the plasmaspheric density required to match the wisp data is within the range of standard model values [e.g., Gallagher et al., 2000; Starks et al., 2008]. It is also possible to compare the assumed wave power to wave field data taken by DEMETER when it was over the vicinity of the NWC ground station. Using the plasma density model, an equatorial wave power S 0 =5 nw/m 2 corresponds to equatorial wave fields E w = 0.5 mv/m and B w = 4 pt, and wave fields at the DEMETER altitude (~700 km) E w = 0.6 mv/m and B w =50 pt. For comparison, an average peak E w mv/m was measured on DEMETER [Sauvaud et al., 2008; Gamble et al., 2008, Figure in each]. [29] The above considerations show that all of the assumed wave model parameters are approximately consistent with known observational or theoretical constraints. Therefore, the theory of electron pitch angle diffusion by resonant scattering from whistler-mode waves is in quantitative agreement with the observed wisp signature. Given this agreement, it is possible to predict the effect of turning off NWC. The simulations showed that the inner belt electron intensity would gradually increase by a factor ~2, but only at low equatorial pitch angles. This is the electron population encountered by a low-altitude satellite, but the change is small relative to natural variations. [30] The low-altitude electron intensity could be further reduced by increasing the transmitted wave power. However, trapped electron losses caused by NWC are limited by low scattering rates at equatorial pitch angles just above the primary cyclotron resonance, which act as a bottleneck in the diffusion to lower pitch angles (e.g., near a 0 =40 for L =.7 and E = 250 kev in Figure 5). Inclusion of whistler-mode waves from plasmaspheric hiss and atmospheric lightning, which likely are present, would not change this because their lower frequencies result in significant electron scattering only at equatorial pitch angles near 90 [e.g., Abel and Thorne, 998]. Addition of higher frequency waves could eliminate the bottleneck and reduce the trapped electron intensity over the entire altitude range. [3] Acknowledgments. The authors thank J.-A. Sauvaud and M. Parrot for the access to the DEMETER data and K. Graf for the help with the initial data interpretation. References Abel, B., and R. M. Thorne (998), Electron scattering loss in Earth s inner magnetosphere:. Dominant physical processes, J. Geophys. Res., 3(A2), , doi:.29/97ja0299. Albert, J. M. (202), Dependence of quasi-linear diffusion coefficients on wave parameters, J. Geophys. Res., 7, A09224, doi:.29/202ja0778. Farley, T. A. (969), Radial diffusion of Starfish electrons, J. Geophys. Res., 74(4), , doi:.29/ja074i04p0359. Finlay, C. C., et al. (20), International Geomagnetic Reference Field: the eleventh generation, Geophys. J. Int. 83, , doi:./ j x x. Gallagher, D. L., P. D. Craven, and R. H. Comfort (2000), Global core plasma model, J. Geophys. Res., 5(A8), 8,89 8,833. Gamble, R. J., C. J. Rodger, M. A. Clilverd, J.-A. Sauvaud, N. R. Thomson, S. L. Stewart, R. J. McCormick, M. Parrot, and J. -J. Berthelier (2008), Radiation belt electron precipitation by man-made VLF transmissions, J. Geophys. Res., 3, A2, doi:.29/2008ja Holzworth, R. H. and F. S. Mozer (979), Direct evaluation of the radial diffusion coefficient near L = 6 due to electric field fluctuations, J. Geophys. Res., 84(A6), , doi:.29/ja084ia06p Imhof, W. L., J. B. Reagan, H. D. Voss, E. E. Gaines, D. W. Datlowe, J. Mobilia, R. A. Helliwell, U. S. Inan, J. Katsufrakis, and R. G. Joiner (983), The modulated precipitation of radiation belt electrons by controlled signals from VLF transmitters, Geophys. Res. Lett., (8), 65 68, doi:.29/gl0i008p0065. Koons, H. C., B. C. Edgar, and A. L. Vampola (98), Precipitation of inner zone electrons by whistler mode waves from the VLF transmitters UMS and NWC, J. Geophys. Res., 86(A2), , doi:.29/ JA086iA02p Kulkarni, P., U. S. Inan, T. F. Bell, and J. Bortnik (2008), Precipitation signatures of ground-based VLF transmitters, J. Geophys. Res., 3, A0724, doi:.29/2007ja Li, X., et al. (202), Study of the North West Cape electron belts observed by DEMETER satellite, J. Geophys. Res., 7, A0420, doi:.29/ 20JA072. Meredith, N. P., R. B. Horne, S. A. Glauert, and R. R. Anderson (2007), Slot region electron loss timescales due to plasmaspheric hiss and lightning-generated whistlers, J. Geophys. Res., 2, A0824, doi:.29/ 2007JA0243. Sauvaud, J.-A., T. Moreau, R. Maggiolo, J.-P. Treilhou, C. Jacquey, A. Crosa, J. Coutelier, J. Rouzaud, E. Penou, and M. Gangloff (2006), High-energy electron detection onboard DEMETER: The IDP spectrometer, description and first results on the inner belt, Planet. Space Sci., 54(5), 502 5, doi:.6/j.pss Sauvaud, J.-A., R. Maggiolo, C. Jacquey, M. Parrot, J.-J. Berthelier, R. J. Gamble, and C. J. Rodger (2008), Radiation belt electron precipitation due to VLF transmitters: Satellite observations, Geophys. Res. Lett., 35, L09, doi:.29/2008gl Selesnick, R. S. (202), Atmospheric scattering and decay of inner radiation belt electrons, J. Geophys. Res., 7, A0828, doi:.29/202ja Starks, M. J., R. A. Quinn, G. P. Ginet, J. M. Albert, G. S. Sales, B. W. Reinisch, and P. Song (2008), Illumination of the plasmasphere by terrestrial very low frequency transmitters: Model validation, J. Geophys. Res., 3, A09320, doi:.29/2008ja032. Vampola, A. L., and G. A. Kuck (978), Induced precipitation of inner zone electrons,. Observations, J. Geophys. Res., 83(A6), , doi:.29/ja083ia06p Walt, M. (964), The effects of atmospheric collisions on geomagnetically trapped electrons, J. Geophys. Res., 69(9), , doi:.29/ JZ069i09p