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

Reviewers' comments:
Reviewer #1 (Remarks to the Author):
Review #2 of Local Heating of Radiation Belt Electrons to Ultra-relativistic Energies by Allison & Shprits
Having reviewed the author responses and changes to the manuscript, I unfortunately still have great concerns about the conclusions of this paper. Overall, I don’t see that the data here supports the conclusions unambiguously. Nowhere in the manuscript do you say that inward radial diffusion was clearly acting over the day of Oct 9th on higher energies, although it is very evident in the data (see point 2 below), so it appears that you are actively avoiding this discussion. I think this topic is extremely timely and of great interest to the community but I do not see the evidence in this event as presented. It may be possible to find another event which unambiguously shows local acceleration directly leading to 7.7 MeV electron enhancements (very clear growing peak signatures – much more clear than shown here), and I encourage authors to look for an event like this.
In summary, I do not recommend publication of the manuscript. It is an interesting analysis of the storm event, but without robust support of the stated conclusion, it is not new enough to constitute publication in this kind of journal.
Major issues still unresolved:
1. In the first review, I asked that you show evidence that the 7.7 MeV electron channel was above background. It turns out it was at the 1 or 2 count level for the beginning of the Oct 8-9 period. The same is true for some of the lower energy channels. Channels 5-7 appear to be below background until the pass starting at ~2 UT on 10/9, and Channels 6-7 are still below background until the inbound pass starting at ~6 UT on 10/9 and the next outbound pass starting at ~11 UT on 10/9, respectively. However, for the Oct 13-14 period, all channels were above background levels and that data is viable.
The concern that comes with this surrounds the validity of the PSD profiles for the Oct 8-9 period. For the first part of this period, the flat PSD curves (dark blue and black in your plots) are meaningless. The data used to derive PSD is not robust. The first light blue curve is also not representative, since the values at low L will be from those data points below background (you can see the PSD values are very close to the dark blue and black curves). The second light blue curve is the most valid point to start the analysis – here, all data points are likely above background and we
can trust the shape of that profile. Except, when I look at the publicly available PSD, I see PSD value are not the same as what you show. The magnitudes are very similar, but the trend doesn’t always look quite the same. This can be true depending on the different methods used to calculate PSD, but in this case I would say it is not clear that there are growing peaks in either storm case. In fact, from your Oct 13-14 plots, I don’t see growing peaks at all. Green and blue curves look like positive or flat gradients – the peak is only evident in the red (maybe orange for 8000 MeV/G) traces, at which time the maximum magnitude has stopped increasing.
You can see this in the Supplemental information as well. Look at your Fig S1, 8000 and above panels. You see no growing peak – or else you would see a step by step increase in color at some mid-L value. You can check the public PSD data on the RBSP Gateway for comparison: http://rbspgway.jhuapl.edu/PSD
2. This next issue is in line with the previous one, but directly relates to my original second major issue (called “Line 88-89” in the first review). I still see clear evidence of inward radial diffusion from Figure 4. It’s hard to see all the Mu values clearly, but at least for the 10000 MeV/G and 8000 MeV/G values (the two red layers on top), there is very clearly an inward movement of the peak before a flattening and/or outward motion. I’m including an annotated figure with my review to show the period I’m referring to.
As for the radial diffusion modeling, this can be tuned according to what diffusion rates are used and we know that many events do not follow the Kp parameterized values but have event-specific rates that can differ greatly from storm to storm. Showing one run of a 1-d diffusion model does not support the conclusion that local acceleration was the main driver here. Other groups have successfully modeled all Van Allen Probes observations using radial diffusion alone (see Mann and Ozeke, 2016, JGR) – it just depends on the rates you decide to use.
3. I suggest plotting RBSP-B PSD profiles as well, since A shows some complicated dynamics during both of these storms, while B seems to catch the belts during the more stable intervals (overall). I don’t think this will strengthen the argument you are putting forth, but it may be worth looking at more closely.
4. In your newly added Supplemental material, you say you used 5 minute averaged REPT data (Line 33-34). How are you using averaged data to get individual sector information for pitch angle direction? Or do you mean that you are averaging after calculating PSD? Or are you averaging within each pitch angle bin by 5 minutes?

Related to that, in your method you say that you interpolate PSD to a target value of K, but don’t mention a model pitch angle distribution. Is it a liner interpolation from one K-value to the next to ascertain the point in space that matches your target K? If so, this may introduce errors since the pitch angle bins can be very under-sampled (even somewhat close to 90 degrees depending on angle of spacecraft to Bfield). Usually a model pitch angle distribution is used to account for this (which I know has its own problems). What happens if you instead target a certain Mu value and base your interpolation on that? Does it change your results much? The reason I asked is based on the discrepancy between your PSD profiles and the ones I have access to on the Gateway, which may have been derived in a different way.
Reviewer #2 (Remarks to the Author):
The authors have addressed some of my comments. However, I still have some concerns regarding the responses to my third major comment. The authors have added some discussions (lines 180 – 190) and also figures (Figs S8 and S9) to the manuscript to address the spatiotemporal ambiguity in the phase space density radial profile. Specifically, it was stated that “Furthermore, the last closed drift shell location is at L* ~5.5 - 6.5 for the first storm and L* ~6 - 6.5 for the second (Fig S8). The minimum energy of the source population that would be required for the observed 7 MeV enhancements is >3 MeV (Fig 2) and it is unclear where this would originate.” However, Fig 2 does not give the electron energy at L*>~5.6, making it hard for readers to know what the corresponding energy of the potential source population around GEO would be. Also, the statement that “it is unclear where this would originate” is hard to understand – is it saying that there are not so many high energy electrons at the high L region to act as the source population for >7 MeV electrons in the center of the outer belt? In addition, it was stated that “These additional observations suggest an absence of a rapidly appearing source population for radial diffusion during both events.” However, GOES data in Fig S9 does show some flux enhancements of >2 MeV electrons especially during the first storm; and because of GOES’s integral channel and often steep-falling electron energy spectrum in the radiation belts, GOES measurements may not show the actual corresponding source populations of >7 MeV electrons in the center of the outer belt. I would suggest to change the wording and point out this limitation of current in situ measurements, which are not sufficient to infer the source populations of ultrarelativistic electrons at the high L region.
Another minor comment: a manuscript recently published by Zhao et al. suggested the dominant role of inward radial diffusion in the acceleration of ultrarelativistic electrons through statistical analysis on 19 electron flux enhancement events during the Van Allen Probe era. While their results

may not necessarily contradict this study as they focused on the general statistics while this study focuses on two specific storms, it is beneficial to discuss their results in the context of this study.
Reference: Zhao, H., Baker, D. N., Li, X., Malaspina, D. M., Jaynes, A. N., &Kanekal, S. G. (2019). On the acceleration mechanism of ultrarelativistic electrons in the center of the outer radiation belt: A statistical study. Journal of Geophysical Research: Space Physics,124, 8590–8599.
https://doi.org/10.1029/2019JA027111.
Reviewer #3 (Remarks to the Author):
This paper addresses the acceleration of ultra-relativistic
electrons using phase space density observations from the Van Allen Probes. This is an important and relevant result and should be an impactful contribution to the community.
The authors revisions have adequately all of my concerns and I am happy to recommend publication.