Peer review of: Origin of two-band chorus in the radiation belt of Earth (2021)

Reviewers' Comments:  
 
Reviewer #1:  
Remarks to the Author:  
Summary  
 
This manuscript presents the generation mechanism for two-banded chorus observed in the 
Earth’s radiation belts using comprehensive satellite measurements of waves and electrons, 
together with a simulation study. The two-band chorus is commonly observed at Earth and other 
magnetized planets such as Jupiter and Saturn, while the generation mechanism has not been 
identified well for decades despite numerous theoretical and observational studies. Chorus waves 
play crucial roles not only the dynamics of the outer radiation belt (such as acceleration and loss 
processes of high energy electrons) but also atmospheric physics, since the waves cause energetic 
particle precipitations that may affect the temperature, density, and composition of atmospheric 
molecules. Thus this study potentially has an impact on the research area.  
 
The authors find signatures of the electron acceleration via Landau resonance with chorus waves 
and argue that the electron acceleration results in a split of a single anisotropic distribution into 
low and high energy anisotropic components. They suggest that the two anisotropic distributions 
are responsible for the generation of lower- and upper-band chorus. This suggestion is tested by 
the simulation study, and they reproduce the electron acceleration and the formation of two-
banded chorus observed by the satellite. Although the signature of the electron Landau resonance 
was reported by the satellite measurements [Min et al., 2014], the authors show more convincing 
observational results and strengthen their argument combining the excellent simulation study with 
the observation.  
 
The reviewer believes that the approach combining the satellite measurements with the simulation 
study is novel to prove their generation model. Their observational data and the simulation result 
are sound and well described, with some exceptions that the reviewer details below. The necessary 
information to reproduce the results is available in the manuscript.  
 
In summary, the reviewer believes that the manuscript has the potential to meet the standard for 
publication on Nature Communications as the presented results may have an impact on the 
research field. On the other hand, the reviewer thinks that the manuscript needs some clarification 
with respect to some issues shown in the following.  
 
Specific comments  
 
Line 57:  
Referencing seems to be inappropriate. Why is the paper on hiss waves referred here?  
 
Line 69-72:  
The reviewer thinks that the appropriate location of this sentence seems to be at the top of the 
next paragraph.  
 
Line 82-86:  
As the authors indicate in the manuscript, the linear growth rate calculation in Figure 2 fails to 
explain the observed wave frequency spectrogram. For example, the observation shows upper-
band chorus lies in the frequency range from 0.5 to 0.7 fce, while the linear theory predicts that 
the wave growth is possible in the frequency range of 0.7-0.8 fce. This result does not support the 
authors’ conclusion that two anisotropic distributions are responsible for excitation of banded 
chorus waves.  
 
Line 117-121:  
The authors argue that the distributions shown in Figure 3 demonstrate the result of Landau 
acceleration by chorus waves. However, in some cases, it seems to the reviewer that the 
distributions are not the result of the Landau acceleration (e.g., 2013-09-24, 2014-02-28, 2014-
04-19, 2014-04-21, 2014-05-09, 2014-08-01), since a kink (or a plateau) appears near the 
resonance energy for all pitch angles. Does the mechanism considered by the authors explain the 
feature? Also, It is not clear which events clearly show f(18deg) > f(36deg).  
 
Figure1:  
Figure 1b in the manuscript and that attached to the manuscript seem to be different. Which is the 
correct version?  
 
Figure 5:  
The reviewer believes that the authors need to redraw the schematic illustration shown in Figure 5 
(especially Figure 5b) after the consideration described below, since the illustration may not be 
correctly understood by experts who have studied chorus waves.  
Many previous works have indicated that discrete rising tone chorus elements seen in Figure 1c 
are excited though nonlinear wave-particle interactions between electrons and whistler mode 
waves predicted by the linear theory. (I should note that importance of the nonlinear aspect on 
chorus excitation is not described in the current manuscript at all, while the reviewer understands 
that the aspect is not the critical point of this manuscript.) Based on the theory of chorus 
excitation, chorus elements are generated after the excitation of linear phase whistler mode 
waves. It is essential to consider the time scale for Landau damping/acceleration and triggering of 
chorus elements to show the schematic illustration. If the damping/acceleration process is faster 
than chorus excitation, it is quite difficult for chorus elements to go through 0.5 fce. If chorus 
excitation is faster than the damping process, one chorus element is split into lower- and upper-
band chorus waves. However, it is quite difficult to explain the lack of one-to-one correspondence 
between lower- and upper-band chorus waves which is seen in Figure 1c.  
If the Figures 5b and 5d show wave power distributions as a function of frequency, the illustrations 
are acceptable for the experts.  
 
Reference:  
Min, K., K. Liu, W. Li, Signatures of electron Landau resonant interactions with chorus waves from 
THEMIS observations, J. Geophys. Res. Space Physics, 119, 5551–5560 (2014), 
doi:10.1002/2014JA019903.  
 
 
 
Reviewer #2:  
Remarks to the Author:  
ELF/VLF chorus emissions are intense electromagnetic plasma waves that are naturally and 
spontaneously excited near the magnetic equatorial plane outside the plasmasphere during periods 
of magnetic disturbance. These emissions are believed to play an important role in the acceleration 
of keV radiation belt electrons to MeV energies during the disturbed time periods. Chorus 
emissions frequently occur in two frequency bands with a gap near half gyrofrequency. Despite 
their common occurrence and importance in electron acceleration, generation mechanism of 
chorus including the double band (two-band) structure remains a subject of ongoing research.  
 
The manuscript (MS) under review has provided simultaneous measurements of two-band chorus 
and electron phase space density (PSD) illustrating a close correlation between the double band 
structure and two distinct anisotropic components in electron PSD at few hundred eV and a few 
keV separated by an isotropic PSD at intermediate energies. Using 1-D particle in cell (PIC) 
simulations, authors have self-consistently produced observed double band chorus and electron 
PSD with two distinct anisotropic PSD components.  
 
The proposed chorus generation mechanism is interesting because it self-consistently explains 
both the observations of the two-band chorus and two distinct components in the anisotropic PSD. 

Though the MS has provided 20 good cases of the simultaneous observations of two-band chorus 
and PSD with two distinct anisotropic populations, neither the data presented in this paper as nor 
the generation mechanism provided are not entirely novel. For example, Schriver et al. [2010], Liu 
et al. [2011], Fu et al. [2014], Ratcliffe and Watt [2017] have proposed similar generation 
mechanisms for two-band chorus. Schriver et al. [2010] and Fu et al. [2014] have provided similar 
wave and particle data from Cluster 4 and Van Allen Probes satellites, respectively. The MS does 
not adequately discuss how the mechanisms proposed and the data presented are fundamentally 
different from those presented in the literature. The MS has not referenced Schriver et al. [2010], 
one of the first papers to consider chorus generation mechanism similar to one proposed in this 
MS.  
 
One of my major concern is that the proposed mechanism by authors to explain the often 
observed double-banded structure implies that there be a strong correlation between the lower 
and upper band chorus. However, there are several previously noted features of the double-
banded chorus that are not consistent with this implication. For example, Burtis and Helliwell 
[1975] have noted that when two bands are present simultaneously the individual elements rarely 
show a one-to-one correlation between bands. That such a correlation is lacking can also be seen 
from Figure 1 of the MS.  
 
The proposed generation mechanism also needs to explain other observed features of the chorus 
spectrum [e.g., Burtis and Helliwell, 1975] and wave normal direction [e.g., Li at al., 2016; 
Hartley et al., 2019] as noted in the literature. Quasi-parallel Chorus wave normal angles used in 
this study for simulations may not be a common feature of either lower or upper band chorus as 
suggested by recent wave normal analysis [Li et al., 2016]. The past research has shown that 
inhomogeneity in the geomagnetic field is essential in explaining the discrete rising/falling 
structure of chorus elements [e.g., Omura et al. 2009]. Authors should explain how their 
simulations without using inhomogeneity in the magnetic field can produce rising emissions.  
 
The details of the methods used are insufficient, and hence the results presented may be difficult 
to reproduce. See below.  
 
a) Applicability of Darwin code for chorus simulations: In the past, mostly full electromagnetic 
(EM) particle in cell (PIC) codes were used for chorus simulations [e.g., Fu et al., 2014]. Darwin’s 
code neglects the transverse component of displacement current. Why was Darwin’s code chosen 
over full EM PIC codes? Also, Darwin’s code permits relaxed integration in time which may lead to 
numerical instability. What is the time step used for the simulations presented? Will simulation 
results be different if a full EM PIC code is used?  
 
b) Insufficient methodological detail  
Examples: Lines 208-211 It is not clear how the authors concluded to fit electron phase space 
density (PSD) distributions measured by the HOPE instrument as a summation of bi-Maxwellian 
distribution and Kappa (power law) distribution. Is such fitting done previously? If so references 
must be provided. What is the methodology used for fitting? Was it trial and error? How were the 
input parameters chosen and varied? What are the reasonable ranges of parameters chosen? Is n0 
same as Ne in Table 2? Is it Ne at the equator?  
 
c) Line 217: It is not clear what authors mean by 5 electron components to fit. Also, from 
observations, electron density was found to be roughly constant (line 52) whereas from table 2 it 
can be noted that Ne varied in the range 7.2 to 0.001. How do the authors justify such large 
variation in Ne to fit the data?  
 
d) Lines: 136-139: What is the rationale for describing isotropic cold plasma by the Kappa 
distribution? Is this kind of a distribution justified? At what location are the inputs prescribed? 
What is the value of n0 used in simulations?  
e) Lines 221-223: How are the growth rates calculated? What is fitted analytical distribution? Was 
this method validated in the past? If so provide references.  
 
f) Other relevant questions to simulations and methodology that need to be addressed include: 
what are the input and outputs of the code/simulation? What is the typical simulation time? Are 
the chosen inputs reasonableness? The validity of the code for the simulations presented in the 
paper? The rationale for choosing the simulation code?  
 
g) It would be useful to show the dynamic spectra of chorus emissions from simulations during 
various stages in simulation and compare simulation results with those observed.  
 
 
h) Missing references: for example, references for bi-Maxwellian distribution, Kappa distribution, 
Landau resonant energy calculations, Box-Muller method are missed. References for the validity of 
the models used in the paper are missing.  
 
 
Minor comments (not extensive):  
 
1. Lines 47-52: It will be useful to give Van Allen Probe orbit information, L-shell, MLT at which 
chorus was observed, measured fuh, calculated values of fpe and fce.  
2. Line 53, Are the fpe and fce values along the orbit roughly constant?  
3. The values of fpe/fce used for calculating resonant energies (Figure 2; fpe/fce=5.5) and particle 
in cell simulations (fpe/fce=5) was different why?  
4. The discussion section is more like summary and concluding remarks  
5. Organization of the paper: It will help the reader if the methods for calculating growth rates and 
fitting electron distributed is presented earlier in the simulations section rather than at the end of 
the paper.  
6. How do the authors explain the variability of the banded chorus gap width?  
 
References:  
Burtis, W. J. and Helliwell, R. A. (1976) Magnetospheric chorus: occurrence patterns and 
normalized frequency. Planet. Space Sci. 24, 1007.  
 
Hartley, D. P., Kletzing, C. A., Chen, L., Horne, R. B., & Santolík, O. (2019). Van Allen Probes 
observations of chorus wave vector orientations: Implications for the chorus-to-hiss mechanism. 
Geophysical Research Letters, 46, 2337–2346. https://doi.org/10.1029/2019GL082111  
 
Li, W., O. Santolik, J. Bortnik, R. M. Thorne, C. A. Kletzing, W. S. Kurth, and G. B. Hospodarsky 
(2016), New chorus wave properties near the equator from Van Allen Probes wave observations, 
Geophys. Res. Lett., 43, 4725–4735, doi:10.1002/2016GL068780  
 
Schriver, D., et al. (2010), Generation of whistler mode emissions in the inner magnetosphere: An 
event study,  
J. Geophys. Res., 115, A00F17, doi:10.1029/2009JA014932.  
 
 
 
Reviewer #3:  
Remarks to the Author:  
In this manuscript, the authors at first observed that two-band structure of chorus waves are 
usually associated with two anisotropic electron components, and then they tried to use 1-D PIC 
simulations to demonstrate that the initially excited single-band chorus waves can alter electron 
distribution via Landau resonance and divides the electron anisotropy into a low and high energy 
components, and at last both the upper- and low-band chorus waves are excited. The idea is 
attractive, however, I think that the evidence is not enough to support the conclusion. The reasons 
are described as follows.  

1. After I read the manuscript, I am a little confused on where the two-band structure of chorus 
waves is formed. From the Figure 1, the waves have obvious rising tone, so they have already left 
the source region of the excited waves. However, in the simulation, the authors are describing the 
excitation of whistler waves by an electron temperature anisotropy, it is in the source region of the 
excited waves.  

2. In the observations, the chorus waves have a two-band structure, and the amplitude of the 
lower band is larger than that of the upper band. However, from Figure 2, the growth rate of the 
upper band is larger than that of the lower band. If the two bands of the chorus waves are excited 
separately by a low and high energy electron components, it is difficult to explain it. Again, if 
according to the electron distribution the whistler waves have a high growth rate, they should be 
in the source region. An electron temperature anisotropy should excite whistler waves propagating 
both parallel and antiparallel to the magnetic field, then how can the waves have an obvious rising 
tone.  

3. In simulations of whistler waves excited by an electron temperature anisotropy, during the 
relaxation of the temperature anisotropy, the frequency will drift to a value. It is not strange to 
observe a gap due to Landau resonance if the excited waves obliquely propagate. So, it is not clear 
whether the low-band of whistler waves are excited by the high energy component.