Chorus wave power at the strong diffusion limit overcomes electron losses due to strong diffusion

Earth’s radiation belts consist of high-energy charged particles trapped by Earth’s magnetic field. Strong pitch angle diffusion of electrons caused by wave-particle interaction in Earth’s radiation belts has primarily been considered as a loss process, as trapped electrons are rapidly diffused into the loss cone and lost to the atmosphere. However, the wave power necessary to produce strong diffusion should also produce rapid energy diffusion, and has not been considered in this context. Here we provide evidence of strong diffusion using satellite data. We use two-dimensional Fokker-Planck simulations of electron diffusion in pitch angle and energy to show that scaling up chorus wave power to the strong diffusion limit produces rapid acceleration of electrons, sufficient to outweigh the losses due to strong diffusion. The rate of losses saturates at the strong diffusion limit, whilst the rate of acceleration does not. This leads to the surprising result of an increase, not a decrease in the trapped electron population during strong diffusion due to chorus waves as expected when treating strong diffusion as a loss process. Our results suggest there is a tipping point in chorus wave power between net loss and net acceleration that global radiation belt models need to capture to better forecast hazardous radiation levels that damage satellites.

This paper describes simulations of electron diffusion using the 2D BAS Radiation Belt Model,in particular associated with strong diffusion induced by chorus waves.I believe the results are correct and to be of interest to radiation belt modellers.This submission is more of a technical note than a scientific paper.As such,it would not be appropriate for GRL or JGR(Space Physics).However,this submission may be appropriate for Nature Communications.The manuscript is based on results of quasi-linear calculations of diffusion coefficients of energetic electrons in the outer Van Allen radiation belt.The authors scale all the diffusion coefficients up to the strong diffusion limit, and show that energy diffusion to relativistic energies can outweigh losses caused by pitch angle diffusion.
Although the main result is obtained by theoretical calculations using simplified models, experimental data from the POES and Van Allen Probes spacecraft are also used in order to support the theory.
Generally, the text is well written and easily readable.
Problems I see in it are mainly linked to experimental data, as detailed below in my specific comments.Nevertheless, the logic of the main message is so straightforward that it makes me wonder why it hasn't been brought up earlier.
This is probably a sign of a good paper and I therefore recommend it for publication in Nature Communications after a revision is done by the authors.Specific comments: line 59...The condition of equal precipitated flux to the trapped flux seems unclear as it is written here, although the context shows that it probably just means that the velocity distribution has to be isotropic.I recommend to reword the sentence and/or properly define the meaning of "flux" in this context.line 78...I recommend to explain why the flux ratio suddenly switches from ~0 to ~1 at a latitude of 50-60 deg.
Coordinates should also be defined, I assume these are geographic (not geomagnetic) coordinates.I also recommend to show that this is different from other cases, where the strong diffusion is absent.One summary sentence in the main text and a well documented set of cases in the Supplementary material would be good to prove the point and this would also certainly fit in the format of Nature Communications.This leads to chorus amplitudes above 1nT for reaching strong diffusion at 300 keV.Such amplitudes have been observed by Van Allen Probes data but this should also be supported by reference(s).
An alternative explanation can be that the interaction takes place at higher latitudes beyond the Van Allen Probes orbit, where the background magnetic field is stronger, modifying the resonance condition.line 126 ... I suggest to mention the scaling factor here line 130 ... One can guess from the context, but a few words to define E_SD at the first occurrence of this symbol would make the text better readable.line 158 ... I recommend to explicitly state that scaling factor for 300 keV is higher than for 30 keV (which should also be given here)

REPLIES TO REVIEWER COMMENTS
Replies are made immediately a er each comment, forma ed in green italics.Thank you to all the reviewers for their inputs.

REVIEWER COMMENTS
Reviewer #1 (Remarks to the Author): Review report of the manuscript "Electron Accelera on During Strong Pitch Angle Diffusion" by Daggi et al.This is an interes ng and important study inves ga ng the possibili es of accelera ng electrons in the strong pitch-angle diffusion regime.Strong pitch-angle diffusion has been regarded as a fast loss mechanism of energe c electrons in the magnetosphere.This study points out that even in the strong diffusion regime, the net effect of chorus waves on MeV electrons can be accelera on.This point has been implicitly included in 3D simula ons including radial diffusion, pitch-angle diffusion, energy diffusion and mixed energy and pitch-angle diffusion.However, previous studies did not include strong diffusion at ~300 keV.For example, for the event considered in this dra , Shprits et al (2015) and Wang et al (2020) reproduced the MeV electron accelera on using simula ons including radial diffusion, pitch-angle diffusion, energy diffusion and mixed energy and pitch-angle diffusion, but these studies did not include strong diffusion at 300 keV.By looking at the precipita ng electrons measured by POES satellite, this study shows that 300 keV electrons reach the strong diffusion regime.Furthermore, they showed that even in this situa on, the net effect of chorus waves on MeV electrons can be accelera on.To make this paper clearer to readers, I suggest the authors to consider addressing the following comments and ques ons.
Major comments (addressing these comments will not change the main conclusion but will help to make the paper clearer): 1. Lines 77-78: at which L-shells are the POES satellite?Did the author consider elimina ng the effect of field line curvature sca ering?I ask this because some mes these "strong diffusion" cases are caused by the field line curvature sca ering rather than wave-par cle interac ons.See figure 1 of Capannolo et al (2022).
Capannolo L, Li W and Huang S (2022) Iden fica on and Classifica on of Rela vis c Electron Precipita on at Earth Using Supervised Deep Learning.Front.Astron.Space Sci.9:858990.doi: 10.3389/fspas.2022.858990 The POES satellites cross a range of L-shells from 4 to 6.This has been specified in line 86, and is visible in the supplementary material fig. 1 for the revised manuscript.
The effect of field line curvature sca ering was not ini ally considered.The manuscript now acknowledges the effects of field line curvature sca ering, and briefly presents evidence of both effects occurring, with an addi onal plot in the style of figure 1 of Cappannolo et al (2022) in the supplementary material.
2. The lower energy boundary condi on of the simula ons is set at 100 keV with constant phase space density.Does this mean that you have a constant source at 100 keV?It is a bit difficult to have constant phase space density at 100 keV.It would be interes ng to test the simula ons with a lower energy boundary at 10 keV.
The constant low energy boundary at 100keV does act as a constant source at 100keV.We have included further discussion of the energy at which the low energy boundary condi on is set has been included at the end of the discussion sec on (line 144), as well as including plots showing the effect of a 10keV low energy boundary in the supplementary material fig. 3. Moving the low energy boundary has a similar effect on the steady state distribu on to simply changing the PSD at the boundary at 100keV.
Minor comments: 1. Line 42: is E the electron 'kine c' energy?
Yes, we have now defined E as electron kine c energy in the revised manuscript.
2. Please consider adding a reference here to show 14 hours gap is enough to eliminate the influence of SEP We have now added a clause specifying that the POES observa ons shown in figure 1 meet the low proton contamina on tests given in Rodger et al. (2010), with a cita on (line 93).Upon review we felt that this was a more rigorous way to show that proton contamina on should not be an issue.

Line 89: men on the method of calcula ng diffusion coefficients here
We have now stated in the cap on that we have used quasilinear theory and the PADIE code for the calcula on of diffusion coefficients (line 101), with a reference to the more detailed methods sec on.
4. Lines 93-97: are the authors using EMFISIS L4 data?I remember the me resolu on of EMFISIS survey mode wave data is 6 seconds.
We are using EMFISIS L4 data.Survey mode data is recorded every 6s, based on a 0.5s sample window, Kletzing er al. (2013).This has been clarified and has been cited in the manuscript (line 115).

Line 97:
What amplitude is the averaged wave power?Can this amplitude sustain several hours as the authors used in their simula ons?
The averaged wave power used for the diffusion coefficient calcula on was 0.2nT^2.We have now stated this in the revised manuscript (line 130).
We do not intend to present evidence that this amplitude can be sustained for the length of the simula on, and our opinion is that this is unlikely.We have now clarified in the revised manuscript that the simula ons are not an a empt to reproduce any par cular event and are only intended to show the effects on steady state produced by high chorus wave power (i.e.accelera on domina ng over loss) (line 198).
6. Line 118: I agree.Van Allen Probe A was on the nightside and it orbits magne c la tude lower than 20 degrees.This makes it hard to see the strong chorus waves on the dayside high la tude.Authors can cite here sta s cal studies of chorus waves (e.g., Meredith et al., 2012;Wang et al., 2019) to make it clearer.Figure 12i of Wang et al (2019) showed that the intensity of lower band chorus waves on the dayside increase with la tude.Then Wang and Shprits (2019) showed the importance of chorus waves at high la tude.We have added addi onal discussion of the dayside chorus wave power and high la tude chorus wave power which may contribute to the discrepancy between the POES data and the waves seen by the VAP (line 144).
7. Line 127: this is an interes ng test, but it is also unrealis c.Daa, DaE and DEE have the same scaling with Bw2.I understand authors would like to test the situa on when Daa is strong while DaE and DEE are rela vely weaker.Please elaborate more.
Our inten on was to simulate a situa on similar to the original Kennel 1969 formula on of the strong diffusion limit, where energy diffusion was considered to be insignificant.We have added a sentence to the revised manuscript explaining this (line 165), and another clarifying that the tests scaling Daa, DaE and DEE by the same factor are more realis c given modern theory.

Line 175: DEE (space here) are
There was a space, but it was forma ed as subscript and italic, and thus smaller.This has been fixed.

Line 191: figure 3D?
The wrong figure panel was referenced, we have now corrected it to say figure 3D.10.Line 204: is 30 the scaling factor of Bw or Bw2?
We have clarified in the revised manuscript that we are referring to a factor of 30 in the squared wave power (line 249).

Line 386: no loss term in the equa on (1)
There was a missing loss term, we have now added it into the revised manuscript.
Reviewer #2 (Remarks to the Author): This paper describes simula ons of electron diffusion using the 2D BAS Radia on Belt Model,in par cular associated with strong diffusion induced by chorus waves.I believe the results are correct and to be of interest to radia on belt modellers.This submission is more of a technical note than a scien fic paper.As such,it would not be appropriate for GRL or JGR(Space Physics).However,this submission may be appropriate for Nature Communica ons.The manuscript is based on results of quasi-linear calcula ons of diffusion coefficients of energe c electrons in the outer Van Allen radia on belt.The authors scale all the diffusion coefficients up to the strong diffusion limit, and show that energy diffusion to rela vis c energies can outweigh losses caused by pitch angle diffusion.Although the main result is obtained by theore cal calcula ons using simplified models, experimental data from the POES and Van Allen Probes spacecra are also used in order to support the theory.
Generally, the text is well wri en and easily readable.Problems I see in it are mainly linked to experimental data, as detailed below in my specific comments.Nevertheless, the logic of the main message is so straigh orward that it makes me wonder why it hasn't been brought up earlier.This is probably a sign of a good paper and I therefore recommend it for publica on in Nature Communica ons a er a revision is done by the authors.Specific comments: line 59...The condi on of equal precipitated flux to the trapped flux seems unclear as it is wri en here, although the context shows that it probably just means that the velocity distribu on has to be isotropic.I recommend to reword the sentence and/or properly define the meaning of "flux" in this context.
We have now specified that we are referring to direc on, integral electron flux, and that this condi on arises because the velocity distribu on becomes isotropic under strong diffusion (line 59).line 78...I recommend to explain why the flux ra o suddenly switches from ~0 to ~1 at a la tude of 50-60 deg.Coordinates should also be defined, I assume these are geographic (not geomagne c) coordinates.I also recommend to show that this is different from other cases, where the strong diffusion is absent.One summary sentence in the main text and a well documented set of cases in the Supplementary material would be good to prove the point and this would also certainly fit in the format of Nature Communica ons.
The transi on occurs near L=4, near the typical plasmapause loca on.As POES crosses the footprint of the plasmapause, it begins to record electrons that may have encountered high chorus wave power, resul ng in rapid pitch angle diffusion.We have added a sentence to this effect to the revised manuscript (line 79).
We have now specified the use of geographic coordinates (lines 65 and 100).This event was shown as it was the best example found in a non-exhaus ve search of storms where POES showed flat pitch angle distribu ons and VAP recorded high chorus wave power, sufficient to cross the strong diffusion limit.We have looked at other events, but did not find others that met our criteria (flat pitch angle distribu on, diffusion coefficients > strong diffusion limit, satellites passing similar MLT and L within a small me window when the other two criteria were met).Most events showed evidence of flat pitch angle distribu ons, but not many showed high wave power.As our inten on is only to demonstrate that these condi ons can occur, we do not feel that the difficulty of including addi onal properly analysed case studies in the supplementary material would enhance the manuscript enough to jus fy their inclusion.A sentence to this effect has been added on line 153.line 93...The frequency band over which the measured power spectral density was integrated should be men oned.
We have now men oned the frequency band over which the measured power spectral density was integrated, from f_LHR to 0.5f_ce (line 109).line 93 bis....The B^2 weighted average of wave vector direc ons can also be easily obtained from the EMFISIS Waves survey mode data, to verify the assump on of a Gaussian wave normal distribu on men oned on line 417.Again, this can by summarized by one sentence in the main text, with a reference to the technique, and some Supplementary material, all of which s ll fits in the format of Nature Communica ons.

We have now specified the use of and width of a Gaussian wave normal angle distribu on (line 112), as well as included a plot of VAP EMFISIS data from the day of the storm fi ed with a Gaussian in the supplementary material fig 3.
A er reviewing the wave normal angle data for this period and seeing that it fi ed a wider than typical Gaussian, we recalculated the diffusion coefficients in figure 1 with a wider wave normal angle distribu on (30deg to 50deg).This only had a no ceable effect on the values of Daa at higher pitch angles.These values are now be er jus fied by the data, but we do not believe that this has change our conclusions.Figure 1B has been updated to reflect the new calcula ons.line 93 tris.... Different techniques for es ma on of the plasma density exist in the literature and it should be said here which of them is used.A reference would cure it.
We have now specified that we used the plasma density derived from the frequency of f_UHR, according to Kurth et al. 2015 (line 109) line 120 ... Figure 1B shows that the equatorial squared amplitude would need to be at least 30-50 me larger to in order to reach the theore cal strong diffusion limit in a broader interval of pitch angles for 300 keV electrons.I recommend the authors to specifically state what squared amplitudes are they actually using for their calcula on.From Fig 1C I can guess that it is probably around 10^5 nT^2.This leads to chorus amplitudes above 1nT for reaching strong diffusion at 300 keV.Such amplitudes have been observed by Van Allen Probes data but this should also be supported by reference(s).An alterna ve explana on can be that the interac on takes place at higher la tudes beyond the Van Allen Probes orbit, where the background magne c field is stronger, modifying the resonance condi on.
We have now stated the squared wave amplitude used for the calcula on (0.2nT^2) (line 130).We have also added a brief discussion of higher la tude interac ons, as well as a cita on for the where this power lies within the observed distribu on of lower band chorus wave power (line 144).line 126 ... I suggest to men on the scaling factor here We have now specified the scaling factor used (line 161).line 130 ... One can guess from the context, but a few words to define E_SD at the first occurrence of this symbol would make the text be er readable.
E_SD is now properly defined in the revised manuscript (line 167).line 158 ... I recommend to explicitly state that scaling factor for 300 keV is higher than for 30 keV (which should also be given here) We have now specified that a smaller scaling factor has been used, as well as its value (line 181).line 191... 1D -> 3D ?
The wrong figure panel was referenced, we have now corrected it to say figure 3D.line 210...I see a discrepancy here: A factor of 1500 is observed between the model diffusion coefficients and the one calculated from measured waves amplitudes.Yet, according to Fig 1B, at 300 keV we s ll are by a factor of 30-50 below the strong diffusion limit.It means that a factor of at least 45000 against the model is needed to reach the limit.The problem is that in Fig 3D -F the circled symbols for 300 keV start at a factor of 2000.Therefore I have a problem of more than one order of magnitude here.I guess that I'm just missing something in this es mate but I recommend the authors to add an explana on to the text.
The discrepancy arises because the originally stated factor of 1500 between the model coefficients and the calculated coefficients near the loss cone was incorrect.This was actually the factor at 85deg, where figure 3 was plo ed, and was quoted mistakenly.
We have now corrected this to specify that there is a factor of 66 between the model coefficients and the calculated coefficients near the loss cone, and a factor of 1500 for nearequatorially mirroring electrons (line 257).line 417...I recommend to repeat what is the width of the Gaussian distribu on in the model We have now stated the width of the gaussian distribu on of wave normal angles here (line 479).line 430...The ini al exponen al decay of the phase space density might be be er described, it seems inconsistent with PSD=0 at 10 MeV and also with the ini al PSDs in fig3.
We have now clarified that the nature of the code results in PSD=0 being treated as PSD=epsilon as log flux is used (line 512).This also resolves the apparent inconsistency between the ini al PSDs and the high energy boundary, as sufficiently small PSD values in the ini al condi ons are fixed to a floor of PSD=epsilon, matching the high energy boundary condi on.

REVIEWERS' COMMENTS
Reviewer #1 (Remarks to the Author): I read the revision version of the draft and found that authors have addressed my comments well.I suggest the paper to be published.As concerns (c) I fully agree that a case study is perfectly OK, and a "full statistical treatment" would not fit in this paper.However, this is not what I suggested.
I still think that a causal link between intense low latitude chorus and the flux ratio ~1 at L>4 (which the paper seems to imply) might be better substantiated by showing an example case, as a supplementary material, where chorus is weak or absent and the flux ratio stays low at L>4.My understanding of the author's response is that this is impossible, because the flux ratio is ~1 at L>4 in most events that they looked at, even in the absence of intense low-latitude chorus.This would mean that other explanations should exist for cases when the intense low-latitude chorus is absent.The problem I see here is that these other mechanisms might be also active when intense chorus is present at low latitudes, and, in fact, these other mechanisms may still be the cause of the flux ratio ~1 at L>4, instead of chorus.
I recommend the authors to consider clearly stating that the flux ratio is ~1 at L>4 in most analyzed cases, even in the absence of intense low-latitude chorus, and adding at least some discussion on this problem.
A small issue: grammar of the text "which will not have been observed by VAP A in this event" on line 147 looks strange to me, but not being a native English speaker I leave it up to the authors to possibly fix it, if needed.
As both these remaining comments are minor and easy to be considered by the authors without another review I recommend the paper for publication in Nature Communications.3 refers to 24 hours of data on 17 March 2013.This includes three orbits of the spacecraft preceding the event, for which the wave vector angles are irrelevant to the presented analysis.I suggest the authors to narrow this time interval to relevant data acquired from 21:00 till 22:00 UTC.The attached quick-look of Level 4 data from Van Allen Probe A shows that the angle theta_k between the wave vector and local field line is still low and mostly below ~30 deg in this interval.
Another important aspect of this correction is that a very different wave normal distribution (see the azimuth angle phi_k, which was previously used instead of theta_k) doesn't alter the main results of this study.This shows that these results are very robust, nearly independent of the measured wave vector directions.I find this very interesting and I suggest the authors to comment on this robustness briefly (one sentence might be sufficient), for example in the Discussion section of the paper.
As this correction does not alter the main results of this study, conclusion of my review is still the same.

Author's replies to comments
Author's replies in green between each comment where necessary.

REVIEWERS' COMMENTS
Reviewer #1 (Remarks to the Author): I read the revision version of the draft and found that authors have addressed my comments well.I suggest the paper to be published.The only small exception is my comment on line 78 of the original manuscript, concerning the transition of the flux ratio from ~0 to ~1 at latitudes above of 50-60 deg.My comment probably was not clear enough as it contained several separate points.The authors responded (a) by clarifying that the transition occurs near the typical plasmapause location, where electrons may have encountered high chorus wave power...lines 79-82 <-here and below the line numbers refer to the revised manuscript with highlighted changes; (b) by specifying the use of geographic coordinates ...lines 65 and 100; (c) by explaining that a full statistical treatment of how often chorus wave driven strong diffusion occurs was not performed, and was beyond the scope of this study...lines 153-155.
As concerns (c) I fully agree that a case study is perfectly OK, and a "full statistical treatment" would not fit in this paper.However, this is not what I suggested.I still think that a causal link between intense low latitude chorus and the flux ratio ~1 at L>4 (which the paper seems to imply) might be better substantiated by showing an example case, as a supplementary material, where chorus is weak or absent and the flux ratio stays low at L>4.My understanding of the author's response is that this is impossible, because the flux ratio is ~1 at L>4 in most events that they looked at, even in the absence of intense low-latitude chorus.This would mean that other explanations should exist for cases when the intense low-latitude chorus is absent.The problem I see here is that these other mechanisms might be also active when intense chorus is present at low latitudes, and, in fact, these other mechanisms may still be the cause of the flux ratio ~1 at L>4, instead of chorus.I recommend the authors to consider clearly stating that the flux ratio is ~1 at L>4 in most analyzed cases, even in the absence of intense low-latitude chorus, and adding at least some discussion on this problem.This comment has made clear that our previous reply was unclear.When we stated that we observed flux ratios ~1 in all the events we looked at, we did not make it clear that we had only looked at storm events.Outside of storms the flux ratio is usually << 1 at all L shells when there are no chorus waves at low latitudes.Now that we fully understand what the reviewer is suggesting, we have included supplementary figure 2 in the supplementary information, showing a case when chorus wave power is not observed by the VAP-A satellite and low flux ratios are continuously observed by POES.This reinforces the link between chorus waves and flux ratios ~1.We have also mentioned this case in the manuscript at line 114.Some discussion of other mechanisms is included at line 118.
A small issue: grammar of the text "which will not have been observed by VAP A in this event" on line 147 looks strange to me, but not being a native English speaker I leave it up to the authors to possibly fix it, if needed.
The sentence has been re-worded to read more naturally, now on line 208.
As both these remaining comments are minor and easy to be considered by the authors without another review I recommend the paper for publication in Nature Communications.These minor comments may be taken into account by the authors while preparing the final version of the paper.

+++
Corrected version re-reviewed by O. Santolik, 21 September 2023 While the text in the corrected version of the main manuscript seems to refer to Figure 1, which highlights one hour of Van Allen Probe A data on 17 March 2013 from 21:00 till 22:00 UTC, the caption of the new Supplementary figure 3 refers to 24 hours of data on 17 March 2013.This includes three orbits of the spacecraft preceding the event, for which the wave vector angles are irrelevant to the presented analysis.I suggest the authors to narrow this time interval to relevant data acquired from 21:00 till 22:00 UTC.The attached quick-look of Level 4 data from Van Allen Probe A shows that the angle theta_k between the wave vector and local field line is still low and mostly below ~30 deg in this interval.
We have narrowed the time interval to the relevant period, and updated the corresponding data and figure in the supplementary information.
Another important aspect of this correction is that a very different wave normal distribution (see the azimuth angle phi_k, which was previously used instead of theta_k) doesn't alter the main results of this study.This shows that these results are very robust, nearly independent of the measured wave vector directions.I find this very interesting and I suggest the authors to comment on this robustness briefly (one sentence might be sufficient), for example in the Discussion section of the paper.
We have included a sentence in the discussion section mentioning this result at line 356.
As this correction does not alter the main results of this study, conclusion of my review is still the same.

Reviewer # 3 (
Remarks to the Author): Review report on manuscript "Electron Acceleration During Strong Pitch Angle Diffusion" by T. A. Daggitt et al. submitted to Nature Communications Reviewed by O. Santolik, 25 July 2023 line 93...The frequency band over which the measured power spectral density was integrated should be mentioned.line 93 bis....The B^2 weighted average of wave vector directions can also be easily obtained from the EMFISIS Waves survey mode data, to verify the assumption of a Gaussian wave normal distribution mentioned on line 417.Again, this can by summarized by one sentence in the main text, with a reference to the technique, and some Supplementary material, all of which still fits in the format of Nature Communications.line 93 tris.... Different techniques for estimation of the plasma density exist in the literature and it should be said here which of them is used.A reference would cure it.line120 ... Figure1Bshows that the equatorial squared amplitude would need to be at least 30-50 time larger to in order to reach the theoretical strong diffusion limit in a broader interval of pitch angles for 300 keV electrons.I recommend the authors to specifically state what squared amplitudes are they actually using for their calculation.From Fig 1C I can guess that it is probably around 10^5 nT^2.
Fig 1B, at 300 keV we still are by a factor of 30-50 below the strong diffusion limit.It means that a factor of at least 45000 against the model is needed to reach the limit.The problem is that in Fig 3D-F the circled symbols for 300 keV start at a factor of 2000.Therefore I have a problem of more than one order of magnitude here.I guess that I'm just missing something in this estimate but I recommend the authors to add an explanation to the text.

Reviewer # 3 (
Remarks to the Author): Review report on manuscript "Electron Accelera on During Strong Pitch Angle Diffusion" by T. A. Daggi et al. submi ed to Nature Communica ons Reviewed by O. Santolik, 25 July 2023

Reviewer # 3 (
Remarks to the Author): Second review report on manuscript "Electron Acceleration During Strong Pitch Angle Diffusion" by T. A. Daggitt et al. submitted to Nature Communications Re-Reviewed by O. Santolik, 4 September 2023 I went through the authors' responses and through the revised version of the manuscript with its supplementary material, and I was pleased to find that the authors took into account nearly all my comments from the first review of this manuscript.The only small exception is my comment on line 78 of the original manuscript, concerning the transition of the flux ratio from ~0 to ~1 at latitudes above of 50-60 deg.My comment probably was not clear enough as it contained several separate points.The authors responded (a) by clarifying that the transition occurs near the typical plasmapause location, where electrons may have encountered high chorus wave power...lines 79-82 <-here and below the line numbers refer to the revised manuscript with highlighted changes; (b) by specifying the use of geographic coordinates ...lines 65 and 100; (c) by explaining that a full statistical treatment of how often chorus wave driven strong diffusion occurs was not performed, and was beyond the scope of this study...lines 153-155.
These minor comments may be taken into account by the authors while preparing the final version of the paper.+++ Corrected version re-reviewed by O. Santolik, 21 September 2023 While the text in the corrected version of the main manuscript seems to refer to Figure 1, which highlights one hour of Van Allen Probe A data on 17 March 2013 from 21:00 till 22:00 UTC, the caption of the new Supplementary figure

Reviewer # 3 (
Remarks to the Author): Second review report on manuscript "Electron Acceleration During Strong Pitch Angle Diffusion" by T. A. Daggitt et al. submitted to Nature Communications Re-Reviewed by O. Santolik, 4 September 2023I went through the authors' responses and through the revised version of the manuscript with its supplementary material, and I was pleased to find that the authors took into account nearly all my comments from the first review of this manuscript.