Very-Low-Frequency transmitters bifurcate energetic electron belt in near-earth space

Very-Low-Frequency (VLF) transmitters operate worldwide mostly at frequencies of 10–30 kilohertz for submarine communications. While it has been of intense scientific interest and practical importance to understand whether VLF transmitters can affect the natural environment of charged energetic particles, for decades there remained little direct observational evidence that revealed the effects of these VLF transmitters in geospace. Here we report a radially bifurcated electron belt formation at energies of tens of kiloelectron volts (keV) at altitudes of ~0.8–1.5 Earth radii on timescales over 10 days. Using Fokker-Planck diffusion simulations, we provide quantitative evidence that VLF transmitter emissions that leak from the Earth-ionosphere waveguide are primarily responsible for bifurcating the energetic electron belt, which typically exhibits a single-peak radial structure in near-Earth space. Since energetic electrons pose a potential danger to satellite operations, our findings demonstrate the feasibility of mitigation of natural particle radiation environment.

Line 88. Can you please explain the 'first order cyclotron resonant energy' in more detail. Is this the minimum resonant energy associated with an electron with zero velocity perpendicular to the ambient magnetic field ?
Line 101. While it may be of interest to plot the radial profile of the averaged observed wave magnetic field amplitudes, the spatial coverage in this relatively short time period will not give the best measure of the average wave magnetic field intensities experienced by the energetic electrons as they drift around the Earth. The wave intensity experienced by an electron at any given time will depend on both the magnetic local time and the geographic longitude. The best way to do this is to build a comprehensive map using data from multiple years of satellite data. I would therefore strongly recommend that the authors consider using the statistical values as opposed to the in situ values. Inspection of Figure 2c suggests that this will increase the loss timescales out to L = ~ 2.5 but reduce them further out. This would reduce the efficiency of the loss process in the region L = 1.8-2.5 but would help remove some of the energetic particles that the simulations are unable to currently remove at higher L shells as time progresses (Figure S5). The paper shows very interesting data, but I would say that the claim that you provide "compelling quantitative evidence that VLF transmitter waves are causing the energetic electron bifurcation" is a bit of an overstatement. I think more work needs to be done on this topic to make this acceptable for publication in Nature Comm.

Major Comments
The approach that the authors use, Fokker Planck diffusion simulations is dated. Recent new work on plasmaspheric hiss (JGRSP, 120, 414-431, doi:10.1002/2014JA020518, 2015JGRSP, 122, 1643-1657, doi:10.1002/2016JA023289, 2017JGRSP, 123, https://doi.org/10.1029/2018JA025975, 2018JGRSP, 124, 10063-10084, https://doi.org/10.1029/2019JA027102, 2019 have shown that plasmaspheriic hiss is intense and coherent. With coherent waves, the loss rate is ~two orders of magnitude faster. The authors should do the simulations/calculations assuming coherent hiss waves (see JGR, 115, A00F15, doi:10.1029/2009JA014885, 2010 for chorus wave-particle interactions) for a more accurate comparison with the VLF transmitter waves. A question for the authors: "Are the VLF transmitter waves coherent in the area that the wave-particle interactions are taking place?" "Have the authors considered the possibility that magnetosonic waves are coherent, and if so, how will wave-particle interactions be changed?" The electron energy being examined should be mentioned in the title of the paper. Most people think of the "electron gap" as being due to 100s of keV electrons, not these lower energy electrons. This should also be mentioned more prominently in the body of the paper. The higher energy electron slot is due to the combination of coherent (?) magnetosonic waves and coherent hiss? Some crude approximations are given in the 2019 paper above.

Minor Comments
Lines 39-40. What does "when a magnetic field line crosses the geomagnetic equator" mean and how does this geometry affect transmitter waves allowing them to penetrate though the ionosphere? It would be good for the reader if you would elaborate a bit more and give references.
Lines 54-56. The energy of ~30 to 200 keV is beyond the limit of your study, so how is this relevant?
Lines 76-77. Moderate substorms. Chorus is generated during substorms. It has been hypothesized that chorus propagates into the plasmasphere. This seems like a reasonable competing mechanism to VLF transmitters?
Lines 102-109. I don't understand the discussion here. If these natural waves (lightning, hiss and magnetosonic waves) "significantly exceed the VLF transmitter intensity", then why do the simulations indicate that it is transmitter signals that are causing the slot? Perhaps what you mean is that at VLF frequencies the transmitter intensities have the highest intensities? Or have the highest intensities in the VLF frequency range? Something seems to be missing here.
Lines 119-121. Here you mention hiss is responsible for the high energy electron slot. Please discuss the possibility of either hiss Landau interactions with the 10s of keV electrons or the high frequency ends of hiss for cyclotron resonance. This is a bit confusing.
Lines 124-126. Previous authors have discussed the combination of magnetosonic waves with plasmaspheric hiss for the pitch angle diffusion of energetic electrons, not magnetosonic waves by themselves. So this statement is a bit unfair.
Line 132. Radial diffusion. Here are a couple of papers on this topic: GRL., 26, 3273, 1999;SW, 2, S10S02, doi:10.1029/2004SW000070., 2004. However this mechanism is usually quoted for relativistic electrons, not the low energies that you are discussing. Could low energy electrons radially diffuse much by this process?
These results are interesting and new. Although quasi-linear theory has been successfully used to understand the structure of the trapped electron belts in the past, its application to this bifurcated configuration of the inner zone electrons is novel. This is in part because the observed structure is difficult to catch, requiring days of geomagnetically quiet conditions so as not to be washed out by other processes. The outcome of the study is particularly interesting because it reinforces the weak influence of most of the terrestrial VLF transmitters on radiation belt electronsan understanding that is beginning to emerge since the early estimates of the relative weights of such transmitters, lightning-generated whistlers, and plasmaspheric hiss.
The paper is clearly written and the figures are both appropriate and convey the results effectively. The reference list is largely comprehensive and supports the methodology and conclusions. The data used are available and the analysis technique is well-described, building on much significant past work.
No major revisions are required prior to publication. It is my judgment that this is a very well-written, clear, impactful manuscript that provides important new insights to the field.
In the section reviewing past connections of terrestrial transmitters with precipitating electrons, the authors may wish to consider referring to Graf, et al., 2009(doi 10.1029 and references therein. Although that work did not provide clear quantitative evidence of the order seen in this manuscript, the authors did estimate pitch angle diffusion in an attempt to perform a similar comparison.

Reply:
We thank the reviewer for this valuable comment. We have added related citations in the main text of the revised manuscript as follows: "Early studies provided evidence of the potential transmitter-induced electron precipitation by correlating the electron flux enhancement inside the drift-loss cone with the VLF wave power 12-14 ". Please see Lines 47 -49.

Reply:
We thank the reviewer for this constructive suggestion. We agree with the reviewer that the difference of the wave amplitude of VLF transmitter waves between the in situ measurements and statistical results is primarily due to the seasonal influences.
The wave power at L > 1.7 mainly comes from the NAA and NLK transmitters located in North America, where the transionospheric wave attenuation decreases due to a lower sunlit electron density in February, so that the wave amplitude during February at L > 1.7 is stronger than the wave amplitude averaged during all seasons. We have added this point to the main text and Supplementary Information. Please see Lines 109 -114 in the main text and Lines 203-207 in the Supplementary Information (including the new Figure S2). We thank the reviewer for pointing this out. We have deleted the word "remarkable". Please see Line 30.
Line 42. What do you mean by a "dense" population? Reply: To avoid confusion, we deleted "dense" here. Please see Line 44.
Line 50. "observed characteristically" should be "observed to be characteristically" Reply: We thank the reviewer for pointing this out. We have changed "observed characteristically" to "observed to be characteristically". Please see Line 53.
Line 88. Can you please explain the "first order cyclotron resonant energy" in more detail? Is this the minimum resonant energy associated with an electron with zero velocity perpendicular to the ambient magnetic field? Reply: Yes, the reviewer is correct that we calculated the minimum first-order cyclotron resonant energy for electrons with 0° pitch angle at the geomagnetic equator. The detailed information of the first-order cyclotron resonant energy calculation is described in the "Methods" section, and we have added the information regarding minimum first-order cyclotron resonant energies of electrons calculated for 0° pitch angle in Lines 206, and 224-225.
Line 101. While it may be of interest to plot the radial profile of the averaged observed wave magnetic field amplitudes, the spatial coverage in this relatively short time period will not give the best measure of the average wave magnetic field intensities experienced by the energetic electrons as they drift around the Earth. The wave intensity experienced by an electron at any given time will depend on both the magnetic local time and the geographic longitude. The best way to do this is to build a comprehensive map using data from multiple years of satellite data. I would therefore strongly recommend that the authors consider using the statistical values as opposed to the in situ values. Inspection of Figure 2c suggests that this will increase the loss timescales out to L = ~ 2.5 but reduce them further out. This would reduce the efficiency of the loss process in the region L = 1.8-2.5 but would help remove some of the energetic particles that the simulations are unable to currently remove at higher L shells as time progresses (Figure S5).

Reply:
We thank the reviewer for this valuable comment. We agree with the reviewer that it is also of great importance to perform simulations using the statistical wave amplitude of VLF transmitter waves. Previous statistical results suggest that the wave amplitude distributions of VLF transmitter waves depend on seasons (e.g., Ma et al., 2017). The wave power at L > 1.7 mainly comes from the NAA and NLK transmitters located in North America, where the transionospheric wave attenuation decreases with a lower sunlit electron density, so that the VLF wave amplitudes during February at L > 1.7 are stronger than the wave amplitudes averaged during all seasons. The comparison of the VLF transmitter wave amplitudes between in situ observation and statistical values (Ma et al., 2017) during different seasons is added in Fig. S2 in Supplementary Information. Clearly, the wave amplitude of VLF transmitters is stronger at L > 1.7 during northern hemisphere winter than summer. Overall, the statistical wave amplitudes during northern hemisphere winter are weaker than the in situ observed values at L < 2.3, while they exceed the observed values at L > 2.5.
Following the reviewer"s suggestion, we adopt the statistical wave amplitude during northern hemisphere winter to perform all the diffusion simulations from 21 February to 06 March 2016, the results of which are shown in Fig. S9 in the same format as those in Fig. 3 in the main text. The simulated results of the energetic electron flux radial profile by only including VLF transmitter waves ( Fig. S9p-r) reproduce the key features of the observed evolution of electron belt bifurcation, which is similar to the simulated results using in situ observed wave amplitude of VLF transmitter waves, although the flux decay is slightly slower at L < 2.3 due to the weaker wave power from the statistical results. By including both human-made and natural plasma waves ( Fig. S9v-x), the simulated results can reproduce the main features of the bifurcated electron belt at 25.6 keV and 39.1 keV, while the results for 62.7 keV do not show a clear feature of bifurcation as the results shown in Fig. 3, which is mainly due to the weaker wave amplitude from the statistical results at L < 2.3. Overall, the simulation results using statistical wave amplitudes of VLF transmitter waves demonstrate a similar trend to the results using in situ observed values.
Besides, previous statistical results demonstrate that the magnetic local time coverage of VLF transmitter waves along the electron drift trajectory is about 50% due to the reason that VLF transmitter waves are considerably stronger on the nightside than the dayside (Ma et al., 2017). In the studied event, the Van Allen Probes traveled over ~1-6 MLT during outbound trajectories over L shells of 1.5-3.0, where the VLF transmitter signals are more likely to be observed and stronger, while the satellites traveled over ~13 -~18 MLT during inbound trajectories over L shells of 1.5-3.0, where the VLF transmitter waves are less likely to be observed and weaker. In spite of the limited time of 15-day observations during this event, the averaged in situ observed wave amplitude during this event can provide a reasonable estimation of the MLT-averaged wave amplitude. We

Review of "Human-Made Very Low-Frequency Transmitters Bifurcate Energetic
Electron Belt in Near-Earth Space" by Man, Li, Ni, Ma, Green, Claudepierre, Bortnik, Gu, Fu, Xiang and Reeves The paper shows very interesting data, but I would say that the claim that you provide "compelling quantitative evidence that VLF transmitter waves are causing the energetic electron bifurcation" is a bit of an overstatement. I think more work needs to be done on this topic to make this acceptable for publication in Nature Comm.

Major Comments
The approach that the authors use, Fokker Planck diffusion simulations is dated.
Recent new work on plasmaspheric hiss (JGRSP, 120, 414-431, doi:10.1002/2014JA020518, 2015JGRSP, 122, 1643-1657, doi:10.1002/2016JA023289, 2017JGRSP, 123, https://doi.org/10.1029/2018JA025975, 2018JGRSP, 124, 10063-10084, https://doi.org/10.1029/2019JA027102, 2019 have shown that plasmaspheriic hiss is intense and coherent. With coherent waves, the loss rate is ~two orders of magnitude faster. The authors should do the simulations/calculations assuming coherent hiss waves (see JGR, 115, A00F15, doi:10.1029/2009JA014885, 2010 for chorus wave-particle interactions) for a more accurate comparison with the VLF transmitter waves. A question for the authors: "Are the VLF transmitter waves coherent in the area that the wave-particle interactions are taking place?" "Have the authors considered the possibility that magnetosonic waves are coherent, and if so, how will wave-particle interactions be changed?" Reply: We thank the reviewer for introducing several interesting papers and the valuable comment regarding the coherency of plasma waves. We cited these references accordingly and added them into the reference list (Lines 148-150). Since the frequency range of VLF transmitter waves is typically very narrow (see an example in Fig. S3 in the Supplementary Information), they are reasonable to be considered as coherent waves. We performed test particle simulations to evaluate the effect of coherent hiss and VLF transmitter waves and included the detailed results in the Supplementary Information (Section 4 and Fig. S4).
The test particle simulations are performed to evaluate the electron scattering effects by coherent hiss and VLF transmitter waves at L = 2.3, which is a typical L-shell where the observed fluxes decreased significantly during this event, and compared to the quasi-linear theory results. We assume that these two types of plasma waves have a single wave frequency (to represent the most coherent wave), which is adopted from the central wave frequency from the statistical wave frequency spectra Ma et al., 2017). For simplicity, we assume the wave normal angle ( ) for hiss and VLF transmitter waves as = 0°. The simulations numerically solve the full electron momentum equation given below (Bell, 1984;Bortnik et al., 2008;Li, J. et al., 2015): where ⃗ and are the electron momentum and charge, and = ( ) is the relativistic Lorentz factor where and c are the electron speed and light speed, respectively. ⃗⃗ and ⃗⃗ are the wave electric and magnetic field, and ⃗⃗ 0 is the background magnetic field. The momentum equation (Eq. R1) can be rewritten as a set of three gyro-averaged ordinary differential equations (Bell, 1984;Bortnik, 2004;Bortnik et al., 2008;Li, J. et al., 2015), which are then numerically solved to perform the test particle simulations. Same as in quasi-linear calculations, we assume that hiss waves cover the latitudinal range of |MLAT| ≤ 45°, while VLF transmitters can reach the magnetic latitude where the magnetic field line reaches the altitude of 800 km from the Earth"s surface, which is |MLAT| ≤ 45.6 ° at L = 2.3. Plasma waves are launched from the equator and propagate to higher magnetic latitudes until the maximum magnetic latitude ( max ) in the northern hemisphere. Energetic electrons are released at latitude of the lower value between  max and the mirror point latitude in the northern hemisphere and move towards the equator. We trace the electrons until they reach the equator for the first time. For each initial energy and pitch angle, 72 electrons are released with the initial phase uniformly distributed between 0° and 360°. The wave amplitude of hiss is based on statistical results from Van Allen Probes measurement , ~24.3 pT at L = 2.3, while the wave amplitude of VLF transmitter waves is based on in situ satellite measurements, ~3.47 pT at L = 2.3, the same as the simulations in the main text. The detailed input wave parameters for test particle simulations including wave frequency, wave normal angle, wave latitudinal variations, and wave amplitude are listed in Table S2 in the Supplementary Information. For comparison, we also calculate quasi-linear diffusion coefficients by adopting similar parameters used in the test particle simulations, which are also listed in Table S2. For field-aligned electromagnetic waves, only the first order cyclotron resonance (N = -1 for R-mode) contributes to the electron scattering effect; therefore, the resonance harmonic N = -1 was included in the quasi-linear calculations for both hiss and VLF transmitter waves. Fig. S4 presents the comparison of bounce-averaged pitch-angle diffusion coefficients due to plasmaspheric hiss and VLF transmitter waves calculated by using test particle simulations (a-b) with quasi-linear calculations (c-d). Overall, the results of the test particle simulations agree well with the quasi-linear results, indicating that the wave amplitudes of plasmaspheric hiss and VLF transmitter waves are not sufficiently strong (< 25 pT) to cause a significant nonlinear effect. Therefore, the coherent hiss or VLF transmitter waves do not significantly affect our quasi-linear simulation results. Our result is also consistent with the previous study (Tao et al., 2012), which indicates that bounce-averaged quasi-linear diffusion coefficients are still valid for narrowband whistler mode waves, as long as the amplitude is small (< a few hundred pT). performed the comparisons of pitch-angle diffusion coefficients for magnetosonic waves using both quasi-linear calculations and test particle simulations, which demonstrates good consistency between the results from test particle simulations and quasi-linear calculations in the high-density plasmasphere, where the transit-time effect is not very prominent. Besides, since the diffusion coefficients of magnetosonic waves (shown in Fig. 1 and Figs. S2-S3) are the weakest among all these four types of plasma waves, their contributions to electron flux decay is very minor compared to plasmaspheric hiss, lightning-generated whistlers, and VLF transmitter waves.
In conclusion, due to the reason that the wave amplitudes of plasmaspheric hiss, VLF transmitter waves, and magnetosonic waves are not strong enough (< ~25 pT) to cause significant nonlinear effects during this relatively quiet event, and the diffusion coefficients calculated by performing test particle simulations are similar to those using the quasi-linear approach. Therefore, we think it is reasonable to evaluate electron scattering effects due to plasmaspheric hiss, lightning-generated whistlers, VLF transmitter waves, and magnetosonic waves by performing Fokker-Planck diffusion simulations. We have added these points to the revised manuscript in the main text and Supplementary  The electron energy being examined should be mentioned in the title of the paper. Most people think of the "electron gap" as being due to 100s of keV electrons, not these lower energy electrons. This should also be mentioned more prominently in the body of the paper. The higher energy electron slot is due to the combination of coherent (?) magnetosonic waves and coherent hiss? Some crude approximations are given in the 2019 paper above.

Reply:
We agree with the reviewer and that"s why we didn"t call it "radiation belt", but "energetic electron belt" in the manuscript, to distinguish the energetic electron populations in our study from the relativistic (MeV) electron populations. We have emphasized the specific electron energy range (tens of keV) throughout the main text. Please see Lines 25,68,70,77,87,122,134,164,184,187,[191][192]. However, since the title has space limit and "tens of kiloelectron volts electron belt" sounds a bit wordy, we prefer not to include this detailed energy limit in the title.
Plasmaspheric hiss is known to dominantly drive electron pitch angle scattering for the higher energies (>~100 keV) in the slot region between the inner and outer radiation belt, different from the VLF transmitter waves that drive the electron scattering at tens of keV energies leading to the bifurcation of the energetic electron belt. A number of studies have demonstrated that magnetosonic waves are capable of accelerating radiation belt electrons and producing electron butterfly pitch-angle distributions via the Landau resonance (e.g., Horne et al., 2007;Xiao et al., 2015;Li et al., 2016). Therefore, although magnetosonic waves can contribute to pitch angle scattering, plasmaspheric hiss still plays the dominant role in forming the slot region between the inner and outer belts at > ~100 keV (e.g., Lyons and Thorne, 1973;Falkowski et al., 2017;Ma et al., 2016). We have added the discussion that hiss dominantly drives the slot region at higher energies (>~100 keV) between the inner and outer radiation belts and added the related references given above. Please see Lines 138 -139.

Minor Comments
Lines 39-40. What does "when a magnetic field line crosses the geomagnetic equator" mean and how does this geometry affect transmitter waves allowing them to penetrate though the ionosphere? It would be good for the reader if you would elaborate a bit more and give references.

Reply:
We thank the reviewer for this helpful comment. We have rephrased the sentence as follows. "where L is the geocentric distance in Earth radii of the location where the corresponding magnetic field line crosses the geomagnetic equator." While propagating mostly within the Earth-ionosphere waveguide, which is bounded by the terrestrial surface and the lower ionosphere at altitudes about ninety kilometers, VLF transmitter signals can penetrate through the imperfectly reflecting ionosphere, being guided by the gradients of the Earth"s magnetic field, to leak a portion of their power into the Earth"s magnetosphere primarily at L < 3 5-8 . We have added this point and the related references. Please see Lines 38 -42. We agree with the reviewer that a portion of chorus waves can propagate from outside the plasmapause into the high-density plasmasphere to form plasmaspheric hiss (e.g., Bortnik et al., 2008Bortnik et al., , 2009, the effect of which has already been considered in the present study, as shown in Figure 3. During the quiet event analyzed in the present study, chorus waves are typically observed at larger L-shells (> 3) (e.g., Meredith et al., 2012), thus it is unlikely that chorus can directly scatter energetic electrons to contribute to the formation of the bifurcated electron belt at L < 2.5. On the contrary, VLF transmitter signals can be continuously observed at low L-shells (< 3) for a long time period, thus can efficiently scatter electrons for a relatively long time. Therefore, electron scattering by VLF transmitter waves is still the most likely mechanism for the formation of the bifurcated energetic electron belts at energies of tens of keV.

Reply:
We thank the reviewer for pointing this out. Indeed, the VLF transmitter wave power intensity at ~24 kHz is higher than the intensity of hiss, lightning generated waves and magnetosonic waves at the same frequency, although the integrated wave amplitude of VLF transmitter wave is weak. Since the wave amplitude of lightning generated whistlers is similar to that of VLF transmitter waves, we replaced "significantly exceed the VLF transmitter intensity" with "exceed or become comparable to the VLF wave amplitude". Please see Lines 118.
One important reason that VLF transmitter waves dominantly drive the bifurcated energetic electron belt at tens of keV is that the resonant electron energies due to VLF transmitter waves match the energies where the most significant electron flux decay is observed (see the white lines in Fig. 1f-h and Fig. R1 below). We have added a sentence to clarify this point in Lines 119 -122. "However, the energy of electrons exhibiting the most evident bifurcation feature is close to the first-order cyclotron resonance energy corresponding to the waves at high frequencies (> 10 kHz), suggesting the potentially dominant role of VLF transmitter waves in bifurcating the energetic electron belt at tens of keV." Figure R1. The first-order cyclotron resonant energies of electrons interacting with plasmaspheric hiss with frequency of 252 Hz (red) and 4000 Hz (blue), and with VLF transmitter waves at 24 kHz (black) for 0° pitch angle at the magnetic equator.
Lines 119-121. Here you mention hiss is responsible for the high energy electron slot. Please discuss the possibility of either hiss Landau interactions with the 10s of keV electrons or the high frequency ends of hiss for cyclotron resonance. This is a bit confusing.

Reply:
We thank the reviewer for this constructive comment. Plasmaspheric hiss can contribute to scatter tens of keV electrons at pitch angles close to 90° by Landau resonance, but the scattering becomes ineffective at the pitch angles below ~60°. The Landau resonance and cyclotron resonances (up to 10) due to hiss are included in our simulations. This point is discussed in Lines 143 -145 and 264 -265.
Our diffusion rate calculation includes hiss power at frequencies up to 4 kHz, but the peak wave power is observed below a few hundred Hz, and the hiss wave power at higher frequencies above ~1 kHz is extremely weak . The pitch-angle diffusion coefficients for plasmaspheric hiss start to become strong above ~100 keV near the bounce loss cone at L < 2.3 (see Fig. 3g & 3h), thus contribute little to electron scattering loss at energies < 100 keV. At L > 2.3 the pitch-angle diffusion coefficients due to hiss near the bounce loss cone tend to become strong below 100 keV. This trend is also shown in Fig. R1  (2019) has investigated the combined electron scattering effect by simultaneously occurring plasmaspheric hiss and magnetosonic waves with groups of different relative wave amplitude, which suggests that the combined scattering effects are dominated by pitch angle scattering due to hiss when hiss wave amplitude is comparable to or stronger than that of magnetosonic waves. In the present study, the wave amplitude of hiss is almost as twice as that of magnetosonic wave (shown in Fig.  2d in the main text). Therefore, the diffusion coefficients due to magnetosonic waves are much weaker than those of plasmaspheric hiss (shown in Fig. 3). Furthermore, Fig.  3s-u shows the combined effects of hiss, magnetosonic wave, and lightning generated whistlers, indicating that there is no clear formation of the bifurcating feature without including VLF transmitter waves. We have rephrased the sentence as follows on Lines 145 -148. "The electron scattering rates due to magnetosonic waves are confined to high equatorial pitch-angles and are negligibly small near the bounce loss cone (Fig.  3j-l). Overall, the effects of magnetosonic waves on electrons are weakest compared to other three types of plasma waves." Reference: Hua, M. et al. Evolution of radiation belt electron pitch angle distribution due to combined scattering by plasmaspheric hiss and magnetosonic waves. Geophys. Res. Lett. 46, 3033-3042 (2019).
Line 132. Radial diffusion. Here are a couple of papers on this topic: GRL., 26, 3273, 1999;SW, 2, S10S02, doi:10.1029/2004SW000070., 2004. However this mechanism is usually quoted for relativistic electrons, not the low energies that you are discussing. Could low energy electrons radially diffuse much by this process? Reply: We thank the reviewer for this valuable comment and introducing interesting papers, which are now cited on Line 158. The study of O" Brien et al. (2016) has estimated the quiet time radial diffusion coefficients for electrons in the inner radiation belt (L < 3) with energies from ~50 to 750 keV based on the Van Allen Probes observations, which agree well and supports the model of Brautigam and Albert (2000). For example, the radial diffusion coefficients based on measurements from the Van Allen Probes during quiet time (Kp < 4) is ~10 -3 day -1 for  = 1.9 and 8.0 MeV/G at L = 2.0, while the radial diffusion coefficients from the model of Brautigam and Albert (2000) during quiet time (Kp = 1) is ~2.5×10 -3 day -1 for  = 1.9 MeV/G, and ~10 -3 day -1 for  = 8.0 MeV/G at the same L shell region (see Figure 4 in O" Brien et al., 2016). Therefore, we think the model of Brautigam and Albert (2000) is a reasonable estimation of radial diffusion coefficients for low energy electrons in the inner belt during quiet times.
We have added this point in the Supplementary Information in Lines 158 -160. Figure R2. In situ observations of plasmaspheric hiss by Van Allen Probe A on 23 February 2016. a, Frequency-time spectrogram of electric spectral density measured by HFR. b, Frequency-time spectrogram of wave spectral density in electric field and c, magnetic field observed by WFR, and the corresponding d, wave normal angles, e, ellipticity and f, integrated wave amplitude of plasmaspheric hiss with the red lines indicating the amplitudes at L-shells over 1.5 -3.0. In Figs. R2a-e, the solid, dash-dotted, and dashed magenta lines indicate f ce , 0.5 f ce , and 0.1 f ce , where f ce is the electron cyclotron frequency; the solid, dotted, and dashed black lines represent f LHR , 0.5 f LHR , and f cp , where f LHR is the lower hybrid resonance frequency and f cp is the proton cyclotron frequency.

REVIEWERS' COMMENTS:
Reviewer #3 (Remarks to the Author): Third Review of "Human-Made Very Low-Frequency Transmitters Bifurcate Energetic Electron Belt in Near-Earth Space" by Man, Li, Ni, Ma, Green, Claudepierre, Bortnik, Giu, Fu, Xiang and Reeves I had accepted the paper in my last review, so I was surprise to see this detailed response to my "aside" in this recent "reply".
However now that I am asked to reply once more, I want to make sure that it is understood that I was referring to the maximum hiss wave intensities during substorms. There are two more recent papers on plasmaspheric hiss (JGRSP, 123, https://doi.org/10.1029/2018JA025975, 2018; JGRSP, 124, https://doi.org/10.1029/2019JA027102, 2019) which are claiming that these coherent and intense waves are causing the high energy electron slot. This is different than the lower energy electrons that you are discussing in your paper. So some clarification is perhaps needed. Maybe putting an energy range in your title? Also the plasmaspheric wave intensities that you have quoted, are those intensities for the hiss waves cyclotron resonant with your electrons? This should be clarified for the readership.