Peer review of: Local heating of radiation belt electrons to ultra-relativistic energies (2020)

Reviewers' comments:
Reviewer #1 (Remarks to the Author):

Review of Local Heating of Radiation Belt Electrons to Ultra-relativistic Energies by Allison & Shprits
The major claim of the paper is that the October 2012 set of storms represented a period wherein radiation belt electrons were accelerated up to ultrarelativistic energies by local acceleration alone. The topic is of prime interest, since disentangling acceleration processes is crucial to understanding the overall dynamics of the system, and tying those dynamics to features in the solar wind that ultimately drive this variability. The conclusions would be of great interest to the community; unfortunately, the data does not support the conclusions made here. I have great concern around the interpretation of the phase space density data derived that serve as the major focus of this paper. I have listed major issues (as well as more minor), but overall do not see how the main conclusion is arrived at from the data presented in this paper.
I also have concerns that the PSD data used in this paper is a derived quantity and is not available to the public, thus restricting any reproducibility of results. The Acknowledgments claim that all data used is available publicly, but this refers to the spin-sectored flux data, not PSD. PSD was calculated using (I assume) a model energy spectrum and pitch angle distribution, but that is not specified in the paper or supplemental, so there is no way for any person to follow the methodology and reproduce these results.
Major issues:
Line 73-75: “Here, we study the October 2012 period, where the flux of >7 MeV electrons remained above the background threshold [16] for more than seven days...” I don’t think the 7.7 MeV flux was above background continuously over the time period of these two storms. Can you show evidence of this? The 6.3 MeV channel very much looks like it was above background, but 7.7 MeV looks count- starved during some of this time.
Line 88-89: “However, for both storms, Fig 3 (top) more closely resembles local acceleration
storm, we can see outward radial diffusion taking place. But during the main phase of the storm, or
 what you shade gray as the acceleration region, we see evidence of inward radial diffusion (Oct 9 – 10.5).
Line 99-100: “Reeves et al. [12] reported that the Mu = 3,433 MeV/G phase space density showed an enhancement between the 8 and 9 October.” You have this data as well – do you also see the enhancement at ~3000 MeV/G?
Line 109: “After the first phase space density enhancement, the peak moved to larger L*.” What does this mean? What first enhancement? If you look carefully at Fig 3b-c, you can see that the peak of PSD moves inward during the time shown. You don’t show the radial profiles after early on 10 Oct, so it’s difficult to see what happens after that but I suspect the peak broadens instead of really strongly peaking at higher L*, such that the one “peak” can be picked out at higher L* but really it’s more of a plateau. Need to see more information – please put in the paper or Supplemental.
Line 111-112: “While the maximum phase space density region expands towards higher L* for all values of Mu shown, for Mu < 6,000 MeV/G, an enhanced population remains around L* = 4, not observed for higher values of Mu.” What exactly are you referring to here? I don’t see this feature in any plots. In supplemental figure S7, I see enhanced PSD at L*=4 for Mu = 5000 MeV/G, 9000 MeV/G *and* 12000 MeV/G. What is this difference you are talking about? Please clarify.
Line 118-122: Again, as for the first double-dip storm, the outward radial diffusion looks like it doesn’t play a role until after the main phase, during recovery (here, starting on Oct 15th). In Fig 3d- e, you can see the local peak growing from red to green traces. Then, from green through cyan to the first blue, the peak clearly shifts inward in L*, indicating *inward* radial diffusion. This is during the acceleration period. After that, you get some complicated dynamics where the peak falls to lower PSD values, shifts outward, then rises and shifts inward again (final pink to red traces). This figure does indeed show the signature of inward radial diffusion, contrary to the final conclusions of the paper.
Line 124-126: Absolutely not. I see evidence of inward radial diffusion throughout both storms from the PSD radial profiles. How else do you explain the *inward* motion of PSD peaks?
Line 130-132: Part of this sentence holds: “Our results demonstrate that local acceleration had a significant effect on radiation belt particles during both of the storms in October 2012” The data shows this. However, the data does not support the last part of that sentence: “[local acceleration is] acting on electrons up to 7 MeV.” There is just no way to disentangle the effects of inward radial diffusion and local acceleration in this set of storms, since you see evidence of both processes happening. It might be possible to disentangle in other storm events.
Line 136-137: “occurring only a handful of times during the Van Allen Probes mission.” Not true – it has happened at least a couple dozen times, depending on your threshold for acceleration events. I suggest changing this wording.

Minor issues:
Line 35-36: Awkward language. “keeps electron’s L* values” should be something like “electron’s drift within constant L*” or similar.
Line 36: Not sure why “producing” is emphasized; shouldn’t it be “growing” that is the crucial term here?
Line 54: More awkward language. “Consider Fig 1b” should be something like “As shown in Fig 1b”.
Line 77-79: I don’t understand. Fig 2 is a cartoon schematic, right? Why is it described as using “PSD values within half-an-order of magnitude of the maximum for the period”? Which period – the one studied here? I thought this was just a schematic representation – not using actual data. Maybe you meant to say “Fig 3”? In any case, I think Fig 2 should be described first before moving on to describe Fig 3.
Line 89: “outward radial diffusion”
Figures:
• Figure 1 needs to be completely redone – it is poor quality and hard to read labels.
• Figure 3 needs to be redone. The L* labels need to be bigger in panel a. Resolution needs to be better. (This is true with all figures and may be an artifact of using PDF in LaTex. Convert to .jpg or .png first and it should help.)


Reviewer #2 (Remarks to the Author):
This study, using the Van Allen Probes’ measurements of multi-MeV electrons, presents a unique way of analyzing electron phase space densities with a wide range of μ values. The results show that during an intense storm of October 2012, electrons are heated up to ~7 MeV by local acceleration. Thus, the authors suggest that the acceleration of ultrarelativistic electrons with energies up to ~7

MeV can be caused by local heating alone and a two-step process of local acceleration combining with inward radial diffusion, which is suggested by some previous studies, is not required in accelerating electrons to ultrarelativistic energies.
This topic on the acceleration of ultrarelativistic electrons is under-explored due to the lack of high quality data prior to the Van Allen Probes era. Fully understanding the acceleration of ultrarelativistic electrons will contribute to a more comprehensive understanding of the radiation belt dynamics and thus the magnetospheric physics. It will also shed light on the energy-dependent dynamics of radiation belt particles and will be of great interest to others in this field. This manuscript is concise and well-written. However, I still have some concerns about this study’s novelty and methods.
First, as the authors also pointed out in their manuscript, several studies on the acceleration of ultrarelativistic electrons have been carried out in the Van Allen Probes era, including both data analysis and modeling. The storm this study focused on is also a widely-studied one. Specifically, Thorne et al. (2013), using a 2-D diffusion model with chorus wave heating, well reproduced the flux enhancements of electrons with energies up to ~7 MeV in the outer radiation belt during this Oct 2012 storm and demonstrated the dominant role of local acceleration in ultrarelativistic electron flux enhancements. This study by Allison et al. shows intriguing observational results confirming these results, however, the novelty may be somewhat compromised due to the previous publications.
Second, this study focuses on the acceleration of ultrarelativistic electrons up to ~7 MeV, which has been also emphasized by the authors in several places in the manuscript (abstract, line 132, etc.). However, the main results regarding the evolution of electron phase space densities focus on μ=8000 MeV/G and μ=10000 MeV/G, K=0.11 G1/2Re electrons. It was stated in the manuscript that at these μ and K values the energy of electrons correspond to ~6 MeV and ~7 MeV at L*~4.2 respectively. However, reading from their Figure S1, these μ values should correspond to ~5.5 MeV and ~6 MeV respectively, and ~7 MeV electrons should correspond to much higher μ values at L*~4 – 4.5 (>~12000 MeV/G). It is possible that during some portion of this storm the magnetic field was more distorted and these μ values corresponded to higher energies at L*~4.2; however, the mismatch between texts and Figure S1 is still a concern and may confuse readers.
Third, the way of showing the spatiotemporal evolution of phase space density maxima for a range of μ values is innovative. However, it still suffers from the similar problem with the traditional way of looking at phase space density radial profile at fixed μ and K: without sufficient spatial coverage and time resolution, the results can be somewhat ambiguous. For example, a local peak could be caused by the local acceleration alone but could also be caused by inward radial diffusion combined with fast loss at high L*. The authors should at least discuss more about this aspect.

Some other comments/questions:
1. The author pointed out the study by Katsavrias et al. (2019) on the importance of two-step acceleration on the ultrarelativistic electron flux enhancements in the April 2017 storm. However, an early study by Zhao et al. (2018) studied the same storm using both phase space density data analysis and radial diffusion modeling, showed the dominant role of inward radial diffusion in the acceleration of ~7 MeV electrons in the center of outer belt, and proposed a two-step acceleration mechanism for ultrarelativistic electron flux enhancements. Since this study by Zhao et al. (2018) focused on K=0.1 G1/2Re electrons instead of near-equatorially mirroring electrons with K≤0.03 G1/2Re in Katsavrias et al. (2019), it is more relevant to this study and should be included as a reference.
Zhao, H., Baker, D. N., Li, X., Jaynes, A. N., & Kanekal, S. G. (2018). The acceleration of ultrarelativistic electrons during a small to moderate storm of 21 April 2017. Geophysical Research Letters, 45, 5818–5825. https://doi.org/10.1029/2018GL078582.
2. Line 39 “... above energies of ~3 MeV, chorus wave acceleration declines...”: since this study mainly focuses on the importance of chorus wave acceleration on ultrarelativistic electron flux enhancements, it would be helpful to have some discussions regarding the reason of chorus wave acceleration declining for ultrarelativistic electrons and why this does not affect the main result of this study.
3. As the results of this study heavily rely on the accuracy of phase space density calculation, the method used to calculate phase space densities and phase space coordinates will need to be provided in more detail. For example, how was the interpolation done and what assumptions have been used when interpolate the energy spectrum/pitch angle distribution? These information will be critical for readers to reproduce their results.
4. Figure S8 and S9: It would be better to show the corresponding μ values, 8000 MeV/G and 10000 MeV/G, as in the main manuscript, in order to make a more direct comparison.



Reviewer #3 (Remarks to the Author):

This paper examines radial phase space density profiles from two events in October 2012, examining what acceleration mechanism is responsible for the enhancement of ultra-relativistic electrons during this period. They conclude that for these events, local acceleration is responsible for heating these electrons up to 7 MeV.
Overall, the analysis and visualizations in this paper are appropriate and well done. In addition, the results could represent an important and influential contribution to the community. However, some additional analysis/discussion is needed to support the overall conclusions as currently written.
Major Comments:
At present, the paper suggests that the presented observations “unequivocally demonstrates that electrons are heated up to 7 MeV from local acceleration alone”. While the paper clearly demonstrates that local acceleration is active during these events and is likely the dominant mechanism, some additional discussion/analysis is needed to justify that local acceleration is solely responsible for the observed enhancements.
For the 9 October event, the authors state: “Throughout the enhancement, negative gradients were observed at L* > 4.5, indicative of local acceleration.” However, looking at Figure 3b-c, there is a clear enhancement near apogee for the 9-Oct 8:45 and 12:40 passes. This conincides with the large enhancement at L=4.25. On a related note, I’m unclear why these enhancements near apogee don’t appear in Figure 3a.
Similarly, for the 14-15 October event: The 14-Oct 22:14:19 pass in purple for 10000 MeV/G shows a clear secondary peak at L* = 5.1. This precedes some the growing peaks at lower L* observed in the subsequent passes (00:07 and 03:25).
Without observations at larger L*, this suggests that the observed enhancements at low L* could be due (at least in part) to rapid inward transport coupled with an on-off source process at higher L*. This possibility and any constraints the observations would place on it should be discussed.
Minor Comments:
- Figure 2: This figure is a very nice visualization of the different acceleration mechanisms. My only minor suggestion would be to consider having the local acceleration peak appear at the same L* in each panel. Relative to panel 1b, panel 1d appears at larger L* and panel 1c at smaller L*. If this makes the plots more difficult to read, this suggestion can be ignored.

- Figure 3: Marking these intervals in some way to show inbound vs. outbound passes would be useful.