Solar Energetic Particles Propagation under 3D Corotating Interaction Regions with Different Characteristic Parameters

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

The manuscript holds promise for publication; however, significant revisions are necessary before it can be deemed ready for publication. The paper delves into crucial topics concerning energetic particles associated with Corotating Interaction Regions (CIRs). Nonetheless, various fundamental issues, spanning from clarity in formulation to methodological consistency and interpretation of results, demand attention.

 

Of particular interest is a recent paper published by Husidic et al. 2024 (https://doi.org/10.1051/swsc/2024009). In their work, a very similar model is employed, wherein the FTE is solved alongside an MHD background solar wind. Husidic et al. 2024 demonstrate that the maximum energy obtained at CIR compression waves depends on the resolution utilized for the underlying MHD simulation. This strongly influences several of the results presented in the paper, including those in figures 3 and 4 of the current manuscript, and therefore merits detailed discussion.

 

Section 1: Introduction

 

The authors appear to conflate two distinct energetic particle populations. While the first two paragraphs discuss solar energetic particles (SEPs) generated during solar eruptive events, the subsequent paragraph (lines 33-48) introduces the work on energetic particles produced by CIRs in the interplanetary medium. These energetic particles are accelerated within the solar wind itself, often well beyond Earth's orbit, and are unrelated to solar eruptions. In other words, they are not SEPs. Consequently, their composition, average streaming direction, and other properties differ from SEP events.

 

Since the authors inject energetic particles (5 MeV) from the inner boundary of their model, it appears that they are studying how an (impulsive) SEP event can be modified by the presence of a high-speed stream and a CIR. This aligns with the work on SEPs conducted by Wijsen et al. 2019a (https://doi.org/10.1051/0004-6361/201833958) and its follow-up work, Wijsen et al. 2019b (https://doi.org/10.1051/0004-6361/201935139). However, it is very different from modeling the energetic particle distributions that are produced by the CIRs themselves, as demonstrated in works such as Wijsen et al. 2021 and Zhao et al. 2015 (https://doi.org/10.3847/2041-8213/abe1cb, https://doi.org/10.1002/2015JA021762). This distinction should be clarified in the manuscript's introduction to clarify the exact scope of the paper.

 

Additionally, the introduction would benefit from more commentary on recent works regarding energetic particle transport near CIRs. While several of these studies are already referenced throughout the manuscript, integrating them into the introduction would provide a more comprehensive overview. These works include the aforementioned works of Zhao et al. 2015, Wijsen et al. 2019a & 2021, and Husidic et al. 2024. Furthermore, although the current paper does not incorporate any transport effects such as particle drifts and cross-field diffusion, it would be beneficial to acknowledge their potential significant impact on SEPs. Recent studies on the effect of cross-field diffusion near CIRs include Wijsen et al. 2019a and Ding et al. 2024 (https://doi.org/10.3847/2041-8213/ad2f3c); for the effect of drifts near CIRs, see Wijsen et al. 2020 (https://doi.org/10.1051/0004-6361/201937026).

 

Lines 25–32: These hypotheses regarding impulsive and gradual events are prevalent, but the current formulation implies complete establishment, whereas numerous other hypotheses exist. Thus, it would be preferable to rephrase these lines to indicate the ongoing debate.

 

Line 33: Remove 'too.'

 

Section 2: Methods

 

The description of the inner boundary conditions (BCs) in the model appears unnecessarily convoluted. The authors employ a potential field in conjunction with the WSA model to derive BCs at 0.1 au through a series of equations without providing adequate explanations (as noted in my comments below). This approach is somewhat surprising, as it seems overly complex and ultimately unnecessary. The PFSS and WSA models were originally developed and refined to translate actual magnetogram observations of the solar photosphere into plasma conditions in the solar wind at distances of 0.1 or 1 au. However, in the present study, no such magnetogram data is utilized, and instead, a simpler dipole magnetic field is employed, which assumes a source surface at infinity. Consequently, this renders the WSA approach invalid, because (1) it is a semi-empirical formula not calibrated for use with such a dipolar magnetic field and (2) the WSA formula contains parameters that are only well-defined for a finite source surface (as explained more in the comments below).

 

However, given that the manuscript utilizes synthetic solar wind data rather than any actual magnetogram data, it would be far clearer to present the inner boundary conditions directly in a figure, akin to Figure 1, but also for a selection of Set A and Set B cases. This approach would enhance clarity and facilitate a better understanding of the inner boundary conditions used in the study. The equations can be moved to an appendix, as it breaks the flow of the text and are ultimately not needed (provided that Figure 1 is updated) to understand the rest of the manuscript. 

 

Line 71: Why is the centrifugal force included? Are the equations solved on a corotating grid? If so, where is the Coriolis force?

 

Line 73: What do the authors mean by "We use geometric meshes in the radial direction ranging from 0.35Rs to 6.19Rs"? Is this referring to the radial resolution? Are stretched grids employed? What is the angular resolution of the mesh?

 

Line 76: Please replace 'very well' with 'reasonably well.'

 

Equations (5): This equation is a very specific case of the PFSS model. That is, it assumes that the source surface (the surface where the magnetic field becomes radial) is located at infinity. This is in stark contrast with the common assumption that the source surface is located at about 2.5 Rs from the solar surface. In addition, note that the WSA model actually requires a source surface at a finite distance, since the parameters θ_b and f_s are supposed to be calculated on this source surface. In addition, WSA model relies on open field lines; in contrast, with a dipolar magnetic field and a source surface at infinity, all field lines are per definition closed.

 

Line 99: Remove the sentence "Therefore, the direction of the magnetic field doesn’t matter very much," as it is unclear to what it refers.

 

Equation (7): From where does this equation originate? Why the sqrt(2)?

 

Equation (8): Please elaborate on why this temperature choice was made. Additionally, what's the rationale behind using an adiabatic index of 1.46 and not 5/3?

 

Equation (9): Please explain the origin of this equation.

 

Figure 1: Please include figures for the other cases as well. Additionally, figures depicting solar wind speed in the solar equatorial plane would be very instructive (perhaps in an appendix).

 

Section 2.2: Provide details on the particle distribution that is injected. Where are they injected? What is their injection time-profile? Is a convolution used to improve the statistics? What energy is being injected? How many particles are traced?

 

Section 3: Results and Discussion

 

Lines 152–154: The constancy of the compression width Δc in Figure 2, and its occasional opposite behavior compared to other measures of the CIR width, raises strong suspicions. This may be an artifact of either the fitting procedure or the analytical model not adequately capturing the underlying MHD wind. Hence, I recommend removing Δc from the manuscript entirely, unless the authors can unequivocally explain its disagreement with Dw or Dc.

 

Line 154: How is the stream interface (SI) located, and how is its perpendicular direction determined? Since you're working with an MHD data cube, specifying the utilized numerical method is necessary.

 

Line 157: What is a 'radius vector'? Is it a vector in the radial direction?

 

Lines 156 –165: I understand the definition of Dc, as it calculates the width under the valid assumption that the solar wind propagates mostly radially. However, I think that Dw = Dc sin(θ) is not simply the width projected onto the solar equatorial plane (if θ indeed represents the spiral angle). Instead, it gives an estimate of the width of the CIR perpendicular to the average magnetic field direction in the CIR. The authors could elaborate on this more.

 

Line 166: Since you have a full 3D simulation of the solar wind, why not directly extract Dc from your spatial mesh, instead of relying on the assumption of a constant velocity W? This approach is only necessary in spacecraft observations, where information about the solar wind is limited to the (single-point) spacecraft location.

 

Section 3.2:

 

Note that if injected at the inner boundary, the particles will have different energies by the time they reach the compression waves due to adiabatic deceleration. This deceleration, in addition to the path length and thus travel time, will vary in the fast and slow winds.

 

Figure 3: the ‘maximum energy’ is not well-defined in a Monte Carlo method. This is because, unless advanced particle splitting techniques are utilized, the statistics at high energies are always necessarily very poor (since you start with no particles at those high energies, and only few get accelerated). As such, it can be a coincidence that one compression wave has a higher maximum energy than the other compression wave, and running the simulation with a different random seed can yield a different result. Instead, a better approach is to look at the higher energy channel, which still maintains reasonable statistics. The compression wave that exhibits the highest intensities in that channel can then be considered the most efficient particle accelerator. Alternatively, one can perform a power-law fit to the energy spectrum (excluding the highest energies with poor statistics) to discern which power-law is the hardest.

 

Lines 255–257: It seems odd that the forward shock is a more efficient accelerator in two completely opposite cases. Could this simply be due to statistical noise in the Monte Carlo method used for the energetic particle model (see previous comment)? And if this is not the case, then what is the physical reason for this?

 

Line 263: What is meant by the 'approximated Parker field at 1 AU'? Does it imply that particles are propagated in an analytical Parker solar wind? If so, please provide a more detailed explanation and specify the assumed solar wind speed of the Parker wind, as adiabatic deceleration will depend on it.

 

Line 267: Shouldn't this be E_reversed/E_parker?

 

Line 283: The comparison with Giacalone’s work is wrong. The width calculated in the manuscript is for the entire CIR structure, while Giacalone's width refers to the compression waves only. To determine the width of the compression waves, you would need to calculate the divergence of the solar wind velocity vector and measure the width where it is negative.

 

Line 289: The comparison with Bucík et al. (2011) is flawed, as this work looked at energetic particles produced by CIRs only. In the present manuscript, you 5 inject  MeV particles from the inner heliosphere (i.e., SEPs), so they are not the same type of energetic particle population.

 

Figure 6: What energy range does Figure 6 depict? Are these intensities limited to particles above the injection energy? Or do they include both accelerated and decelerated particles?

 

Lines 360–361: Particles in the slow wind need to travel a longer distance to reach a certain radial distance due to the stronger curvature of the magnetic field lines.

 

Section 4: Summary

 

The conclusions and summary will need to be revisited after the authors have addressed all the comments above. Additionally, the authors should relate their work results to the currently existing results in the literature.

 

Comments on the Quality of English Language

The overall quality of the English is good. However, there are some sentences that could be rephrased for clarity, particularly in the section where the different width measures are introduced and discussed.

Author Response

Please see the attachment.

Author Response File: Author Response.pdf

Reviewer 2 Report

Comments and Suggestions for Authors

This paper describes energetic particle propagation in a model heliosphere with a variety of corotating interaction regions. The heliospheric conditions are defined through the inner boundary of a solar wind MHD model, with magnetic field structures that have been dervied form PFSS extrapolations. Different sets of models, with varying slow and fast solar wind speeds and tilt angles of the heliospheric current sheet, are studied. They lead to  heliospheric models with different CIR properties, especially CIR widths.

Then energetic particles are injected into the model heliosphere with given energies. Their acceleration/deceleration, peak intensities, and intensity  variation with time, heliographic longitude, and radial distance are systematically studied.

I have one major concern, that is the treatment of CIR-related shocks. With differences between slow and fast solar wind streams of several 100 km/s, the formation of shock waves should be inevitable. However, it is not mentioned how the authors have solved the MHD equations (1) - (4). Does their method allow for a description of shocks, i.e. discontinuities? If not, aren't the widths of the CIRs determined by numerical effects?
The limitations of the model are very concisely discussed in the very last paragraph of the Summary and Conclusion section. I wonder if interaction with CIR shocks could substantially alter the energies of the energetic particles through effects like shock-drift acceleration, depending on the shock geometry, and if this wouldn't change the conclusions significantly. If this is not the case, then a discussion on this aspect should be added to the paper. Otherwise, a major revision is necessary, since the results presented here can hardly be compared with observational data. Often the shocks themselves are the sources of energetic particles in interplanetary space. The model presented here then can only be used for cases where the speed difference between slow and fast solar wind is less than magnetosonic speeds, so that no shock forms.

Beside of this, I have a number of minor comments:

- What data are used as input for the PFSS model described in Sect. 2?

- Line 89: The acronym "WSA" coronal solar wind model should be explained.

- Equation (8): The temperature TP has the dimension of a velocity squared,   how does this relate to an actual temperature?

- Line 120: The acronyms STA, STB for Stereo A,B should be explained.

- The FTE (12) cannot be used to describe the interaction of particles with a   shock, is this correct? This question refers to my major comment above.

- Figure 4 and its discussion: What is the "Parker field at 1 AU", an undisturbed solar wind model with Parker spiral magnetic field geometry and no CIRs? How do the energetic particles injected into the model heliosphere with energy E0 change their energy there? In other words, how is this different from comparing particle energies to E0 like in Fig. 3?

- Fig. 6 and its discussion: The Figure nicely shows the evolution of particle intensities depending on time, longitude, and distance. If a bunch of energetic particles is injected with energy E0, is there also diffusion in energy as they propagate through the model heliosphere?

Comments on the Quality of English Language

The presentation is clear, I have no problem understanding what the authors mean. However, there are numerous grammatical irregularities, so the paper would benefit from some language editing.

Author Response

Please see the attachment.

Author Response File: Author Response.pdf

Reviewer 3 Report

Comments and Suggestions for Authors

 Comments on ‘Solar energetic particles propagation under 3D corotating interaction regions with different characteristic parameters’ by Y. Zhu and F. Shen

 The authors studied characteristics of CIRs affecting the particles propagation using the 3D MHD model and the FTE. When we speak of solar energetic particles (SEPs), we mean that they are accelerated by magnetic reconnection at the Sun or shocks of CMEs as reviewed by Reames (2020). The authors should clearly state that their study focused the propagation and the compression acceleration of particles in CIRs in the beginning of this manuscript. Adding to this, the authors should more clearly state their new points. The authors also need to clearly describe what they want to say in the manuscript.

Comments

The authors should clearly state that this study focused the propagation and the compression acceleration of particles in CIRs in the beginning of this manuscript.

 The authors should more clearly state their new points.

 It is necessary for the authors to describe more clearly what they want to say.

 Add an energy distribution of the particles injected at the inner boundary.

 In the manuscript, define a terminology or a variable first and the use it in the following part to avoid redundancy.

 Use Vb^min when ‘the slow solar wind speed’ means  Vb^min in the manuscript to make the authors’ meaning clear.

Use  Vb^max when ‘the fast solar wind speed’ means  Vb^max in the manuscript to make the authors’ meaning clear.

 Use the correct tense for past and present in the manuscript.

 Add a full description to an abbreviation for its first appearance and use the abbreviation following part in the manuscript.

 Detailed comments

L4 ‘different CIRs’ should be ‘CIRs with different characteristics’.

L5 ‘are’ should be ‘were’.

L7 ‘the background field including CIRs’ should be ‘the background solar wind with CIRs’.

L9 ‘Impulsive particles are injected’ should be ‘Particles were impulsively injected’.

L9 ‘are’ should be ‘were’.

L9 ‘at the inner boundary’ should be ‘at the inner boundary of the 3D MHD’ model’.

L9 ‘study’ should be ‘studied’.

L10 ‘SEPs in different backgrounds’ should be ‘particle propagation and compression acceleration in different background solar wind’.

L10 ‘show’ should be ‘showed’.

L13−17 This is known in previous works.

L17−18 More clearly state relationship between the finding of this study and forecasting the characteristics of SEPs.

L22 ‘are attracting’ should be ‘have attracted’.

L23 ‘are being carried out’ should be ‘have been conducted’.

L25-32 The relationship between this part and the authors’ study is unclear.

L27 ‘plus’ should be ‘and’.

L34-35 ‘background configuration’ should be ‘background solar wind structure’

L35 ‘large-scale background configuration’ should be ‘large-scale background structure’.

L35 ‘Corotation Interaction Region (CIR)’ should be ‘corotating interaction region (CIR)’.

L36 ‘catches’ should be ‘catches up’.

L36-37 ‘In previous observations’ should be ‘In previous works’.

L49 ‘hard’ should be ‘difficult’.

L51 ‘configuration’ should be ‘structure’.

L54 ‘configurations’ should be ‘’structures.

L55 ‘MHD model’ should be ‘magnetohydorodynamic (MHD)’.

L59 Add an explanation of ‘impulsive protons’.

L59 ‘in the inner boundary’ should be ‘at the inner boundary of the 3D MHD model’

L60 'different background parameterws’ should be ‘parameters characterizing background solar wind structures’.

L61 ‘structured’ should be ‘organized’.

L63 ‘other CIR parameters’ should be ‘parameters changing the widths’.

L65 ‘intensity distribution variation’ should be ‘variations of particle intensity’.

L69 ‘The background is’ should be ‘The background solar wind structure was’.

L69 ‘magnetohydorodynamic (MHD)’ should be ‘MHD’.

L72-74 Add radial, azimuth, and elevation resolutions of the simulation.

L73 ‘use’ should be ‘used’.

L75 ‘choose’ should be ‘chose’.

L78 ‘assume’ should be ‘assumed’.

L79-80 ‘we can obtain the Laplace equation ...’ should be ‘the Laplace equation ... is obtained’.

L83 ‘choose’ should be ‘chose’.

L86 ‘change’ should be ‘changed’.

L89 ‘use’ should be ‘used’.

L89 ‘WSA’ should be ‘Wang-Sheeley-Arge’.

L92 ‘calculate’ should be ‘calculated’.

L93 ‘choose’ should be ‘chose’.

L96−100 Is this assumption reasonable? CIRs are often observed near sector boundaries.

L98 ‘don’t’ should be ‘did not’.

L108 ‘construct’ should be ‘constructed’.

L108 ‘vary’ should be ‘varied’.

L110 ‘change’ should be ‘changed’.

L113 ‘in the inner boundary’ should be ‘at the inner boundary’.

L116 ‘Set C’ should be ‘and Set C’.

L119 ‘SIRs’ should be ‘stream interaction regions (SIRs)’.

L121 ‘STA and STB’ should be ‘STEREO-A and STEREO-B’.

L122 ‘observation range’ should be ‘the observed range’.

L122 ‘case 2, 3, and 4’ should be ‘cases 2, 3, and 4’.

L123 ‘observation range’, case 1 and 5’ should be ‘the observed range and cases 1 and 5’.

L125 ‘in the inner boundary’ should be ‘at the inner boundary’.

L127 ‘SEP model’ should be ‘Particle propagation model’.

L128−129 ‘We describe … function f(x,p,my,t). We solve FTE to model its evolution’ should be ‘We described … function f(x,p,my,t) and sloved their evolution using the FTE.’.

L139 ‘consider’ should be ‘considered’.

L141 ‘solve’ should be ‘solved’

L149 The meaning of ‘The widths of different CIRs’ is unclear. This should be ‘Different definitions of CIR width and parameters controlling their widths’.

L159−160 ‘where the pressure structure emerges from and decays back to the background’ should be ‘where the pressure starts increasing from and returns to the background’.

L168 ‘the Sun rotation rate’ should be ‘the solar rotation rate’.

L176 Is the radial extent (Dc) same as radius vector (Dc)?

L179−207 Use Vb^min instead of ‘slow solar wind speed’ and   Vb^max instead of ‘fast solar wind speed’ following to Table 1.

L203−204 ‘The definitions and criteria should be paid attention to when discussing this quantity.’ should be ‘We need to pay attention to the definitions when discussing them.’

L204−207 The meaning of this part is unclear.

L215 ‘Cycles’ should be ‘cycles’.

L220−221 Is ‘the compression azimuthal width’ same as ‘the compression width’?

L221 Why do the authors divide the compression width by 1AU?

L221 ‘background parameters’ should be ‘parameters of background solar wind’.

L227 ‘The red and bule markers’ should be ‘The red asterisks and blue circles’.

L239 & L253 & L255−256 Use  Vb^min instead of slow solar wind speed.

L263 Add an explanation on ‘that in the approximated Parker field at 1 AU’.

L270−271 This is known in previous works.

L272 ‘The intensity of SEP’ should be ‘The particle intensity’.

L273 ‘examine’ should be ‘examined’

L274 ‘at +/-10 deg. of latitude in the inner’ should be ‘within +/-10 deg. of latitude of the inner’.

L276 ‘is’ should be ‘was’.

L277 ‘Peak intensity’ should be ‘Peak intensity of particles’.

L278 ‘investigate’ should be ‘investigated’.

L278 ‘the particle peak intensity’ should be ‘the peak intensity of particles’.

L280 ‘peak intensity’ should be ‘peak intensity of particles’.

L286 ‘theirs’ should be ‘their result’

L287−288 Rewrite this part more clearly.

L295 Add an explain a difference between ‘the radial extent’ and ‘the pressure-derived radial extent’.

L297-298 Add a reference on this.

L300 ‘intensity’ should be ‘particle intensity’.

L301 ‘investigate’ should be ‘investigated’.

L307 ‘Panel’ should be ‘Panels’.

L307 ‘longitudinal-averaged’ should be ‘longitudinally averaged’.

L311−313 Rewrite this sentence more clearly.

L312 ‘the slow solar wind speed’ should be Vb^min.

L317 ‘Panel’ should be ‘Panels’.

L317−318 ‘the distribution of particle intensity at 1 AU with longitude at 60 hours.’ should be ‘’the longitudinal distribution of particle intensity at 1 AU after 60 hours since the injection.’.

L320 ‘variability’ should be ‘variation’.

L321−324 Rewrite this part more clearly.

L327 ‘the slow solar wind speed’ should be Vb^min.

L332 Define a terminology first and then use it in the following parts for ‘the longitudinal width of the particle intensity’ in L332 & L346, ‘the width’ in L334 & L339, ‘the particle width’ in L335 & L344, and ‘the particle intensity width’ in L336 & L340.

L333−334 Rewrite this part more clearly.

L335 The meaning of ‘the more CIR structures will be formed’ is not clear. Rewrite this part.

L335 Add an explanation of ‘the particle width’.

L336−338 Rewrite this part more clearly.

L338 ‘A1’ should be ‘A2’.

L338& L339 Use  Vb^min instead of slow solar wind speed.

L348−358 Rewrite this part more clearly.

L352 ‘the longitudinal-averaged particle’ should be ‘the longitudinally averaged particle’.

L353 ‘at 30 hours and 120 hours’ should be ‘after 30 hours and 120 hours since the injection’.

L355 ‘At 30 hours’ should be ‘After 30 hours’.

L356−363 Rewrite this part to more clearly explain the panels in the right column.

L364 ‘At 120 hours’ should be ‘After 120 hours’.

L369 ‘sold’ should be ‘dotted’.

L372 ‘the +/-10 deg. latitude range’ should be ‘within +/-10 deg. of latitude’.

L378 ‘work has’ should be ‘works have’.

L379−380 Rewrite this part more clearly.

L382 ‘three-dimensional magnetohydrodynamic (MHD)’ should be ‘3D MHD’.

L383 ‘focused transport equation (FTE)’ should be ‘FTE’.

L383 ‘the background field, which includes CIRs’ should be ‘the background solar wind structure with CIRs’.

L386−387 ‘Impulsive particles are introduced’ should be ‘Particles were impulsively injected’.

L387 ‘the SEPs’ should be ‘the particle propagations’.

L392 ‘the slow (mean) solar wind speed’ should be Vb^min.

L393−394 This is known in previous works.

L396−398 Rewrite this part more clearly.

L401 Use Vb^min instead of the slow solar wind speed.

L405 Add an explanation of ‘structural parameters’.

L406 Add an explanation of ‘structural modulations’.

L405−406 Rewrite this part more clearly.

L407 ‘our model found’ should be ‘we found’.

L407−408 The meaning of this sentence is unclear.

L408−410 This is known in previous works.

L411 ‘acceleration of SEPs’ should be ‘compression acceleration of particles’

L412−415 Rewrite this part more clearly.

L416−417 ‘Our model considers mainly the compression acceleration mechanism in CIRs.’ should be ‘We mainly considered the compression acceleration mechanism in CIRs in this study.’

L418 ‘are’ should be ‘were’.

 in Reference

L432 ‘Doi10.1016’ should be ’10.1016’.

L451 ‘Doi10.1029’ should be ’10.1029’.

L460 ‘Doi10.1023’ should be ’10.1023’.

L469 ‘Doi10.1007’ should be ’10.1007’.

in Table and Figures

Caption of Table 1 ‘The parameters set in the background.’ should be ‘The parameter sets of the background solar wind,’.

Caption of Figure 1 ‘in the inner boundary’ should be ‘at the inner boundary’.

Caption of Figure 2 ‘the cases selected’ should be ‘the selected cases’.

Caption of Figure 3 ‘The red and bule markers’ should be ‘The red asterisks and blue circles’.

Caption of Figure 5 ‘peak intensity’ should be ‘peak intensity of particles’.

Caption of Figure 6 ‘The distribution of particle intensity’ should be ‘The variations of particle intensity’. ‘the distribution of particle intensity varying with’ should be ‘the variations of particle intensity with’.

Figures 3, 5, and 6 Add minor ticks on the vertical axis.

Comments on the Quality of English Language

Improve English in the manuscript carefully referring the comments.

Author Response

Please see the attachment.

Author Response File: Author Response.pdf

Reviewer 4 Report

Comments and Suggestions for Authors

The understanding on solar energetic particle (SEP) events considerably evolved recently due to charge state and composition analysis of ions. It turned out that in addition to the classic impulsive/gradual events, shock waves can reaccelerate the accumulated remnant ions supplied by earlier impulsive SEPs. The largest gradual SEP events are produced when high-speed shock waves driven by wide CMEs are propagating in the ambient coronal seed population of 1-2 million K plasma. To fully explain these observations, the effect of corotating interaction regions (CIRs) which can strongly alter the energy spectra of the seed particle populations must be understood. The work described in this paper claims to be the first attempt to study of the effect of large-scale parameters of 3D CIRs on the propagation and acceleration of SEPs by numerical simulation.

The introduction correctly summarizes the difficulties due to the large variety of background populations. I disagree, however, with the statement “there are too many factors” affecting SEPs (line 33), this can be rather considered as a challenge to the models.

Several additional papers that could be usefully cited: CME evolution Riley, Ben-Nun 2022 Univ 8, 447 and Aguilar-Rodriguez et al 2024 MNRAS 529, 1250: CME-CIR interaction Geyer et al 2023 AA 672 A168:

aligned MHD Wraback et al 2024 ApJ 962 182, magnetofrictional model of the solar corona Aslanyan et al, 2024 ApJ Lett 961 L3

Section 2 provides the details of the models used to describe the background in the simulations. The solar wind plasma is considered to be an ideal MHD fluid. The coronal magnetic field is described by the potential field source surface model. The coronal solar wind is by a simplified version of the empirical Wang-Sheeley-Arge model specifying the (uniform) radial velocity at the inner boundary. For the CIR background four different scenarios/sets are chosen and compared by varying the minimum and maximum plasma speed as well as at the inner boundary and at 1 AU. Additional parameters used are the tilt angle of the magnetic dipole axis w.r. to the solar rotation axis and the azimuthal width of the fast stream. As for the transport and acceleration of energetic particles, the compression acceleration is assumed. The focused transport equation is solved numerically using the time-forward stochastic difference equation, which neglects stochastic diffusion, perpendicular diffusion, and drift velocity.

Questions: can you estimate how would modify the results including the current sheet on particle propagation? CIRs generate turbulence, can this effect be included in the simulation?

The simulation results are presented in Section 3. The parameter sets describing the background includes the minimum and maximum solar wind speed at the inner and outer boundary, respectively, as well as the tilt angle and longitudinal angular width of the fast streams. Typically, 5 different values of the parameters are chosen for each set. The authors demonstrate that, in agreement with observations, the change of various speed profile parameters modifies the width of the CIR, however, this is not reproduced in classic numerical simulations. In Figures 3 and 4 the relative energy gain is displayed as a function of background parameters and indicate significant dependence. Nearly the same variation is found in the compression width vs. acceleration curve for all scenarios, and a quite similar one for the radial extent vs. energy gain. The peak flux of energetic particles as a function of compression width and radial size is also given and exhibits little variation between different data sets.

The figure most important and most suitable for direct comparison with observations is the time-intensity profiles at different locations (Figure 6) together with the dependence of intensity on longitude and radial distance from the Sun.

I would find useful to present a comparison with a single classic widespread SEP event observed by STEREO or other s/c.

Section 4 summarizes the results of the simulations and emphasizes the importance of the plasma structures on large scales played in the energetic particle acceleration and propagation.

 

General remarks: there are many recent MHD/SEP simulations available (see a short list above). How is the present work related to these?

 

Minor – mostly grammatical – corrections

line 12 are mainly

line 97 affect

line 153 the stream

line 220 independent of

line 300 intensity

line 369 roll-over

line 395 CIR parameters

Author Response

Please see the attachment.

Author Response File: Author Response.pdf

Round 2

Reviewer 1 Report

Comments and Suggestions for Authors

Thank you for your detailed revisions and responses to my previous comments. I have reviewed your changes and have additional feedback to ensure clarity and accuracy in your manuscript.

1) Lines 35–51:

I would like to reiterate Comment 1 of my previous report and ask the authors to explicitly state that the suprathermal particle populations observed near CIRs are expected to be generated within the solar wind, and are thus not SEPs. This is important to avoid confusion since references [2] to [7] are all about CIR events and not SEPs. For example, add to line 39 something along the lines of:

 

"[...] when fast solar wind catches up slow solar wind. Moreover, these CIRs are sometimes associated with suprathermal particle populations, which are typically believed to be accelerated by the compression waves bounding the CIR (e.g., Richardson 2004). In previous works, [...]"

 

2) Lines 123–139

When introducing the boundary conditions, I suggest the authors refer to the work of Pizzo et al. 1991 (https://ui.adsabs.harvard.edu/abs/1991JGR....96.5405P/abstract), as they used the same setup. It would also be good to add a sentence(s) explaining that the tilt angle is the angle between the solar rotation axis and the magnetic dipole axis of the sun and that it is assumed that the slow wind originates from a region centered on the magnetic equator, i.e., centered on the heliospheric current sheet.

 

3) Please add the appropriate references to equations (9) and (10).

 

4) Lines 158–159: What about the longitude range? Is it 360 degrees?

 

5) Line 169:  Specify \( M \), \( \delta t \), and \( \Delta_{\text{bin}} t \).

 

6) Section 2.3: Please add an introductory sentence at the beginning of the section to clarify the scope of the section.

 

7) Lines 209–216: I would like to reiterate my previous comment and concern about the compression width \(\Delta_c\) parameter. The analytical model of Giacalone & Kocharov consists of a rarefaction region and a single compression wave. However, the author’s full MHD model of the CIR will consist of a rarefaction region, a reverse compression wave, shocked fast wind, a stream interface, shocked slow wind, and finally a forward compression wave with slow wind upstream. In other words, the MHD-generated CIR includes two separate compression waves, and hence one cannot expect that the very simple single-compression-wave model of Giacalone & Kocharov provides a good fit to this. Hence, I do not believe the width \(\Delta_c\) parameter has any proper physical meaning, which would also explain why it does not match with the other coefficients. One way to still apply the model would be to fit the forward and reverse compression waves in the MHD simulation separately. To locate the compression waves, the authors can look for the regions where \(div(V) < 0\), indicating converging (compressional) flows. However, given the relatively large difference between the fast and slow wind speed, the width of the compression waves will be strongly dependent on the resolution of the underlying computational mesh (see Husidic et al. 2024).

 

8) Lines 313–324: this explanation does not seem to agree with the assumptions of the underlying simulation. In particular, the statement "particles moving across the magnetic" cannot be correct.  Particles are only moving along the magnetic field lines since the simulation does not include perpendicular diffusion nor guiding center drifts.

 

Comments on the Quality of English Language

The overall quality of the English is good. However, there are several typos, and some sentences could be rephrased to improve clarity. Hence, I would suggest the authors to proofread the manuscript thoroughly.

Author Response

1.Comment:

 Lines 35–51:

I would like to reiterate Comment 1 of my previous report and ask the authors to explicitly state that the suprathermal particle populations observed near CIRs are expected to be generated within the solar wind, and are thus not SEPs. This is important to avoid confusion since references [2] to [7] are all about CIR events and not SEPs. For example, add to line 39 something along the lines of:

"[...] when fast solar wind catches up slow solar wind. Moreover, these CIRs are sometimes associated with suprathermal particle populations, which are typically believed to be accelerated by the compression waves bounding the CIR (e.g., Richardson 2004). In previous works, [...]"

 

Response:

We have added the statement in the introduction.

 

2.Comment:

 Lines 123–139

When introducing the boundary conditions, I suggest the authors refer to the work of Pizzo et al. 1991 (https://ui.adsabs.harvard.edu/abs/1991JGR....96.5405P/abstract), as they used the same setup. It would also be good to add a sentence(s) explaining that the tilt angle is the angle between the solar rotation axis and the magnetic dipole axis of the sun and that it is assumed that the slow wind originates from a region centered on the magnetic equator, i.e., centered on the heliospheric current sheet.

Response:

We have added the reference of the work of Pizzo and the explanation of the tilt angle in Section 2.1.

 

3.Comment:

Please add the appropriate references to equations (9) and (10).

Response:

We have added the references.

 

4.Comment:

Lines 158–159:What about the longitude range? Is it 360 degrees?

Response:

Yes. We have added the longitude range.

 

5.Comment:

Line 169: Specify \( M \), \( \delta t \), and \( \Delta_{\text{bin}} t \).

Response:

Added.

 

6.Comment:

Section 2.3: Please add an introductory sentence at the beginning of the section to clarify the scope of the section.

Response:

Added.

 

7.Comment:

Lines 209–216: I would like to reiterate my previous comment and concern about the compression width \(\Delta_c\) parameter. The analytical model of Giacalone & Kocharov consists of a rarefaction region and a single compression wave. However, the author’s full MHD model of the CIR will consist of a rarefaction region, a reverse compression wave, shocked fast wind, a stream interface, shocked slow wind, and finally a forward compression wave with slow wind upstream. In other words, the MHD-generated CIR includes two separate compression waves, and hence one cannot expect that the very simple single-compression-wave model of Giacalone & Kocharov provides a good fit to this. Hence, I do not believe the width \(\Delta_c\) parameter has any proper physical meaning, which would also explain why it does not match with the other coefficients. One way to still apply the model would be to fit the forward and reverse compression waves in the MHD simulation separately. To locate the compression waves, the authors can look for the regions where \(div(V) < 0\), indicating converging (compressional) flows. However, given the relatively large difference between the fast and slow wind speed, the width of the compression waves will be strongly dependent on the resolution of the underlying computational mesh (see Husidic et al. 2024).

Response:

We have deleted the results and discussions about the width of the compression waves. The discussions for widths of compressed waves are not very meaningful in this work and may cause confusion for understanding.

 

8.Comment:

Lines 313–324: this explanation does not seem to agree with the assumptions of the underlying simulation. In particular, the statement "particles moving across the magnetic" cannot be correct. Particles are only moving along the magnetic field lines since the simulation does not include perpendicular diffusion nor guiding center drifts.

Response:

We have rewritten this explanation and added a figure to explain it more clearly.

Reviewer 2 Report

Comments and Suggestions for Authors

The authors have addressed all of my comments, so I can recommend the current version of the manuscript for publication.

Comments on the Quality of English Language

English is not my native language, and the presentation is clear to me. But I still have the impression that some language editing could improve them manuscript.

Author Response

Comment:

English is not my native language, and the presentation is clear to me. But I still have the impression that some language editing could improve them manuscript.

 

Response:

Thanks for the suggestion, and we have checked the language carefully.

Author Response File: Author Response.pdf

Reviewer 3 Report

Comments and Suggestions for Authors

 Comments on ‘Solar energetic particles propagation under 3D corotating interaction regions with different characteristic parameters’ by Y. Zhu and F. Shen

 The manuscript was revised considering the suggestions. However, several points still need improvements.

 Comments

The authors used several notations for the CIR width. The authors should make their definitions clear when they appear first. Once the authors defined the notations, use them afterwards. Do not repeat the definitions of the same notations in the manuscript to avoid redundancy. (L222, L225, L229, L229-230, L233, L239, L257, L262-264, L267, L363, L371, L372, L37, and so on)

 How did the authors calculate the solar wind speed shown in Figure 1? Add a description on this in the appendix.

 In the introduction, the overview of the following sections (L71-77) is not proper.

 Name of Section 2 is improper. It does not fully represent the contents of the section.

 A problem of the tense is still left in the manuscript. Please check it again.

 Detailed comments

L5 ‘are’ should be ‘were’.

 L52 The meaning of ‘in addition to CIR event’ is unclear.

 L71-72 ‘Section 2 provides a brief description of our model and how we control the background parameters.’ might be ‘Section 2.1 provides a brief description of background solar wind structures calculated using the 3D MHD model. Section 2.2 describes the particle transport model.’

 L78 ‘2. ‘Methods’ should be ‘2. Methods and results’

 L123 & L126-127 These parts are redundant. ‘we constructed four sets of CIR backgrounds. Table 1 shows the four sets of background field we constructed.’ should be ‘we constructed four sets of CIR backgrounds shown in Table 1.’

 L138 ‘,’ should be ‘.’.

 L144 ‘2.2 Particle transport model’ might be better than ‘2.2 Particle propagation model’.

 L162-163 The meaning of this part is unclear.

 L184 Add a definition of D_3d where it firstly appears.

 L184-185 The meaning of this part is unclear.

 L210-211 ‘Giacalone et al. (2002) [7] and Kocharov (2003) [30]’ should be ‘[7] and [30]’.

 L364-365 ‘the compression width’ should be ‘DELTA _c’.

 L492 ‘affects’ should be ‘affect’.

 L494 What does ‘the early event’ mean?

 Figures 2, 3 and 4 Right-bottom panel: ‘The azimuthal width of the fast stream (degree)’ should be ‘The azimuthal width of the fast stream DELTA PHI (degree)’.

 Figure 5 Left panel: ‘Compression width (AU)’ should be ‘Compression width DELTA c (AU)’. Right panel: ‘Radial extent (AU)’ should be ‘Radial extent D_c (AU)’.

Comments on the Quality of English Language

Please check the manuscript carefully before submission. 

For example, a problem of the tense is still left in the manuscript.

 

 

Author Response

1.Comment:

The authors used several notations for the CIR width. The authors should make their definitions clear when they appear first. Once the authors defined the notations, use them afterwards. Do not repeat the definitions of the same notations in the manuscript to avoid redundancy. (L222, L225, L229, L229-230, L233, L239, L257, L262-264, L267, L363, L371, L372, L37, and so on)

Response:

We have deleted the repetitive definitions.

 

2.Comment:

How did the authors calculate the solar wind speed shown in Figure 1? Add a description on this in the appendix.

Response:

Added.

 

3.Comment:

 

In the introduction, the overview of the following sections (L71-77) is not proper.

Name of Section 2 is improper. It does not fully represent the contents of the section.

A problem of the tense is still left in the manuscript. Please check it again.

Detailed comments:

L5 ‘are’ should be ‘were’.

L52 The meaning of ‘in addition to CIR event’ is unclear.

L71-72 ‘Section 2 provides a brief description of our model and how we control the background parameters.’ might be ‘Section 2.1 provides a brief description of background solar wind structures calculated using the 3D MHD model. Section 2.2 describes the particle transport model.’

L78 ‘2. ‘Methods’ should be ‘2. Methods and results’

L123 & L126-127 These parts are redundant.‘we constructed four sets of CIR backgrounds. Table 1 shows the four sets of background field we constructed.’ should be ‘we constructed four sets of CIR backgrounds shown in Table 1.’

L138 ‘,’ should be ‘.’.

L144 ‘2.2 Particle transport model’ might be better than ‘2.2 Particle propagation model’.

L162-163 The meaning of this part is unclear.

L184 Add a definition of D3d where it firstly appears.

L184-185 The meaning of this part is unclear.

L210-211 ‘Giacalone et al. (2002) [7] and Kocharov (2003) [30]’ should be ‘[7] and [30]’.

L364-365 ‘the compression width’ should be ‘DELTA c’.

L492 ‘affects’ should be ‘affect’.

L494 What does ‘the early event’ mean?

Figures 2, 3 and 4 Right-bottom panel: ‘The azimuthal width of the fast stream (degree)’ should be ‘The azimuthal width of the fast stream DELTA PHI (degree)’.

Figure 5 Left panel: ‘Compression width (AU)’ should be ‘Compression width DELTA c (AU)’. Right panel: ‘Radial extent (AU)’ should be ‘Radial extent Dc (AU)’.

Response:

We have modified or rewritten these parts.

 

4.Comment:

Please check the manuscript carefully before submission.

For example, a problem of the tense is still left in the manuscript.

Response:

Thanks for the comment, and we have checked the manuscript carefully.

Author Response File: Author Response.pdf