the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
| 30 Jun 2026
Thermospheric shock waves and lensing of light in the Barium Release, Optical and Radio rocket experiment
Abstract. The Barium Release, Optical and Radio (BROR) rocket experiment, launched from Esrange near Kiruna, Sweden, involved eight releases of barium at different altitudes in the thermosphere to study electric fields near small scale auroral structures. The barium was ejected into the thermosphere by the explosion-like combustion of ignited copper oxide thermite. Shock waves could be observed optically from the ground to follow the barium ejections when the rocket speed was supersonic, but not when it was subsonic. The shock waves are attributed to copper droplets that resulted from the thermite combustion and other particulate matter in the ejecta that traveled at supersonic speed. The observed deceleration of the shock waves can be explained by frictional drag together with gravity on copper droplets having a mean radius of about 1 mm. The actual observation of the shock waves from the ground is attributed to scattering of sunlight on the particulate matter in the ejecta. Also, following the ejections at the highest speeds, optical lensing of sunlight reflected from the rocket itself was observed, in that the rocket appeared brighter just after the barium release than before the release.
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RC1: 'Comment on egusphere-2026-2925', Navin Parihar, 20 Aug 2026
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AC1: 'Reply on RC1', Thomas Leyser, 21 Sep 2026
Reply to Referee #1 on the manuscript Thermospheric shock waves and lensing of light in the Barium Release, Optical and Radio rocket experiment", by Leyser et al.
We thank the referee for the constructive comments on the manuscript. We have discovered an error in the data analysis concerning the lensing effect so that we are not convinced of its presence any longer. All text and one figure concerning the lensing has therefore been removed. Also, the reference to lensing in the title has been removed. However, this does not affect the main theme of the manuscript, namely the results on the shock waves themselves. Below is our response to the comments in the review report.
- A brief review of the scientific purpose of the BROR experiment has been added in the Introduction. However, a more detailed overview of previous experiments than that already given, and also to add both Zhu et al. (2020) and Fletcher et al. (2023) which are on plasma effects from barium release experiments, is beyond the scope of the present work. As described in the Introduction, the present manuscript is on effects in the neutral thermosphere, not on plasma (or ionospheric) effects. Although the main goal for the BROR experiment was the ionospheric and electrodynamic effects, it would side track too much to review these in addition to neutral gas effects that are the subject of the present manuscript. The reference to Taki et al. was included already in the original manuscript for the main goal of the BROR experiment.
- Figure 1 has been added to show the geometry of the experiment as relevant to the present study. Additional information on the BROR experiment and conditions has been added in the text, mainly in the Introduction and the first paragraphs in Observations. However, as mentioned above the focus of the present manuscript is on local effects in the neutral thermosphere immediately following a barium release, it is therefore not relevant to give an overview of the global characteristics of the BROR experiment. This is the topic of the paper by Taki & al. which is on ionosphere-magnetosphere coupling and which is referred to, and possibly other papers to come. However, all data has been given that is needed for the purpose and level of accuracy in the present treatment.
- The section Discussion was accidentally numbered as a subsection to section 2, although it should be a separate section 3. This has been corrected so that the derivation of the speed of the shock waves is in section 2 (Observations) and the interpretation in terms of the radius of the copper droplets is in section 3 (Discussion). Examples of all cases are shown in figures 2-5 (Observations). In this way results obtained directly from the observations, such as the shock speeds, are kept separate (in Observations) from the interpretation of the these results in terms of copper droplets, which belongs to the Discussion. We use this structure in the manuscript for scientific clarity, to keep observations separate from the interpretation of the observations.
- The observations are already presented individually in separate figures and in separate descriptions of the observations, although not in separate subsections. For clarity, we present examples of series of images from all cases discussed. This is then followed by presenting, again in separate figures, the speeds obtained from the series of images. We judge that to repeat the presentations in three separate subsections, one for each release, would introduce repetitions that would make the text less fluent. Also, as noted from the outset in the Introduction, previous measurements of shock waves were done only through their ionospheric effects, not directly in the neutral gas of the thermosphere as in the present study. And, as already mentioned in the Introduction, the previous observations of shock waves through their ionospheric effects were from much larger and more powerful rockets than the BROR rocket. Taken together, a further comparison with previous measurements is not possible.
- We do not understand this comment. The observations are repeated in this section and interpreted in terms of shock waves due to sprays of copper droplets in the neutral thermosphere (so no electrodynamics is involved for our interpretation).
- We do not understand this comment. The observations and our interpretation are summarized. We have changed the section heading from Conclusions to Summary, to be more consistent with the content of the section.
- We do not understand this comment. Links to the video data that was used were given. In the revised manuscript the link to the video from the Vittangi camera on the lensing effect has been removed, as mentioned above, and only that for the Sodankylä video remains.
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AC1: 'Reply on RC1', Thomas Leyser, 21 Sep 2026
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RC2: 'Review report and comments on egusphere-2026-2925 "Thermospheric shock waves and lensing of light in the Barium Release, Optical and Radio rocket experiment"', Anonymous Referee #2, 23 Aug 2026
This manuscript can be considered a derivative work based on the BROR (Barium Release, Optical and Radio rocket) experiment. As the main objective of the experiment is to understand the electrodynamics of the auroral region under geomagnetic storm conditions; the present manuscript focuses on a secondary and unforeseen phenomenon: the shock waves observed as a result of several barium ejections. The unique conditions of the experimental setup certainly made it possible to reveal the shock waves associated with these barium ejections; as this is a phenomenon that has received little discussion, it lends scientific merit to the manuscript.
The decision to divide the document into Introduction, Observations, Discussions and Conclusions (it is more of a Summary section than a Conclusion section) is correct, although I recommend making the Discussions section an independent section (section 3) instead of the current one 2.1. The organization and presentation of the content are adequate and exhibit a sequence of reasoning that can be followed acceptably well.
Below I will list in detail the aspects that I detected and that need to be reviewed and improved along with questions that must be answered by the authors.Section Introduction:
Although the main results are presented in the paper by Taki et al., 2026, It is worth reinforcing the original purpose of the experiment. Highlight the relevance of barium-release experiments to study the MLT and ionosphere regions. Also the significance of this unusual detection of supersonic shock waves, and its potential interference with the interpretation of optical data from the barium cloud itself must be addressed (and further develop in the Conclusion section, which would truly do justice to the name, since in its current state it is more of a Summary of what was done/found).
Line 12: Especify UTC-LT difference e.g. (LT =UTC + 2) or (20:23:00 LT)
Line 24: What can be estimated? The intensity, the direction, or both properties of the electric field?
The most important change to be implemented is the following:
Line 40-42 It is recommended to insert a figure showing the rocket's trajectory, the position of the cameras, its FOV and the solar terminator during the launch time, with the geographical map in the backgroundSection Observations:
The placement of the figures negatively affects the smooth reading of the description of what was observed. There is a huge gap between the text on line 102 and its continuation on line 103, two pages later. Something similar occurs between the text on line 122 (page 7) and its continuation on line 123 (page 10). Some basic information regarding the rocket launch and the geomagnetic conditions during the execution of the experiment should be placed at the beginning of this section: duration of flight, numbers of rocket´s stages, time of stages burning, main and (if any) secondary payload, trajectory details, ballistic flight time, rocket rotation and precession frequency, and general geomagnetic condition during the experiment. The foregoing can be presented in a table form.
Figure 1 caption: Its not clear if this speed rocket profile is during upleg, downleg or the whole trajectory
Line 86 and 87: A cartoon explaining how the barium is released respect the rocket body could shed light on the experimental set up. What was the rocket's rotational speed and how it may have influenced the release of the barium and the remnants of the thermite?
Line 96: "Figure 6a depicts the light intensity (black) along the direction of the rocket velocity a few seconds..." It´s possible to include this direction overlapped in one of the panel in Figure 2? This would clarify for the reader in which part of the figure (anywhere from 2 to 5) the pixel count shown in Figure 6a was performed.
Line 98: What is the temporal resolution of the camera? If is a video, then what is the FPS?. This could have been clarified at the beginning of this section, along with the rocket's characteristics.
Line 105 and 106: Better express the Cs1,2,3 in m/s instead of km/s. The horizontal axis in Fig 1 is in m/s and in the rest of the text, the velocities are expressed in m/s.
Line 107: This second part of the sentences needs to be improved
Line 118: While it is true that u1f > u1, the fact that it is enclosed in parentheses indicates to the reader that this relationship is a consequence of the immediately preceding argument: "shock maximum decelerated slightly faster than the shock front" and this cannot always be the case, since du1/dt > du1f/dt does not imply u1f > u1. Better remove the "(u1f > u1)" because is already informed in Figure 7.
Line 147 and 148:The comment made in lines 40-42 can be applied to clarify this last comment.Section Discussion: Although this part is the most successful and coherent, I have two concerns, especially the one related to the determination of r (equation 14)
Line 185 (last part): Are you implicitly assuming that the direction of the vertical wind in the thermosphere (~200 km) for a high latitude (~68 deg N), near the equinox and around sunset is upward? If yes. You must show which model or previous empirical result confirms that statement. Hint: During that day Earth was struck by a severe G4-class geomagnetic storm.
Line 196, 198, 199, 225 to 227: Replace kg/m/s for the correct I.S. unit kg/(m . s)
Line 203: The comment made on lines 86 and 87 applies here as well.
Line 235 and first half of 236: Based on [7] and [10], the viscous friction force—and consequently the deceleration—is proportional to *r* (the size of the Cu droplets); therefore, one would expect that the larger the droplet, the greater the viscous friction it experiences and the greater the deceleration. From Figure 9, it can be observed that the shock front does not undergo deceleration like the main part of the shock; this may be because the shock front is composed of smaller Cu droplets and, consequently, experiences less deceleration due to viscous drag. What I gathered from what was stated in this lines was exactly the opposite.
Line 236 (second half) and 237 Additionally, it is unclear which part of the shock is being referred to by the second half of Line 236 and the first half of line 237.
Line 243 (equation 14): The purpose of the text between lines 240 and 249 is to demonstrate that the Reynolds number is much less than 1. The calculated values of the copper droplet radius are used for this purpose. This radius was calculated by comparing experimental values—specifically acceleration, initial velocity, and the angle between the rocket's trajectory and the vertical—with the theoretical value expressed in Equation 12. In turn, to arrive at the expression in (12), it is presumed that the frictional force was accurately described by Stokes' law, which assumes a low Reynolds number (to be checked later on).
The Reynolds number in 14 depends on experimental values except for r, which was calculated in a way that assumes a small Reynolds number. I see a circular bias here, and I would like to better understand the reasoning applied in this case. I would expect the determination of the Reynolds number not to depend on a quantity (r) that—in order to be calculated/estimated—assumes a small value for the very number it helps to determine.
Line 288 and 289: I believe the angle formed between the rocket body and the incident sunlight should also be taken into account when determining whether or not it plays a role in the effect under discussion. Upon watching the video available on YouTube, I noticed that there is no significant variation in lighting during the flight. Still I recommend insert a figure showing the rocket's trajectory, the position of the cameras, its FOV and the solar terminator during the launch time, with the geographical map in the background. This will help the reader understand how the rocket's trajectory—relative to the position of the sun—might have influenced the effect discussed in this last paragraph.Section Conclusion: My main concert here is that given the content of this version, the section cannot strictly be considered a set of conclusions; rather, it is better viewed as a summary description of the work carried out in the preceding sections. There are aspects that could rightly be called conclusions, such as the hypotheses that may arise from the fact that ejection speed decrease with increasing altitude and the consequences for future experiments of Barium release using thermite given that shock wave from a release propagated in the wake of the preceding shock wave. This could not affect the experiment in the sense that a barium cloud will no longer propagate in a common thermosphere (the object of study) but will propagate in an environment affected by a previous ejection?
These aspects were not addressed and diminish the potential scientific impact this study could generate.Citation: https://doi.org/10.5194/egusphere-2026-2925-RC2 -
AC2: 'Reply on RC2', Thomas Leyser, 21 Sep 2026
Reply to Referee #2 on the manuscript Thermospheric shock waves and lensing of light in the Barium Release, Optical and Radio rocket experiment", by Leyser et al.
We thank the reviewer for the careful reading and constructive comments on the manuscript. We have discovered an error in the data analysis concerning the lensing effect so that we are not convinced of its presence any longer. All text and one figure concerning the lensing has therefore been removed. Also, the reference to lensing in the title has been removed. However, this does not affect the main theme of the manuscript, namely the results on the shock waves themselves. The section Discussion was accidentally numbered as 2.1 and is now given the separate section 3. The section Conclusions has been renamed to Summary, to reflect its content. Below is our response to the comments in the review report.
Introduction:
Information has been added for the original purpose of the BROR experiment as well as the usefulness of optical imaging of barium releases. Some additions to highlight the usefulness of barium-release experiments have been made. A note has been added at the end of the Summary on that the shock wave observations do not interfere with those of the barium clouds, because of different time scales. However, the significance of the observations of the shock waves is still an open question to us, but we feel that the observations are interesting enough to motivate publication.
The line numbers below refer to those of the original manuscript and the referee report, which may be different in the revised manuscript.
Line 12: Local time has been specified.
Line 24: The relevant electric field component has been clarified. It is understood that an electric field has both amplitude and direction.
Line 40-42: A figure showing the geometry of the experiment has been added as figure 1. However, the terminator is difficult to show as its altitude is difficult to depict in the projection of a 3D landscape on a 2D figure. We have instead given additional information on the terminator in the first paragraph in the Introduction.
Observations:
The unfortunate placement of the figures is a feature of the manuscript style used. The figure placements generally are more appropriate in the published version. Additional details of the rocket experiment pertinent to the present study have been added, primarily in the beginning of Observations. Information on the duration of the flight is given in the captions of figures 3, 4 and 6 which state the times after launch for the depicted releases. We have now also added the times after launch for the first and last barium ejection in the first paragraph in Observations, which are a measure of the ballistic flight time.
Figure 1: We have added that it is the ballistic rocket speed that is shown, so the altitude dependence of the speed is approximately the same on the upleg and downleg.
Lines 86, 87: A note on the rocket rotation (40°/s) has been added in the first paragraph of the Observations and that no effect of the rotation can be discerned in the optical data for the barium cloud nor the shock waves. The direction of the ejecta relative to the rocket has now been more detailed in the second and third paragraph in Observations. This information is repeated where relevant in the Discussion, as in the original manuscript. However, as we know too little about the actual range of directions in which the barium was ejected, we cannot say more than what is already stated (that the ejection occurred approximately in the direction of the rocket nose) and therefore refrain from providing a cartoon of this. In view of the rocket having a much higher speed than that of the ejected remnants relative to the rocket, we only consider the direction of the rocket speed and trajectory in our simplified analysis of the shock wave speed.
Line 96: An additional panel has been added to figure 4 to show the line along which the light intensity curve of the shock is taken.?
Line 98: The video frame rate of 10 fps has been added in the first paragraph of the Observations.
Lines 105-106: All velocities are now given in m/s.
Line 107: The sentence has been reformulated.
Line 118: Done.
Line 147-148: As mentioned above all results related to lensing has been removed.
Line 185: We have reformulated the sentences. With ”wind” in the original manuscript we meant the air resistance due to the motion of the rocket. The thermospheric conditions were quiet in this early part of the experiment and the background thermospheric wind is assumed negligible relative to the rocket speed. The conditions developed to the storm only later in the evening. We have now added in the first paragraph of Observations that nearby aurora did not affect the images of the shock waves.
Line 196, 198, 199, 225 to 227: Done.
Line 203: We have added information on the direction of the rocket velocity to clarify.
Lines 235-236: The reviewer is correct in that the frictional force is proportional to the size r. But the deceleration due to this frictional force is inversely proportional to the mass, according to equation (10), and the mass too depends on r. This is why a heavier particle is decelerated less by friction than a lighter particle, although the frictional force is larger on the larger and heavier particle.
Line 236: The sentence has been clarified.
Line 243 (equation 14): The purpose of the paragraph is not to strictly calculate the Reynolds number itself and demonstrate that Re <<1, but the purpose is only to check for consistency. We are aware that the reasoning is not logical. But if the Reynolds number would not be small with the obtained diameter L, although we had assumed Re<<1, we would have a problem. The consistency that we checked for is a necessary requirement, although not sufficient. We have reformulated the paragraph to bring this out.
Lines 288-289: As mentioned above, we discovered an error in the data analysis and are not convinced that lensing occurred. All data and discussion on this effect has therefore been removed.
Conclusions: The text is rightly a summary, rather than a conclusion. The section heading has therefore been changed correspondingly. A note has also been added that the shock waves exist during a much shorter time than the barium clouds, so that the possible effect of the shock waves on the barium clouds is likely negligible.
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AC2: 'Reply on RC2', Thomas Leyser, 21 Sep 2026
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Review Report for the manuscript "Thermospheric shock waves and lensing of light in the Barium Release, Optical and Radio rocket experiment", by Leyser et al.
General Comments:
Manuscript presents Barium Release, Optical and Radio rocket (BROR) experiment carried out over Esrange near Kiruna, Sweden. As an active and rare experiment, this study has high scientific merit, warrants publication and I am strongly in favour of its publication. However, major concern is poor organization of this submission and is not as per Annales Geophysicae format/guidelines. Owing to this manuscript, in its present form, is difficult to follow in terms of logical sequencing and readability. Overall, my recommendation is “Major Revision”; however, the below-mentioned major shortcomings need to be addressed.
Restructuring and reorganization of the manuscript should be done (as suggested below) to improve overall readability and logical flow:
1. Introduction Section:
Significance of barium-release experiments to study the mesosphere-lower thermosphere and ionosphere. Why? A brief overview of previous reports, and their limitations. Following latest works are missing and should be included.
a. Fletcher, A. C., Crabtree, C., Ganguli, G., Siefring, C., Soto-Chavez, A. R., & Netwall, C. (2023). Rocket-released neutral clouds in the ionosphere: Formation, evolution, and detection. Journal of Geophysical Research: Space Physics, 128, e2022JA031039. https://doi.org/10.1029/2022JA031039
b. Zhu, X., Hu, Y., Zhao, Z., Ni, B., & Zhang, Y. (2020). Ionospheric disturbance caused by artificial plasma clouds under different release conditions. Earth, Planets and Space, 72(1), 183. https://doi.org/10.1186/s40623-020-01317-9
Scientific objectives/Motivation of the BROR experiment, brief introduction about thermospheric shock, etc..
2. An overview of BROR experiment
Section should include location, launch date, time and duration of flight, payload(s), rocket trajectory, information on release characteristics, and location of optical cameras/details of other ground-based experiments, brief information of solar elevation, solar activity and geomagnetic conditions, etc.. Figure 01 is reasonable; however, should by preceded by a map showing Rocket trajectory. Release characteristics can be furnished in tabular format.
3. Methodology
3.1 Derivation of the speed of shock waves
3.2 Derivation of the radius of copper droplet
For each measurement, a typical example (showing best results) should be presented.
4. Observations and results
In this section, sub-sections devoted to each release should be presented individually covering shock waves observations and different measurements. Wherever possible, imaging observations should also be presented, and comparison with earlier measurements should be performed.
5. Discussion
Please highlight key observations, and dynamics/electrodynamics involved.
6. Summary and Conclusions
Summarize BROR experiment, key findings, limitations, etc.
“Data Availability” should be corrected to clearly mention if data used in this study is publicly available or restricted or mention contact (subject to Annales Geophyiscae policy).