Dynamical development of strength and stability of asteroid material under 440 GeV proton beam irradiation

Domain: physics
Published: 2025-11-28
Editorial outcome: major_revision

Abstract
Asteroid materials experience rapid thermoelastic and plastic stress evolution when subjected to high-energy irradiation – an effect that has not previously been captured through non-destructive, time-resolved experiments. Yet, accurate modeling of asteroid deflection scenarios, such as those proposed for planetary defense, critically depends on precise knowledge of the material’s mechanical behavior under extreme conditions to predict kinetic energy transfer and orbital deviation. In an experimental campaign at CERN’s High Radiation to Materials facility (HiRadMat), we irradiated a Campo del Cielo iron meteorite sample with 440 GeV protons from the Super Proton Synchrotron. Using Laser Doppler Vibrometry, we captured the resulting thermally induced stress waves in real time. Our results demonstrate that asteroid materials can absorb significantly more energy without structural failure than normal material parameters would suggest. Crucially, we were able to reproduce – under controlled laboratory conditions – the discrepancy factor observed between laboratory-derived yield strength values and those inferred from atmospheric meteor breakup events.

Introduction
Planetary defense has been a topic of growing scientific and strategic interest over the past decades, with a range of mitigation concepts proposed, including kinetic impactors and stand-off nuclear explosions1. While numerous simulation studies have modeled asteroid deflection scenarios under such conditions, the reliability of these models critically depends on an accurate understanding of the material response of asteroid constituents under extreme energy deposition.

Recent missions such as NASA’s Double Asteroid Redirection Test (DART) mission have demonstrated the feasibility of kinetic impactor strategies2. However, experimental data on the rapid thermoelastic and plastic stress evolution of asteroid material under high-energy irradiation remains extremely scarce. Accurate modeling of asteroid material response under extreme conditions necessitates overcoming two principal challenges: (1) the lack of real-time data on the evolution of mechanical properties under irradiation, and (2) a significant discrepancy between laboratory-based measurements and yield strengths inferred from atmospheric meteor breakups. For instance, nanoindentation studies (e.g., Ueki et al.3) often yield values up to a factor of seven higher than those derived from ram-pressure models3,4. Mulford et al.5 hypothesized that meteorites may exhibit mechanical behavior akin to that of complex composite materials. Smirnov and Konstantinov6 demonstrated that the strain-rate dependence of yield strength in complex materials can be attributed to internal structural dynamics. A similar mechanism could account for the behavior observed in meteorites, including the pronounced discrepancy between yield strength values obtained from nanoindentation and those inferred from ram-pressure models3,4.

Iron meteorites, which originate from metal-rich asteroids, offer a unique opportunity to investigate these effects. While various studies have characterized their mechanical properties, most were conducted on cold or unaltered samples7. Studies like that of Jain et al.8 analyzed stress signatures from ancient asteroid collisions using 119 meteorite specimens, and Siraj et al.4 inferred strength parameters from atmospheric breakup events. However, neither study captured the real-time evolution of material properties under energetic impact.

Laboratory efforts have also attempted to emulate impact conditions. For example, the Z-pinch pulsed power facility at Sandia National Laboratories was used to irradiate meteorite samples with soft X-rays, simulating nuclear-sourced surface energy deposition9,10. Yet, the destructive nature of these tests precluded direct measurement of the resulting material response. More recently, Moore et al.11 demonstrated the complete momentum transfer onto scaled asteroid targets in laboratory conditions. While groundbreaking, their setup again did not permit tracking material deformation or yield strength evolution, despite the known dependence of momentum transfer efficiency on the material’s internal state.

In this study, we present an experiment conducted at the High-Radiation to Materials (HiRadMat) facility of CERN12, in which a meteorite sample was exposed to a high-intensity, high-energy proton beam. The dynamic response of the sample, including momentum transfer and elastic/plastic behavior, was recorded in real time via non-destructive methods. To our knowledge, this is the only laboratory experiment to measure the real-time evolution of yield strength and damping behavior of asteroid-representative material under high-energy irradiation. The experiment was developed in collaboration with OuSoCo (Outer Solar System Company), which is developing a proprietary method for generating high-energy proton beams in space, with beam properties comparable to those of CERN’s Super Proton Synchrotron (SPS). While the technical details of in-space beam generation fall outside the scope of this paper, the results presented here are, in principle, transferable to any deflection method where the applied energy penetrates deeply into the target material. We focus this study on metal-rich asteroids, whose relative material homogeneity facilitates characterization and modeling. However, since stony asteroids represent the most common class of near-Earth objects, future experimental campaigns are already planned to extend this analysis to silicate-rich meteorite samples.

Results
It is common for meteorite samples to be composed of multiple phases of iron-nickel alloy. The utilized fragment (imaged in Fig. 1) is taken from the Campo del Cielo iron meteorite and it features a characteristic two-phase crystal structure consisting of Kamacite, i.e., ferritic iron (α structure), and Taenite, i.e., Austenite (γ structure)13. Once cut into a cylindrical shape, the phase boundaries become clearer (not to be confused with cracks). Scanning electron microscopy (SEM) and energy-dispersive X-ray spectroscopy reveal clearly visible phase boundaries (pictures are provided in Supplementary Information).

The dynamical response and development of yield strength of asteroid material are examined experimentally by irradiating an iron meteorite sample with beams of high-energy 440 GeV protons extracted from CERN’s SPS. When such high-energy protons collide with atomic nuclei in the sample, hadronization of quarks and gluons leads to the generation of hadronic and electromagnetic cascades of secondary particles. These include (but are not limited to) pions, electrons, positrons, kaons and γ-rays14,15, which predominantly lose energy via ionization of atoms in the sample and lead to a fast, isochoric, high-energy deposition that penetrates deeply into the meteorite sample. By measuring the surface vibrations of the sample using Laser Doppler Vibrometry (LDV), the response of the iron meteorite sample resulting from the corresponding thermally-induced stress wave was measured in real time for 27 successive beam irradiations (setup shown in Fig. 1). While longitudinal oscillations are coupled to radial ones via the Poisson ratio and are non-negligible, the current diagnostics set-up only captured the radial material response, since it reflects most sensitively changes in the material’s yield strength, and the Poisson ratio was not expected to change significantly. In addition, the gathered material response data have been used to derive the fraction of the primary beam kinetic energy converted into bulk kinetic energy of the sample, providing the momentum transfer. As such, the irradiation of the meteorite sample by the proton beam can also be understood as a laboratory-based surrogate used to test the efficiency of particle beam-based asteroid maneuvers - a not-yet-explored method for asteroid deflection.

The maximum primary proton beam intensity is chosen to be 3×1011 protons at 440 GeV in a single-bunch with a Gaussian transverse profile (σ x,y=1mm) and duration of σ t=250ps to study the plastic deformation regime, isolated from solid-to-solid phase transitions which are expected at higher energies.

The intensity of the primary proton beam used for each sample irradiation is shown in Fig. 2, and examples of the LDV raw data, showing the radial surface displacement as a function of time, are shown in Fig. 3. For the first 10 shots onto the sample, the primary beam intensity is 1×1011 protons, and damped oscillatory behavior is observed in the radial displacement of the sample surface. When the primary beam intensity is increased to 3×1011 protons, non-oscillatory behavior is suddenly observed. This behavior persists even when the beam intensity is reduced to 1×1011 protons for 3 shots. Eventually, oscillatory behavior returns. Our experiments provide a detailed view of how metal-rich asteroid material responds dynamically to high-energy irradiation. Using the thermal stress model introduced by Bertarelli et al.16, we estimate that proton beam intensities of 1×1011 protons induce a peak thermal stress σ thermal of ~40 MPa, while intensities of 3×1011 protons result in stresses of up to 120 MPa (see “Methods, Thermal stress model of the meteorite”).

To assess the mechanical response of the meteorite material, we compared these stress levels to reported yield strength values for iron meteorites. Local yield strength measurements from nanoindentation of Kamacite yield values of ~350 MPa3, which we denote as σ y,local. In contrast, yield strength values derived from ram-pressure modeling of meteor breakups in Earth’s atmosphere are significantly lower, around 50 MPa4, reflecting an effective macroscopic response (σ y,bulk).

If σ y,local were directly applicable to our beam experiments, the measured thermal stress would remain well below the yield threshold, and no plastic deformation would be expected. However, our LDV data clearly indicate a transition in oscillatory behavior at higher beam intensities, consistent with the onset of plastic deformation.

This discrepancy reflects the fundamental difference between local and bulk yield strength measurements: nanoindentation captures micromechanical response under quasi-static loading, while bulk estimates account for internal structure, phase boundaries, and inertial coupling across the heterogeneous meteorite volume. To bridge these regimes, we introduce a scaling factor:

f = σ y,local / σ y,bulk (1)

σ y,local is the local yield strength and (σ y,bulk) is the bulk yield strength. The factor f has a value of ~7 and can be interpreted as a stress amplification factor resulting from internal redistribution of von Mises stress under internal inertial degrees of freedom, consistent with the dynamic composite-like behavior17 of meteorites proposed by Mulford et al.5.

Applying this factor to the peak thermal stress σ thermal implies that the Kamacite phase effectively experienced stresses of f · σ thermal, i.e., 280 MPa for low and 840 MPa for high beam intensities. These values are consistent with the LDV signal profiles and with the threshold defined by σ y,local. Moreover, this hardening process is not limited to the stress regimes explored here. Higher beam intensities could drive further increases in yield strength or even induce solid-solid phase transitions, consistent with observations from meteorite recovery and planetary core modeling, where transitions to ε-phase iron occur under extreme conditions8,24. This is further confirmed by more recent results, e.g., from Torchio et al.20. But these would at least need 12–13 GPa pressure in the stress wave for a transition to the martensitic phase.

Finally, to interpret the frequency spectra observed in the LDV data, we consider the fundamental geometrical scale of the sample, defined by its 10 mm diameter (see “Methods, Meteorite sample and target envelope”). The fundamental radial frequencies are governed by the material’s elastic properties and wave propagation speed. However, due to the heterogeneous nature of the meteorite – composed of alternating Kamacite and Taenite phases – the effective speed of sound is not uniform. Reported values range from ~5500 m/s in Kamacite to 3000 m/s in Taenite3. As a result, the shortest travel-time paths and local resonance conditions are strongly influenced by the spatial distribution of Taenite inclusions.

Despite this complexity, the observed Fast Fourier Transform (FFT) spectra consistently show dominant frequencies in the 375–450 kHz range (see Fig. 4), which is in good agreement with the expected fundamental radial modes based on the sample geometry and effective sound velocity. This further supports the interpretation that the measured oscillations are governed by volumetric stress-wave propagation and are sensitive to the internal structure of the meteorite sample.

We also observed an unexpected damping phenomenon: the strain amplitude-dependent attenuation of LDV signals. For low-intensity shots, the decay of oscillations is well described by an exponential function. However, high-intensity shots show systematic deviations from exponential decay, indicating the presence of higher-order damping terms. Regression analysis of the residuals (Fig. 5) reveals that these deviations are correlated with oscillation amplitude, strongly suggesting a strain-dependent damping effect – an observation typically associated with advanced composite materials17. This damping behavior might be linked to dislocation dynamics17 within the hardened Kamacite matrix and is of particular relevance for planetary defense: strain-dependent damping prevents resonant amplification and self-destruction under repeated excitation, making the material inherently more resilient to follow-up perturbations.

Together, these results suggest that high-energy proton irradiation not only hardens iron meteorite material but may transform it into a composite-like structure with improved damping characteristics. This behavior was anticipated in early modeling efforts5, but we provide a real-time experimental confirmation.

Moreover, this implies that much larger amounts of energy can be deposited into asteroid material than previously assumed – without structural failure. This opens yet unexplored possibilities for nuclear energy-density asteroid deflection techniques, where deep energy coupling is desired without fragmentation. Future work will explore this scenario in detail, including implications for momentum transfer efficiency, phase transition thresholds, and the scalability of the hardening process.

Methods
Meteorite sample and target envelope
A piece of the Campo del Cielo iron meteorite was cut into a cylindrical shape of 10 cm in length and 1 cm in diameter, having a mass of 60 g. Campo del Cielo is known to be composed mainly of iron (92.7%) and nickel (6.15%), as well as cobalt (0.42%), carbon (0.37%) and phosphorous (0.28%)25 with silicon, titanium, vanadium, gallium, copper, and sulfur present at trace levels26. The two mineral phases are Kamacite-having a body-centered cubic (BCC) lattice-, and Taenite-having a face-centered cubic lattice.

The proton beam deposition behavior is principally determined by the density of the irradiated material. With 7.86 g/cm3 for iron and 8.90 g/cm3 for nickel, the weighted average density utilized in the Monte Carlo simulations was 8.06 g/cm3. The minor density variations within the meteorite sample from the ppm-level inclusions like e.g., phosphorous are not expected to play a significant role in the elastic wave behavior of the material.

The meteorite sample was irradiated by the proton beam along its longitudinal axis. Both ends of the target envelope were protected by 2 mm thick SIGRADUR® glassy carbon windows. The target envelope was made of aluminum with a wall thickness of 15 mm.

Pulse intensity and shot number selection
The experimental design was guided by the objective to probe and compare distinct mechanical response regimes of iron meteorite material under high-energy proton irradiation. Two pulse intensities were selected to this end:
• A lower intensity of 1×1011 protons per pulse was chosen to keep the sample response within the elastic regime, ensuring minimal permanent deformation.
• A higher intensity of 3×1011 protons per pulse was employed to deliberately trigger the onset of plastic deformation, enabling a direct comparison between elastic and plastic material behavior.

As the experimental setup constitutes a unique configuration that has not previously been implemented for meteorite irradiation, the higher intensity level was conservatively chosen. It remained well below thresholds associated with phase transitions or structural failure, ensuring safe operation within established facility limits. The pulse list and the corresponding detailed beam parameters are available in the Supplementary Information provided with this article.

The number of shots per condition was determined to strike a balance between statistical significance and safety. The total integrated beam energy was carefully kept below levels that could cause irreversible damage to the sample or compromise experimental infrastructure. This allowed for robust characterization of the material’s response in both regimes without exceeding risk thresholds.

Laser Doppler Vibrometry (LDV)
The LDV used, consisted of an acquisition unit connected to a manual-focusing head without electronics, allowing for a focal distance of 15 mm to 5 m. The acquisition unit contains the necessary electronics to convert the analog signals from the LDV head into digital measurements of displacement, velocity, and acceleration. A PXI (PCIe eXtensions for Instrumentation) acquisition system was also connected to the LDV acquisition unit to trigger the recording and make the LDV data available remotely. In this work, a PXIe-6124 (National Instruments) digitizer card with 16-bit resolution and selectable input ranges (±1 V, ±2 V, ±5 V, ±10 V) was employed to record the analog output signals of the LDV. The LDV acquisition unit and the LDV head were connected by a pair of single-mode polarization-maintaining fibers that ran through the wall of the tunnel, ensuring that the electronics were placed away from radiation. In the experimental set-up, the distance between the LDV head and the focal spot on the meteorite was 550 mm, with a focal spot diameter on the order of 100 μm. The data quality and reliability of the LDV laser on the meteorite surface was tested in several iterations before the experiment. The tests confirmed that the initially curved surface of the meteorite sample, with its small radius of 5 mm, made the alignment of the LDV Laser very difficult and prone to errors. To ensure high-quality LDV signal acquisition, the convex curvature of the cylindrical meteorite surface was flattened by carefully removing ~1 mm of material with a fine-grained steel file, creating a polished, flat surface measuring about 4 mm. This preparation enabled 100% signal strength in the LDV measurements.

The present study focused exclusively on radial surface displacement, which directly reflects changes in yield strength. While longitudinal and surface wave modes also exist, they were not captured due to experimental access limitations. However, the return to clean oscillatory response after strain hardening suggests that the dominant dynamics were captured adequately by the radial LDV measurements. All utilized LDV displacement data are available as raw data under Zenodo.

Temperature measurement with PT100
The temperature of the meteorite surface was measured with a 4-wire PT100 platinum resistance thin film detector, attached to the meteorite sample on the opposite side of the LDV focal spot. Temperature data were gathered continuously at a frequency of 1 Hz. Temperature data are available as raw data, accessible on Zenodo.

Monte Carlo simulations of energy deposition profile
Simulations of the temperature profile of the meteorite cylinder were performed using COMSOL Heat Transfer in Solids module21. Energy deposition data from GEANT4 simulations was used as input for the heating source22,23; the corresponding source data are provided in Supplementary Data 3 of this paper. The meteorite was given an initial uniform temperature of 293.15 K. The temperature increase closest to the position of the PT100 temperature was found to be between 4.95 and 5.9 K. (see Fig. 6).

Thermal stress model of the meteorite
The applied thermal stress was σ thermal estimated from the thermal expansion relation as e.g., presented in ref. 16
σ thermal = E · α · ΔT (2)

where E denotes the Young’s modulus, α the thermal expansion coefficient and ΔT the temperature increase. To assess material failure and plastic deformation onset, the resulting thermal stress was expressed as the von Mises equivalent stress. For the calculation, literature values for Kamacite and Taenite were utilized, as listed in Table 1.

Our approach focuses on comparing these analytically calculated stress levels to the yield strength values inferred from the LDV-measured surface vibrations. The observed consistency between the analytically predicted stress thresholds and the experimentally detected transitions—from elastic behavior to plastic deformation, and subsequently to oscillatory behavior indicative of strain hardening—is fully consistent with the selected material parameters.

Calculation of local pressures with Grüneisen parameter
To estimate the transient pressure rise associated with ultrafast, quasi-isochoric heating during the proton pulse, we applied the Grüneisen parameter. The Grüneisen parameter γ relates the thermal pressure P th to the energy density E th through
P th = γ E th = γ ρ c v ΔT, (3)

where ρ is the mass density, c v the specific heat at constant volume, and ΔT the temperature increase derived from the COMSOL simulations21.

The Grüneisen parameter was calculated for the dominant kamacite phase using
γ = α V K T / (ρ c v) (4)

where α V is the volumetric thermal expansivity and K T the isothermal bulk modulus. Using the values listed in Table 1 with α V = 3 · α = 3 · 11.1 × 10−6 K−1, E = 240 GPa, ν = 0.3, ρ = 8060 kg m−3, and c p = 461 J kg−1 K−1 (approximating c v ≈ c p), we obtained the bulk modulus K T = E / [3(1 − 2ν)] = 200 GPa and Grüneisen parameter γ of ~1.8.

Assuming local heating of ΔT = 300–440 K within the beam-intercepted volume, the corresponding local pressures are
P th = γ ρ c v ΔT (5)

The resulting thermal pressure is ~2–3 GPa. This range exceeds by roughly one order of magnitude the stress values predicted by the analytical thermal-stress model of Bertarelli et al.16, yet remains well below any known equilibrium phase-transition thresholds for Fe–Ni alloys20. For comparison, Torchio et al.20 report that in Fe–Ni alloys the bcc → hcp (α → ε) transition begins at pressures above ~12 GPa and completes by ~17 GPa for compositions of about 20 wt% Ni, while shifting to even higher pressures (>100 GPa) with increasing Ni content. The average Ni concentration in our iron meteorite sample is significantly lower (around 6.15 wt% overall, around 5.5 wt% for the dominant bcc kamacite phase). Consequently, the 2–3 GPa local pressures estimated here lie well below any known equilibrium phase-transition thresholds, and the deposited energy is therefore interpreted as contributing primarily to plastic deformation and defect production, rather than to melting or structural phase change.

It should be noted that the LDV measurements provide volumetrically averaged parameters, as discussed in the LDV subsection of the “Methods” section. The localized zone of maximal temperature increase, defined by ΔT ≥ 300 K (as assumed for the local heating), accounts for only ~0.7% of the total cylinder volume, whereas the resulting thermal-stress wave propagates throughout the entire sample. Consequently, the experimentally observed LDV response represents a spatially averaged response of these local processes.

Calculation of plastic deformation energy
The LDV measurements were taken at a single point on the surface of the sample, halfway along its cylinder axis. Since this location does not capture the spatial variation in energy deposition across the bulk, we applied a correction based on temperature profiles obtained from simulations using COMSOL Heat Transfer in Solids module. The LDV-derived energy values were scaled by the ratio between the simulated local temperature and the temperature measured by a PT100 sensor21. This procedure allowed us to estimate the total energy that contributed to plastic deformation across the entire sample volume. The final result of this step was a plastic deformation energy of E plastic = 360 μJ, attributed to the generation of dislocations in the meteorite sample.

Calculation of dislocation density
The estimation of the dislocation density increase proceeded in two steps: (1) determination of the energy converted into plastic deformation, and (2) calculation of the corresponding dislocation density based on dislocation line energy.

Step 1: To estimate the increase in dislocation density, we first determined the amount of energy converted into plastic deformation. We assumed that any energy not stored in oscillatory modes was dissipated through plastic mechanisms. Accordingly, the plastic deformation energy was calculated as E plastic = E oscillating − E non-oscillating.

To evaluate these energy terms, we extracted the average kinetic energy from the displacement profiles. For non-oscillating diagrams, we applied the classical kinetic energy expression E = 1/2 mv2, where the velocity v was estimated from the small residual displacements. For oscillating diagrams, the energy stored in the oscillatory motion was calculated as E = m π2 (ν A)2, where m = 60 g is the mass of the sample, ν = 1.5 kHz is the average oscillation frequency, and A is the measured amplitude. For low-intensity shots, the average amplitude was A = 0.85 μm; for high-intensity shots, A = 2.9 μm. Using these values, the plastic deformation energy was calculated, amounting to E plastic = 360 μJ.

Step 2: We then calculated the dislocation line energy E disloc, i.e., the energy required to generate a unit length of dislocation in Kamacite. This is given by
E disloc = 1/2 G b2 (6)

where G is the shear modulus and b is the magnitude of the Burgers vector27. Kamacite has a BCC lattice structure with a lattice constant a of ~2.88 Å, resulting in b = √3/2 a with a value of ~1.44 Å. Using G = 75 GPa, we find a value for E disloc of about 7.78 × 10−10 J/m.

Assuming that the entire plastic deformation energy is stored in newly formed dislocation lines, the total dislocation length created is given by L disloc,total = E plastic / E disloc, yielding a value of ~4.63 × 105 m. Dividing this by the sample volume yields an estimated increase in dislocation density of ~6.1 × 1010 m−2, consistent with values reported for moderate hardening in BCC Kamacite.

Time-frequency analysis via continuous wavelet transform
To resolve the temporal evolution of vibrational modes following proton beam impact, we performed a time-frequency analysis of the radial displacement signal obtained from LDV. A continuous wavelet transform (CWT) was applied using a complex Morlet wavelet. The analysis was applied to a 225 μs time segment (75–300 μs after beam impact), capturing the key dynamic response of the meteorite. Frequencies between 50 kHz and 1.5 MHz were evaluated in 5 kHz steps by translating each frequency into the corresponding wavelet scale, based on the sampling rate and wavelet center frequency. Before applying the CWT, the radial displacement signal was bandpass-filtered between 5 kHz and 1.5 MHz to suppress baseline drift and instrumental noise, ensuring that only physically meaningful frequencies were retained for analysis.

Analysis of Campo del Cielo sample
The average composition and material characteristics were optically analyzed using scanning electron microscopy (SEM) and energy-dispersive X-ray spectroscopy (EDS). Pictures of the optical analysis are included in the Supplementary Material.

Data availability
Source data are provided with this paper. Additional raw data supporting the findings of this study are available in the public repository at https://doi.org/10.5281/zenodo.17582347.

Code availability
Simulations were performed using FLUKA, COMSOL Multiphysics (v6.2; https://www.comsol.com), and the open-source Geant4 Monte Carlo toolkit (https://geant4.web.cern.ch) developed at CERN. A custom analysis script was used to process and visualize the Laser Doppler Vibrometry (LDV) voltage output data over time. The script is available from the corresponding author upon request.

Peer review rounds
[{"round": 1, "reviewer_comments": {"reviewer_1": "In this paper, the authors study the dynamic strength on iron meteorites under irradiation via a proton beam at CERN. Using Laser Doppler Vibrometry techniques, the authors are able to measure the stress wave in the sample in time over successive irradiation events. They find that under these proton irradiations, the yield strength of the material significantly increases, potentially up to seven times the standard yield strength of Kamacite. While these results are intriguing, it is unclear how this extends to planetary defense in general. Further, the analysis performed on the LDV data is slightly ambiguous and more details on the experimental set-up and analysis are needed prior to publication.\n\nMajor Comments\n-Some major details about the irradiation timing are needed in the paper. While the authors list that the pulse duration of the proton bean is 250ps, they do not list the frequency at which the pulses are incoming. This is relevant to the LDV analysis – all the LDV data are shown out to 5 ms but is the sample allowed to fully stop its motion or are the pulses arriving faster than 5 ms?\n-In the methods, the authors state that a notch was filed into the sample to increase the LDV signal – how does this notch effect the LDV? Surface roughness could change the signal response from LDV resulting in difficult to analyze data – was the sample polished to remove any roughness? If not, how could this roughness affect the results?\n-In reference to Figure 4: on line 232-233, it is said that “show in average larger deviations for the high-intensity shots than for low-intensity shots” with a reference to the methods for more details. Looking at Figure 4, it appears to me that the low-intensity shots show larger deviations than the high-intensity. Is this simply a typo or is there something more fundamental that I am missing.\n-Additionally, why does the sample return to oscillating as it did initially, even during the higher intensity pulse? Does this indicate that the hardening is complete or is there something else going on? Later in the discussion, it seems to imply that the material was not fully hardened so some more details would be useful.\n-The authors present two potential strength hardening scenarios – one in which the sample increases in yield strength by a factor of ~ 2 and one by a factor of ~7. As noted in the paper, for planetary defense simulations, the choice of yield strength is of great importance. It would be valuable to explain which one of these two scenarios are the best for simulations as the authors suggest that proton beam irradiation could be a viable planetary defense mitigation method.\n-Some discussion would be useful on how these results extend to other planetary defense methods. As of now, proton beam irradiation is not one of the common techniques for asteroid deflection. Does this radiation induced hardening extend to other forms of radiation – such as that produced from a nuclear explosive device – or is it unique to GeV protons? Further, is this unique to iron-nickel meteorites or would you expect to see this hardening in more common rocky asteroid materials?\n\nMinor Comments\n-Lines 49 – 54 are a single sentence which is quite long and somewhat difficult to parse. I would suggest separating it into two, which could add further emphasis on the Planetary Defense aspects you are highlighting in the paper.\n-Line 98 – no ‘-‘ in inhomogeneous\n-Figure 4 – placing both data sets on the same y-axis would help with comparison.\n-Line 324 – weighting is misspelled.", "reviewer_2": "Please consider the attached pdf file for comments.", "reviewer_3": "Overview:\nThe authors examine the effect of high-energy (440 GeV) proton irradiation on a meteorite sample using the HiRadMat facility at CERN. The subject is of broad scientific interest, and the experiment itself is quite interesting. The authors observed a change in the structural dynamic response of the cylindrical meteorite sample, as measured with a laser doppler vibrometer, most of the time occurring when the beam irradiance was increased. The authors attribute this change in signal to energy loss and assert it arises from plastic deformation. Based on this interpretation, they estimate the amount of strain hardening the sample may have experienced. While the authors reasonably show that this is plausible, it is not convincing without further discussion to eliminate other possibilities and/or without further quantification of uncertainties.\n\nMajor:\nThe single LDV measurement directed orthogonally to the rod should be primarily sensitive to flexure and/or radial dilation, whereas longitudinal modes should also exist (see Ref.22) yet are not accounted for in the analysis. Rather, all energy is assumed to be contained within the radially directed wave, which may not be strictly correct. In particular, there is no comparison of the wave energy to the beam energy for the so-called “elastic case”, or to some other control, to prove this methodology or to otherwise quantify uncertainties in determining the quantity of energy dissipated through plastic deformation.\nSimilarly, there is no discussion of other modes, including the possibility of surface waves, and if those could produce the change in signal pattern at the higher beam irradiance.\nThe observed resonance frequencies (Fig.3b) are not sufficiently explained. For example, if one assumes a nominal wave speed of ~3000 m/s, the primary resonances (Fig.3a) have wavelength ~1.8 m, which does not appear to correspond to a primary geometric feature of the sample. One wonders if this could indicate leakage of mechanical energy to the fixture (“envelope”).\nThe initial temperature of the rod before each pulse should be described. Was it allowed to equilibrate? Did the rod always start at room temperature, or did it get hotter with each radiation pulse? What is the effect of successive heating? It may also help to describe the time between radiation pulses.\nOne would like to see a quantitative measure of dislocation density before and after irradiation, or some other independent measurement, to confirm the author's hypothesis regarding structural change.\nIn general, I do not find the explanation of strain hardening convincing. I agree that this is an intriguing possibility with important implications and is worth exploring. However, reaching this conclusion depends on correctly interpretating a very complex series of behavior that occurred sequentially, whereas the experiments only measured one aspect of this behavior or the interpretation may not be correct (see my other comments).\n\nMinor:\nThe motivation for placing a phase boundary beneath the focal spot of the LDV needs more explanation. In particular, how would a “preferred direction” of the stress wave be determined from this single point measurement? How was it determined that there was no “preferred direction”?\nFig.1b: Scale bar does not exist or is too small to see, which makes interpretation of the image difficult.\nFig.2: There is no discussion of the shots with “no clear response”. Does this imply difficulties with the measurement? What is the implication for accuracy of the other shots?\nFig.2: Authors should check the units in the energy scale; they do not appear consistent with the energy deposition values in Fig.1a.\nLine 119—122: This sentence appears overstated, as the present study does not show how proton beams could be used to deflect or maneuver asteroids. The present study only addresses the wave behavior.\nFig.3a: The two right-most of the three graphical panels have the same labels. Consider differentiating them. Also, it is unclear why the response returns to “elastic” on shot 23 even though the beam energy remains high.\nLine 178: “peak-induced stress” is not clearly defined.\nLine 189: “internal dynamics” is not clearly defined.\nLines 166-167, 178-180, 196-205: Consistency with ram conditions or shock impact conditions is not necessarily expected, as yield strengths are known to be sensitive strain-rate and/or shear conditions.\nFig.5: The meaning of the color bar is unclear, specifically the normalization “per bin of 1 cm3” is sometimes used for energy but not usually for temperature. Should the units instead be “K/pulse? Or this normalization should be described.\nLine 301-303: It does not seem correct to say “the PT100 sensor measured roughly the same amount of temperature increase as for the oscillating diagrams” because the diagrams do not measure temperature. Or the method behind this inference should be explained more fully.\nLine 324-325: Why was this weighting performed? Does it imply a systematic error in the model?\nLine 329-330: The values (with units) when used in (2) do not appear to give units of energy; they give units of force. Also, it is unclear how the dislocation density was calculated from (2)."}, "author_response": "25 September 2025\nDear Reviewers,\nWe would like to thank you once again for your valuable comments and constructive suggestions on\nour manuscript entitled “Dynamical development of strength and stability of asteroid material under\nFollowing the editor’s and reviewers’ guidance, we have undertaken substantial additional work\nbeyond textual revision. In particular, we have:\nExpanded Motivation and Scientific Context:\n• We strengthened the motivation by situating our work more clearly in the context of planetary\ndefense and explicitly highlighting the lack of real-time, non-destructive dynamic material\nresponse data for asteroid materials.\nNew result added based on additional Simulations\n• In response to the referees’ request for further quantification, we have conducted additional\ntemperature profile simulations in COMSOL that demonstrate the consistency of vibrational and\ntemperature measurements as a new conclusion in the paper (see Discussion).\nClarified Experimental Setup and Methodology:\n• We added details on beam parameters (pulse list), sample mounting, and meteorite preparation. We\nalso discussed how the heterogeneous material structure (e.g., Kamacite-Taenite phases) affects\nwave propagation.\nRestructured Results, Discussion and Methods Sections:\nTo improve clarity, we reorganized the results, discussion, and methods sections:\n• The derivation of dynamic hardening is now presented in clearly delineated steps, with supporting\nreferences provided.\n• We introduced a scaling factor f to quantify the effect of internal inertial dynamics, bridging local\nand bulk yield strength.\n• Calculation assumptions and values are now explicitly listed in the methods section, distinguishing\nbetween tabulated data and measured values.\n• Terminology for LDV displacement analysis was refined for consistency and clarity.\nWe believe that these revisions have significantly sharpened the manuscript’s central statements\nregarding the dynamic development of strength, while also clarifying the overall argumentation. We\nare therefore pleased to resubmit the manuscript for your consideration.\nTo facilitate the review process, we have prepared a point-by-point response to each referee’s\ncomments, indicating where revisions were made in the manuscript. We are also providing a\ncomparison document that highlights all changes between the original and revised versions.\nWe are very grateful for the referees’ detailed feedback and for the opportunity to revise and resubmit\nour work.\nThank you for your consideration.\nSincerely,\nMelanie Bochmann (on the behalf of all co-authors)\nReviewer #1 (Remarks to the Author):\nIn this paper, the authors study the dynamic strength on iron meteorites under irradiation via a proton\nbeam at CERN. Using Laser Doppler Vibrometry techniques, the authors are able to measure the stress\nwave in the sample in time over successive irradiation events. They find that under these proton\nirradiations, the yield strength of the material significantly increases, potentially up to seven times the\nstandard yield strength of Kamacite. While these results are intriguing, it is unclear how this extends to\nplanetary defense in general. Further, the analysis performed on the LDV data is slightly ambiguous and\nmore details on the experimental set-up and analysis are needed prior to publication.\nMAJOR COMMENTS\n1) Some major details about the irradiation timing are needed in the paper. While the authors list that\nthe pulse duration of the proton beam is 250ps, they do not list the frequency at which the pulses are\nincoming. This is relevant to the LDV analysis – all the LDV data are shown out to 5 ms but is the\nsample allowed to fully stop its motion or are the pulses arriving faster than 5 ms?\nReply: This question is a very good hint to further clarify the overall frame conditions, in which\nthe beam shots were conducted. The 27 beam shots were distributed over approximately 7 hours,\nwith time intervals of several minutes between shots. This allowed sufficient thermal and\nmechanical equilibration before each shot. The LDV acquisition window was limited to 5 ms\nafter each pulse, as all oscillations fully decayed within this period. Thus, no overlap occurred\nbetween shots.\nThe detailed pulse list with times was provided in the supplementary material in the previous\nmanuscript version. We added more details on the pulse frequency and irradiation timing in the\n“results” section, comprised in the caption of figure 2.\n2) In the methods, the authors state that a notch was filed into the sample to increase the LDV signal\n– how does this notch effect the LDV? Surface roughness could change the signal response from\nLDV resulting in difficult to analyze data – was the sample polished to remove any roughness? If\nnot, how could this roughness affect the results?\nReply: The sample surface beneath the LDV laser was polished after removing the convex\nmeteorite material. Following this preparation, LDV tests showed 100% signal strength. The\nreviewer rightly points out that surface roughness plays a crucial role in achieving high-quality\nLDV signals. We took this into account by adding a remark in the methods section under\nparagraph Laser Doppler Vibrometry, explaining that a fine-grained steel file was used in order\nto achieve a polished, plane surface.\nRegarding the impact of the notch on the LDV measurement data, we had similar concerns due\nto the highly inhomogeneous structure of the meteorite material. In both cases—altering the\ncylindrical shape of the probe and accounting for the material’s internal structure—we would\nhave expected strong high-frequency components in the Fourier-transformed spectrum if such\neffects were significant. However, no such indications were observed in the data, suggesting\nthat the influence is negligible.\n3) In reference to Figure 4: on line 232-233, it is said that “show in average larger deviations for the\nhigh-intensity shots than for low-intensity shots” with a reference to the methods for more details.\nLooking at Figure 4, it appears to me that the low-intensity shots show larger deviations than the\nhigh-intensity. Is this simply a typo or is there something more fundamental that I am missing.\nReply: The remark that this phrasing has potential for misinterpretation is an important\nclarification and highly appreciated. Figure 4 displays amplitude-adjusted residuals, defined as\nthe residuals divided by the minimum amplitude of each respective beam shot. In contrast, the\ncomparison discussed in the text refers to the unadjusted residuals, i.e., the difference between\nthe measured displacement and the best-fit exponential curve, without any normalization.\nTo eliminate this ambiguity, the revised manuscript now focuses on the key finding and presents\nonly amplitude-adjusted residuals for high-intensity shots. We have also revised the figure\ncaption accordingly to clarify this distinction.\n4) Additionally, why does the sample return to oscillating as it did initially, even during the higher\nintensity pulse? Does this indicate that the hardening is complete or is there something else going\non? Later in the discussion, it seems to imply that the material was not fully hardened so some more\ndetails would be useful.\nReply: We sincerely thank the reviewer for this insightful question, which allowed us to clarify\nthe underlying hardening mechanism in more detail. The return of oscillatory behavior at high\nbeam intensity — following a regime of non-oscillatory displacement — indicates that the\nmaterial experienced a strain-induced hardening process, rather than reaching a hardening\nsaturation or failure threshold. As shown in Figure 2 and Figure 3, the collapse of oscillations\nat beam intensities of 3 ×1011 protons corresponds to the onset of plastic deformation, while the\nsubsequent recovery of oscillations reflects a dynamic increase in yield strength resulting from\ndislocation buildup in the Kamacite phase.\nIn other words, the sample initially softens due to plastic deformation, but then hardens\nprogressively as dislocations accumulate. This increases the local and bulk yield strength such\nthat the same high thermal stress (up to ~120 MPa) no longer exceeds the (now higher) yield\nthreshold, allowing the sample to sustain elastic oscillations again.\nThis interpretation is supported by the following:\n• Dislocation density increased by a factor of ~6, as estimated from energy deposition and\ndislocation line energy.\n• Yield strength scales with the square root of dislocation density, implying an increase of\nlocal yield strength from ~350 MPa to ~875 MPa.\n• Applying the same factor to the bulk yield strength yields ~125 MPa, which is just above\nthe peak thermal stress — consistent with the observed reappearance of oscillations.\n• The LDV spectra before and after hardening show no sign of damage or anisotropic\nwave propagation, suggesting structural integrity and uniform response.\n• GEANT4 simulations also require a correction factor consistent with this hardening\nbehavior to match observed displacements.\nThus, the return of oscillations does not imply that the material is “fully” hardened in an absolute\nsense, but rather that the current yield strength has risen above the applied stress, stabilizing the\nelastic response. Additional hardening could still occur under even higher stress regimes, as\ndiscussed in the manuscript.\nTo address this more clearly, we reorganized the manuscript to provide a more structured\nexplanation of the plastic regime, the onset of hardening, and the interplay between the different\neffects involved. We have now clarified in the “Discussion” section that the observed recovery\nof oscillations reflects a strain-hardening effect reaching a new dynamic threshold — not an\nindication of complete hardening or saturation.\n5) The authors present two potential strength hardening scenarios – one in which the sample increases\nin yield strength by a factor of ~ 2 and one by a factor of ~7. As noted in the paper, for planetary\ndefense simulations, the choice of yield strength is of great importance. It would be valuable to\nexplain which one of these two scenarios are the best for simulations as the authors suggest that\nproton beam irradiation could be a viable planetary defense mitigation method.\nReply: Thank you for this important remark. It helped us reorganize the Discussion section to\nmore clearly distinguish between the different effects influencing yield strength.\nIn the revised manuscript, we now emphasize the distinction between two types of yield strength\nvalues commonly used in planetary defense modeling:\n• Local yield strength (𝜎 ~ 350 MPa): This higher value is based on nanoindentation\nlocal\nmeasurements and reflects the micromechanical response of the Kamacite phase in iron\nmeteorites (Ueki et al.)\n• Bulk yield strength (𝜎 ~ 50 MPa): This lower value, smaller by a scaling factor 𝑓≈7,\nbulk\nis derived from atmospheric ram pressure modeling of meteorite breakup events and\naccounts for internal structure, phase boundaries, and inertial coupling across the\nheterogeneous meteorite volume (Siraj et al.).\nSeparately, we observe a factor of ~2 increase in yield strength during the experiment, which\nwe attribute to proton-beam-induced strain hardening. This is consistent with the known relation\nbetween dislocation density and yield strength, where yield strength scales with the square root\nof dislocation density. We have clarified this relation in more detail in the Methods section.\nTo this end, we explored the possibility of conducting measurements at a large-scale neutron\ndiffraction facility, with the objective of comparing a reference sample from the same Campo\ndel Cielo meteorite block (unirradiated) to its counterpart irradiated at CERN’s HiRadMat\nfacility. However, due to the activation level of the irradiated sample and the stringent precision\nrequirements, the necessary beamline modifications are not yet available. Consequently, such\nmeasurements are unfortunately not feasible at this time.\nFor planetary defense simulations, the bulk yield strength is typically the more appropriate input\nparameter, as it governs the response of the entire heterogeneous body under dynamic loading.\nThe observed factor-of-two increase in this bulk property suggests that irradiation-induced\nhardening may enhance the energy absorption capacity of asteroid material during a deflection\nevent.\n6) Some discussion would be useful on how these results extend to other planetary defense methods.\nAs of now, proton beam irradiation is not one of the common techniques for asteroid deflection.\nDoes this radiation induced hardening extend to other forms of radiation – such as that produced\nfrom a nuclear explosive device – or is it unique to GeV protons? Further, is this unique to iron-\nnickel meteorites or would you expect to see this hardening in more common rocky asteroid\nmaterials?\nReply: The results of the experiment can be extended both to other forms of radiation and to\nother forms of asteroid material. We added two paragraphs at the end of the introduction section\n(lines 95 and the following), summarizing the following:\na) Other forms of radiation\nThere is no indication that the proton charge played a crucial role. The material behavior was\nmainly determined by the deep penetration into the material at 440 GeV. Therefore, as long as\na comparable high penetration depth is achieved, similar results can be expected with neutrons\nor gammas.\nThe output of a nuclear device are mainly soft x-rays, that do not penetrate deeply into the\nmaterial (Miles, 2008).\nIn our experiment, the beam focus was relatively small compared to the sample’s diameter. The\nmeasured oscillations were the result of a thermo-elastic wave in the material which is secondary\nto the p+ energy deposition.\nThis suggests that a sufficiently strong shockwave as a secondary result of a nuclear device\ncould lead to similar results. This is further supported by results from nuclear tests where metal\nplates survived far beyond the melting point. Asteroid data of collisional shocks show that\npressures at 10 GPa and beyond suffice to get comparable results to our experiments. By\nchoosing a suitable combination of the required standoff and corresponding yield that allow for\nproducing even TPa-sized pressures, nuclear devices can lead to a similar behavior.\nb) Other asteroid types with other material\nThe question concerning other asteroid types, i.e. other asteroid materials than iron-nickel is\nhighly relevant since stony asteroids are the most common type of near-Earth asteroids. For in-\nbeam experiments at CERN, material parameters need to be sufficiently known to fulfill\nexperimental safety requirements. Iron-rich meteorite material is more homogeneous than stony\nmeteorite material, which makes it easier to describe the material with single parameters such\nas yield strength. A reliable safety model – applicable for further in-beam experiments at CERN\n- for using stony meteorites, would require a 3D model comprising a set of material properties.\nWe are currently developing such a model, which would allow for a proper safety model opening\nup the possibility of experiments with more inhomogeneous materials. Very generally one\nwould indeed expect that stony objects could show a similar behavior of increasing yield\nstrength since at least similar patterns of phase transitions as compared to metal-rich objects are\nknown for these objects under very high pressures.\nReviewer #2 (Remarks to the Author):\nIn this study the authors present an experiment conducted at the High-Radiation to Materials\n(HiRadMat) facility of the European Organization for Nuclear Research (CERN) in which a meteorite\nsample is exposed to a high intensity of high energy radiation and the dynamical response of momentum\ntransferred to the sample is precisely measured in real-time. An accurate knowledge of the material\nresponse of the asteroid is critical in various fields: in particular, in asteroid deflection techniques the\nobject response is to be known very precisely to model deflection orbits accurately and to predict the\ntransfer of kinetic energy. In the experimental Campaign presented in the manuscript, an iron-meteorite\nsample is, for the first time, irradiated with 440 GeV Protons delivered by the Super Proton Synchrotron.\nMAJOR COMMENTS\n1) In the tests a Laser Doppler Vibrometer is utilized to measure the thermally induced stress waves in\nreal-time, produced by energy deposition in the sample. This means that only radially polarized\nWaves are measured, neglecting the contribution to moment transfer due to longitudinal oscillations\nwhich may assume non-negligible amplitudes in this sort of tests [1]. If so, please justify this\nassumption.\nReply: We highly appreciate this insightful comment. It is indeed correct that only radial\noscillations were measured. The primary objective of the Laser Doppler Vibrometry (LDV)\nmeasurements was to obtain real-time data on changes in the material's yield strength, which is\nmost sensitively reflected in the radial response. While longitudinal oscillations are indeed\ncoupled to radial ones via the Poisson ratio and are therefore non-negligible, our assumption to\nfocus on the radial component is based on two main considerations:\nA) The Poisson ratio, which governs this coupling, is not expected to change significantly\nduring the beam exposure, in contrast to the yield strength, which is known to vary under\nthese extreme conditions.\nB) The available measurement geometry and access constraints made radial measurements\nmore feasible and reliable for real-time data acquisition.\nNevertheless, we agree that a more complete picture would benefit from capturing both\ncomponents. In future experiments, we plan to implement complementary diagnostics capable\nof resolving longitudinal oscillations to further refine the interpretation of stress wave dynamics\nand momentum transfer.\nWe added a clarification on this in the Experimental setup section, as well as in the Methods\nsections.\n2) In line 125 it is written that the pulse intensity is chosen so to be isolated from solid-to-solid phase\ntransitions: in the following lines, however, it is said that such transitions are present in Asteroid\nimpacts whose momentum transfer characterization constitutes the primary scope of the study.\nPlease explain.\nReply: We appreciate the reviewer’s observation. The reference to asteroid impacts in the\nmanuscript serves only to illustrate the broader relevance of momentum transfer processes in\nplanetary defense scenarios. However, our study focuses on experiments designed to remain\nbelow the threshold for solid-to-solid phase transitions in order to isolate and study specific\nmaterial response mechanisms under controlled conditions.\nThe solid-to-solid phase transitions mentioned in the context of asteroid impacts occur at much\nhigher energy densities and serve as an ultimate point of comparison—not as a direct analog to\nour present test conditions. Our experimental strategy follows a staged approach: the current\nwork focuses on regimes without phase transitions to establish a clear baseline, while future\nexperiments with adjusted beam parameters are planned to explicitly explore phase transition\neffects.\nTo prevent any potential misunderstanding, we included this distinction starting at line 242,\nalongside the explanation already given in the Experimental Setup section.\n3) The use of thermal stress models as the one cited in [2] requires either the knowledge of the material\nproperties of the samples or the implementation of numerical simulations to be compared to\nexperimental data for benchmarking and derivation of the said constitutive parameters, as done in\n[1]. With regard to the latter case, only reference to “calculations” is made in the manuscript (e.g.\nin line 185). Please explain.\nReply: Indeed, as correctly noted, the application of thermal stress models requires input\nmaterial properties such as Young’s modulus, Poisson ratio, and thermal expansion coefficient.\nThese were incorporated into the analytical model in the manuscript, using literature values for\nKamacite and Taenite as listed. Since this was not explicitly comprised in the manuscript, we\nadded the corresponding values in table 1.\nThe \"calculations\" mentioned in the manuscript were obtained using the semi-analytical\napproach described in Bertarelli et al. [2], rather than from full numerical simulations as\nconducted in [1].\nOur approach focuses on comparing these analytically calculated stress levels to the yield\nstrength values inferred from the LDV-measured surface vibrations. The observed consistency\nbetween the analytically predicted stress thresholds and the experimentally detected transitions\n— from elastic behavior to plastic deformation, and subsequently to oscillatory behavior\nindicative of strain hardening — is fully consistent with the selected material parameters.\nWe acknowledge that a full numerical treatment, as performed in [1], could provide additional\ninsight. Incorporating such simulations is part of our planned future work, especially as we\nextend the experimental program to more complex geometries and loading conditions.\n4) In line 211 it is claimed that an unchanged spectrum of the sample’s response in presence of induced\nplasticity indicates a very homogeneous hardening process of the material. A homogenous change\nof the material properties, however, would typically reflect in a substantial change in the frequency\ncontent of the acquired response. Please explain why this is not the case.\nReply: We agree with the reviewer that a homogeneous change in material properties would\ngenerally be expected to alter the frequency content of the response. In our case, however, we\nhave no evidence that the Young’s modulus, changed significantly during the experiment. Since\nthe eigenfrequencies primarily depend on the elastic modulus and geometry, we would not\nexpect a substantial shift in the spectrum if the Young’s modulus remains constant.\nThe observed plastic deformation appears to have manifested primarily as strain hardening,\nincreasing the yield strength, but without significantly affecting the elastic behavior that governs\nthe vibrational spectrum. Furthermore, we found no indication of macroscopic geometric\nalterations, which would typically induce noticeable changes in the spectrum, especially at\nhigher frequencies.\nThus, the unchanged frequency content supports the interpretation that plasticity was\naccommodated through homogeneous strain hardening without substantial modification of the\nelastic properties or geometry that would affect the measured spectrum.\n5) In line 222 it is reported that strain hardening and amplitude-dependent damping effects are\nobserved in the experimental response of the sample: please explain how these effects are included\nin the material model adopted in the study to predict the stress levels indicated.\nReply: Thank you for this important observation. The thermal stress model by Bertarelli et al.\n[2], which we used to estimate the stress levels in the sample, is based on linear elasticity and\ndoes not incorporate nonlinear material effects such as strain hardening or amplitude-dependent\ndamping. These effects were identified retrospectively through analysis of the LDV data and\nare therefore not part of the original predictive model.\nFollowing this comment, we revised the Discussion section to more clearly distinguish between\nthe material model used for stress estimation and the experimental observations. Specifically:\n• Thermal stress model (Bertarelli et al.): Used to estimate the applied stress, based purely on\nlinear elasticity. This model does not include nonlinear effects such as strain hardening or\namplitude-dependent damping. A more detailed description is now provided in the Methods\nsection.\n• Strain hardening: Inferred from the comparison between the applied thermal stress and the\nestimated bulk yield strength. At higher beam intensities, the stress exceeds the yield\nstrength, leading to plastic deformation.\n• Plastic deformation energy: Quantified from the suppression of oscillation amplitude in the\nLDV data. This energy was interpreted as being stored in newly formed dislocations,\nresulting in an increased dislocation density—and thus an increase in yield strength\nconsistent with strain hardening behavior.\n• Amplification factor (f = 7): Introduced to reconcile the discrepancy between local\n(nanoindentation-based) and bulk (fragmentation-based) yield strength values. This factor\nreflects internal inertial effects and heterogeneous failure behavior within the sample.\n• Amplitude-dependent damping: Observed in the high-intensity LDV data and attributed to\ninternal inertial motions due to microstructural features (e.g., inclusions, phase boundaries).\nThis nonlinear effect was not captured by the material model, as it was not anticipated.\nThese updates clarify the distinction between predictive modeling and experimentally observed\nnonlinearities, both of which are now treated separately and in more detail both in the Discussion\nand in the Methods section.\nMINOR COMMENTS\n6) How is the implemented number of pulses and the pulse intensity chosen? Please justify.\nThe selection of pulse intensities and number of pulses was driven by the objective to compare\ntwo well-separated material response regimes. The lower intensity of 1×1011p+\nwas chosen to keep the material response within the elastic regime, while the higher intensity\nof 3 ×1011 p+ was selected to deliberately induce a distinguishable onset of plasticity, allowing\nfor direct comparison between elastic and plastic behavior.\nSince this was the first experiment of this type performed worldwide on iron meteorite samples\nunder these conditions, the higher intensity was conservatively selected to remain within safety\nmargins, providing sufficient buffer below critical thresholds where phase transitions or\nstructural failure might occur.\nThe number of shots was chosen to ensure that the total integrated beam energy remained safely\nbelow levels that could cause fatal damage to the sample or compromise facility safety, while\nstill allowing the accumulation of sufficient statistics for the analysis of both elastic and plastic\nresponse regimes.\nWe added a new subsection “Pulse intensity and shot number selection” on this in the Methods\nsection.\n7) Please provide a superposed view of the FFT response spectra associated to low/high-intensity\npulses shown in Fig. 3b.\nWe have replaced the initially provided FFT graphs by a FFT overlay view, showing the\ndominant frequency components in the 375 – 450 kHz range shortly after beam impact. Further\ndetails are included in the subsection “Time-frequency analysis via continuous wavelet\ntransform” under Methods.\nReferences\n[1] Pasquali, M., Bertarelli, A., Accettura, C. et al. Dynamic Response of Advanced Materials Impacted\nby Particle Beams: The MultiMat Experiment. J. dynamic behavior mater. 5, 266–295 (2019).\nhttps://doi.org/10.1007/s40870-019-00210-1\n[2] Bertarelli, A., Dallocchio, A., Kurtyka, T.: Dynamic response of rapidly heated cylindrical rods:\nLongitudinal and flexural behavior. Journal of Applied Mechanics 75(3) (2008).\nhttps://doi.org/10.1115/1.2839901\nReviewer #3 (Remarks to the Author):\nThe authors examine the effect of high-energy (440 GeV) proton irradiation on a meteorite sample using\nthe HiRadMat facility at CERN. The subject is of broad scientific interest, and the experiment itself is\nquite interesting. The authors observed a change in the structural dynamic response of the cylindrical\nmeteorite sample, as measured with a laser doppler vibrometer, most of the time occurring when the\nbeam irradiance was increased. The authors attribute this change in signal to energy loss and assert it\nrelies on plastic deformation. Based on this interpretation, they estimate the amount of strain\nhardening the sample may have experienced. While the authors reasonably show that this is plausible,\nit is not convincing without further discussion to eliminate other possibilities and/or without further\nquantification of uncertainties.\nMAJOR COMMENTS\n1) The single LDV measurement directed orthogonally to the rod should be primarily sensitive to\nflexure and/or radial dilation, whereas longitudinal modes should also exist (see Ref.22) yet are not\naccounted for in the analysis. Rather, all energy is assumed to be contained within the radially\ndirected wave, which may not be strictly correct. In particular, there is no comparison of the\nwave energy to the beam energy for the so-called “elastic case”, or to some other control, to prove this\nmethodology or to otherwise quantify uncertainties in determining the quantity of energy dissipated\nthrough plastic deformation.\nSimilarly, there is no discussion of other modes, including the possibility of surface waves, and if\nthose could produce the change in signal pattern at the higher beam irradiance.\nReply: We thank the reviewer for raising this important point. The primary objective of the\nLaser Doppler Vibrometry (LDV) measurements was to obtain real-time data on changes in the\nmaterial's yield strength under beam exposure, which is most directly and sensitively reflected\nin the radial response of the cylindrical sample. Particularly, we added further clarification on\nthis in the Experimental setup section, but also tried to account for this by reorganizing the\nDiscussion section.\nWe fully acknowledge that longitudinal modes also exist (see Ref. 22/ Bertarelli et al.) and are\ncoupled to radial modes via the Poisson ratio. However, our analysis focused on the radial\nresponse for the following reasons:\na) Dominant Sensitivity to Yield Strength Changes:\nThe radial response provides the most direct signature of changes in yield strength, which is the\nprimary parameter affected by the beam-induced rapid heating and subsequent strain hardening.\nIn contrast, the Poisson ratio governing radial-longitudinal coupling is not expected to vary\nsignificantly during irradiation, while the yield strength does.\nb) Experimental constraints and signal quality:\nThe measurement geometry and experimental access favored radial LDV measurements, which\nallowed us to obtain high-quality, real-time displacement data with sufficient signal-to-noise\nratio for quantitative analysis. Longitudinal measurements would have required a significantly\nmore complex setup, which was beyond the scope of the present study.\nc) Elastic vs. plastic regime:\nWe primarily compare the oscillation behavior before and after the onset of plastic deformation.\nIn the elastic regime, the sample exhibits stable oscillations. After plastic deformation, these\noscillations are damped due to energy dissipation into dislocation formation and movement.\nBased on our dislocation density calculations, approximately 10 shots are sufficient for the\nsystem to reach a new equilibrium, after which stable oscillations reappear — consistent with\nthe experimental observation.\nd) Energy deposition and FLUKA simulations:\nWe did not explicitly compare the measured mechanical energy to the incident beam energy\nbecause, at 440 GeV, the nuclear length of the protons exceeds the sample length (10 cm), and\nthus the total beam energy is only partially deposited in the sample. The spatial distribution and\nmagnitude of deposited energy were quantified using FLUKA simulations, which account for\nboth radial and longitudinal energy deposition profiles. In our LDV analysis, the radial energy\ndeposition was weighted according to these FLUKA results. Thus, in the energy loss\ncalculations to arrive at a value for hardening, the longitudinal dependence was indirectly taken\ninto account by weighing the radial data with the energy deposition map of the Monte Carlo\nsimulation.\ne) Other modes and surface waves:\nWe agree that additional modes such as surface waves could, in principle, contribute to the\nobserved signal, particularly at higher beam intensities. However, given the observed spectral\nstability of the oscillations after multiple shots and the clear correlation with plastic hardening,\nwe interpret the dominant contribution to stem from bulk radial modes. Nevertheless, we fully\nrecognize that capturing a more complete modal picture — including longitudinal and surface\nwaves — would further improve the interpretation. We plan to address this in future experiments\nby implementing complementary diagnostics capable of resolving these additional components.\n2) The observed resonance frequencies (Fig.3b) are not sufficiently explained. For example, if one\nassumes a nominal wave speed of ~3000 m/s, the primary resonances (Fig.3a) have wavelength\n~1.8 m, which does not appear to correspond to a primary geometric feature of the sample. One\nwonders if this could indicate leakage of mechanical energy to the fixture (“envelope”).\nReply: We thank the reviewer for this valuable observation. To clarify the origin of the observed\nresonance frequencies in the LDV data, we now explicitly discuss the relevant geometrical and\nmaterial parameters in the revised manuscript. Specifically, we consider the fundamental\ngeometrical scale of the sample, defined by its 10 mm diameter, which governs the radial\nresonance modes.\nWhile a nominal sound speed of 3000 m/s could suggest larger-scale wavelengths, the\nmeteorite’s heterogeneous composition—primarily Kamacite and Taenite phases—leads to a\nbroad range of effective sound velocities. Reported values range from approximately 5500 m/s\nin Kamacite to 3000 m/s in Taenite (Ueki et al), and the effective propagation paths are\ninfluenced by the specific spatial arrangement of these phases. As a result, the resonance\nconditions reflect complex internal structure rather than a single uniform wave speed.\nWe have added a paragraph in the Results section clarifying that the dominant frequencies in\nthe FFT spectra (375–450 kHz) are in good agreement with expected fundamental radial modes\nfor the sample’s size and composite sound velocity. Furthermore, the consistent reappearance\nof these frequencies across multiple shots suggests that the measured response originates from\ninternal volumetric stress waves within the sample, not from coupling to the envelope. We have\nreplaced the figures with an FFT overlay view, showing the dominant frequencies after beam\nimpact.\n3) The initial temperature of the rod before each pulse should be described. Was it allowed to\nequilibrate? Did the rod always start at room temperature, or did it get hotter with each radiation\npulse? What is the effect of successive heating? It may also help to describe the time between\nradiation pulses.\nReply: We thank the reviewer for pointing this out. The temperature development over time and\nbeam shot was only provided in the supplementary material. We now added further information\non the beam irradiation timing and mechanical and thermal equilibration of the sample in the\ncaption of Figure 2. While the temperature did not always return fully to room temperature\nbetween pulses, the sample was allowed to equilibrate prior to each beam shot, and the time\nbetween consecutive shots was sufficiently long. Due to the nature of the experiment, where\nvery high stress and strain levels dominate the response, these comparatively small variations\n(of only a few Kelvin) in initial temperature are not expected to have a significant influence on\nthe mechanical response or on the interpretation of the strain hardening effects observed. The\ntypical time between subsequent radiation pulses was on the order of minutes.\n4) One would like to see a quantitative measure of dislocation density before and after irradiation, or\nsome other independent measurement, to confirm the author's hypothesis regarding structural\nchange. In general, I do not find the explanation of strain hardening convincing. I agree that this is\nan intriguing possibility with important implications and is worth exploring. However, reaching this\nconclusion depends on correctly interpretating a very complex series of behavior that occurred\nsequentially, whereas the experiments only measured one aspect of this behavior or the\ninterpretation may not be correct (see my other comments).\nReply: We fully acknowledge the reviewer's point that an independent quantification of\ndislocation density would provide valuable confirmation of the hypothesized structural changes.\nTo this end, we explored the possibility of conducting measurements at a large-scale neutron\ndiffraction facility, with the objective of comparing a reference sample from the same Campo\ndel Cielo meteorite block (unirradiated) to its counterpart irradiated at CERN’s HiRadMat\nfacility. However, due to the activation level of the irradiated sample and the stringent precision\nrequirements, the necessary beamline modifications are not yet available. Consequently, such\nmeasurements are unfortunately not feasible at this time. As discussed in Osuch et al., the initial\ndislocation density in Kamacite is typically low, making the material highly sensitive to\ndislocation generation under increasing stress and strain conditions. The general mechanism of\nstrain hardening via dislocation density increase is well-established from related studies. Our\ncurrent experimental data demonstrate that strain hardening effects can still be inferred on short\ntime scales under the high stress and strain-rate conditions of the irradiation. Prior to our\nexperiments it would still have been possible that the well-known quick hardening of Kamacite\nunder stress might not appear under very high strain rates and the material might not react on\nthese very short time scales. Our results closed this knowledge gap which is of fundamental\nimportance to any nuclear deflection scheme for asteroids.\nMINOR COMMENTS\n5) The motivation for placing a phase boundary beneath the focal spot of the LDV needs more\nexplanation. In particular, how would a “preferred direction” of the stress wave be determined from\nthis single point measurement? How was it determined that there was no “preferred direction”?\nReply: Thank you for this thoughtful question. The placement of the LDV sensor above a known\nphase boundary was a deliberate choice to test whether stress waves induced by high-energy\nproton heating would exhibit directional propagation effects associated with microstructural\ninhomogeneities.\nIn heterogeneous materials like meteorites, even ppm-level inclusions can lead to anisotropic\nstress wave behavior under dynamic loading, as shown in prior studies (see Jain et al). This can\nresult in preferential wave propagation paths or spectral splitting, especially across phase\nboundaries. To test whether such effects occurred in our experiment, we placed the LDV sensor\ndirectly over a visible Kamacite–Taenite boundary.\nA key observation is that no directional or spectral asymmetries were detected in the resulting\nLDV signal. The Fourier spectra showed consistent peak positions and amplitudes across\nrepeated shots, with no evidence of spectral splitting or shifts. This strongly suggests that the\nstress field induced by the proton pulse was volumetric and spatially uniform — in stark contrast\nto impact-driven shock waves, which are known to exhibit anisotropic propagation along\nmicrostructural features.\nOur decision was further motivated by previous observations that structural transitions in iron-\nrich meteorites (e.g., formation of the Ɛ-phase) tend to initiate at phase boundaries, particularly\nunder high-pressure impact conditions (see e.g. Jain et al or Osuch et al). While our experiment\ninvolves thermal stress rather than mechanical shock, we hypothesized that the boundary could\nstill act as a sensitive probe for inhomogeneous stress propagation — which, however, was not\nobserved. This supports the assumption of a largely homogeneous thermoelastic field in our\nexperimental setup.\nIn the revised version of the manuscript, we sharpened the focus on the crucial effects of\nhardening and strain-amplitude dependent damping.\n6) Fig.1b: Scale bar does not exist or is too small to see, which makes interpretation of the image\ndifficult.\nReplyThe reviewer’s comment revealed that Figure 1 was not labeled correctly. In response,\nwe have divided the figure into two panels: (a) on the left-hand side and (b) on the right-hand\nside. The scale bar refers to panel (a), while panel (b) illustrates the untreated and cut samples\nof the Campo del Cielo meteorite.\n7) Fig.2: There is no discussion of the shots with “no clear response”. Does this imply difficulties with\nthe measurement? What is the implication for accuracy of the other shots?\nReply: The shots with “no clear response” refer to beam shots #24 and #27. These were not\nincluded in the aggregation of the main groups, as their displacement profiles exhibit a\nsignificantly higher standard deviation compared to the other measurements. Out of the total 27\nshots, 2 were used for calibration, 2 exhibited no clear response, and 23 could be reliably\nclassified as showing either elastic or plastic oscillatory profiles. Therefore, the presence of\nthese two outlier shots does not affect the accuracy or reliability of the classification and analysis\nof the remaining data.\nTo further support this, we updated Figure 3a to include the standard deviation for each of the\nthree main groups of LDV response profiles. The resulting error bars demonstrate that the\ngrouped data are highly consistent, with only small intra-group variation.\nThis clarification has been added to the revised Results section and is now reflected in the\ncaption of Figure 3.\n8) Fig.2: Authors should check the units in the energy scale; they do not appear consistent with the\nenergy deposition values in Fig.1a.\nReply: Thank you for pointing this out. We confirm that the energy units in Figures 1a and 2\nare consistent, though they represent different quantities:\n• Figure 2 shows the energy deposition density per primary proton, given in units of\nGeV/cm³ per proton.\n• Figure 1a shows the total energy deposition density, given in J/cm³ for a full beam shot.\nTo illustrate the consistency:\n• A value of 5.9 GeV/cm³ per proton in Fig. 2 corresponds to:\n5.9 GeV/cm3 × 1.602 × 10−10 J/GeV = 9.45 × 10−10 J/cm3 per proton\n• For a shot with 3 × 1011 protons:\n9.45 × 10−10 J/cm3 × 3 ×1011 = 283 J/cm3\nThis value is fully consistent with the upper end of the color scale in Figure 1a, which tops out\nat approximately 300 J/cm³.\nWe have added a clarification to the revised figure captions to avoid confusion.\n9) Line 119—122: This sentence appears overstated, as the present study does not show how proton\nbeams could be used to deflect or maneuver asteroids. The present study only addresses the wave\nbehavior.\nReply: Thank you for this important clarification. We fully agree that the present study does not\ndirectly demonstrate the feasibility of asteroid deflection or maneuvering using proton beams.\nRather, our goal is to address a critical gap in the understanding of material behavior under\nextreme energy deposition — a key prerequisite for modeling such scenarios realistically.\nPrevious simulation studies, including those by Moore et al. and the Lawrence Livermore\nNational Laboratory team, have relied on static or assumed material parameters when modeling\nhigh-energy deflection concepts. Our work provides, to our knowledge, the first real-time\nexperimental data capturing dynamic changes in yield strength and mechanical response during\nhigh-energy proton irradiation of asteroid material.\nMoreover, the study helps resolve a long-standing discrepancy between laboratory-based yield\nstrength measurements (e.g., from nanoindentation) and bulk strength estimates derived from\natmospheric meteorite breakup modeling. By quantifying a consistent scaling factor between\nlocal and bulk yield strength, we contribute relevant input data for future, more accurate\nplanetary defense simulations.\nWe appreciate the remark and have adjusted the manuscript accordingly by explaining the\nrelation to planetary defense and asteroid deflection scenarios more clearly (Introduction and\nExperimental setup section).\n10) Fig.3a: The two right-most of the three graphical panels have the same labels. Consider\ndifferentiating them. Also, it is unclear why the response returns to “elastic” on shot 23 even though\nthe beam energy remains high.\nReply: We thank the reviewer for this comment. Based on this, we restructured the manuscript\nto clarify the material response effects and streamlined nomenclatures to avoid any\nmisunderstandings.\nThe goal of the three panels in figure 3a) was to show the exemplary progression of the material\nresponse behavior. Starting with low intensity beam shots at 1x1011 protons an oscillatory\nbehavior is observed, then beam intensity is increased to 3 x1011 protons, resulting in non-\noscillatory behavior and finally the oscillatory behavior returns at 3 x1011 protons.\nThe return of oscillatory behavior at high beam intensity — following a regime of non-\noscillatory displacement — indicates that the material experienced a strain-induced hardening\nprocess, rather than reaching a hardening saturation or failure threshold. As shown in Figure 2\nand Figure 3, the collapse of oscillations at beam intensities of 3 ×1011 protons corresponds to\nthe onset of plastic deformation, while the subsequent recovery of oscillations reflects a dynamic\nincrease in yield strength resulting from dislocation buildup in the Kamacite phase.\nIn other words, the sample initially softens due to plastic deformation, but then hardens\nprogressively as dislocations accumulate. This increases the local and bulk yield strength such\nthat the same high thermal stress (up to ~120 MPa) no longer exceeds the (now higher) yield\nthreshold, allowing the sample to sustain elastic oscillations again.\nThis interpretation is supported by the following:\n• Dislocation density increased by a factor of ~6, as estimated from energy deposition\nand dislocation line energy.\n• Yield strength scales with the square root of dislocation density, implying an increase\nof local yield strength from ~350 MPa to ~875 MPa.\n• Applying the same factor to the bulk yield strength yields ~125 MPa, which is just\nabove the peak thermal stress — consistent with the observed reappearance of\noscillations.\n• The LDV spectra before and after hardening show no sign of damage or anisotropic\nwave propagation, suggesting structural integrity and uniform response.\n• GEANT4/COMSOL simulations also require a correction factor consistent with this\nhardening behavior to match observed displacements.\nTo address this more clearly, we reorganized the manuscript to provide a more structured\nexplanation of the plastic regime, the onset of hardening, and the interplay between the different\neffects involved. We have now clarified in the Discussion section that the observed recovery of\noscillations reflects a strain-hardening effect reaching a new dynamic threshold — not an\nindication of complete hardening or saturation.\nAlso, we added a note in Figure 3 that vertical scaling differs between graphs for visual clarity.\n11) Line 178: “peak-induced stress” is not clearly defined.\nReply: We thank the reviewer for this remark. To avoid misunderstandings we changed the\nnomenclature from “peak-induced stress” and clarified the definition in the Methods sections.\n“Peak-induced stress” is equivalent to von Mises stress, i.e.\n𝜎 = 1 [(𝜎 −𝜎 )2+(𝜎 −𝜎 )2+ (𝜎 −𝜎 )2], with\n𝑣𝑚 𝑧 𝜃 𝜃 𝑟 𝑟 𝑧\n√2\n𝜎 is axial stress, 𝜎 is tangential stress and 𝜎 is radial stress.\n𝑧 𝜃 𝑟\n12) Line 189: “internal dynamics” is not clearly defined.\nReply: Thank you for this helpful remark. Indeed, the term “internal dynamics” was not\nsufficiently defined in the manuscript. The key observation underlying this term is that yield\nstrength measurements of iron meteorite material differ by a heuristic factor depending on the\nmeasurement method. Specifically, nanoindentation measurements yield higher values for the\nyield strength than estimates derived from ram pressure during meteorite explosions in the\natmosphere. One hypothesis is that the heuristic factor of approximately ~7 between these two\nmeasurements may be attributed to internal inertial movements within the heterogeneous\nmaterial structure, which we have summarized under the term “internal dynamics.”\nCurrently, this heuristic factor is not explained by an integrated mechanical model of the\nmaterial. However, following the reviewer’s valuable suggestion, we conducted additional\nMonte Carlo simulations using the GEANT4/COMSOL code. These simulations provided a\nhigh-resolution temperature profile of the entire meteorite cylinder volume, including the\nsurface region where the temperature was measured via PT100 sensors.\nBased on the simulated surface temperature, we estimated the corresponding thermal strain\nusing the relation:\nStrain = 𝛼 × Δ𝑇 where 𝛼 is the average coefficient of thermal expansion (20–100°C) and\nΔ𝑇 is the temperature increase at the surface. When comparing the resulting strain derived from\nthe GEANT4/COMSOL simulations to the measured displacement obtained from LDV, we\nobserve a factor of approximately ~5 between them. While no quantitative model yet exists to\nfully describe this effect, our simulations qualitatively support the hypothesis that internal\ninertial movements — linked to the microstructural complexity of the material — contribute to\nthis discrepancy, which we have referred to as \"internal dynamics\".\nThe manuscript structure was reorganized and sharpened to improve clarity and emphasize the\ndistinctions between these effects.\n13) Lines 166-167, 178-180, 196-205: Consistency with ram conditions or shock impact conditions is\nnot necessarily expected, as yield strengths are known to be sensitive strain-rate and/or shear\nconditions.\nReply: We fully agree with the reviewer that consistency with ram or shock impact conditions\nis not necessarily expected, as yield strengths are indeed highly sensitive to strain rate and shear\nconditions. The large discrepancy between yield strength values obtained from different\nmeasurement methods — namely, nanoindentation versus atmospheric entry (ram pressure)\nestimates — points to a factor of ~7 difference. Generally, this discrepancy is interpreted as\nbeing indicative of the specific internal structure and microstructural complexity of the\nmeteorite material.\nTo better understand this, we have included a new paragraph in the revised manuscript\ndiscussing additional GEANT4 Monte Carlo simulations that were performed following the\nreviewer’s valuable comments. These simulations allowed us to obtain high-resolution\ntemperature profiles of the meteorite cylinder and, by applying the relation Strain = 𝛼 × Δ𝑇, to\nestimate surface displacements. The comparison of simulated and experimentally measured\ndisplacements supports the hypothesis that internal inertial movements within the\nmicrostructure contribute to the observed damping behavior and to the measured\ndiscrepancies.11.1 x 10-6 K-1and a sample radius of 5 mm, we derive a displacement on the order\nof 0.6 m. The measured average displacement averaged over oscillating high intensity\ndiagrams is 2.9 m. The discrepancy of a factor of ~5 is on the order of the factor observed\nbetween ram pressure-derived values and nanointendation measurements. This supports the\nview that the sample as a whole – when irradiated by the proton beam – experiences an effective\nstress which includes the effect of internal inertial movements.\nThis conclusion is further supported by the observed damping behavior at high intensity. The\nobserved strain amplitude-dependent super-exponential damping is usually also explained as\nexcitation of internal inertial degrees of freedom in complex materials.\nNote that the suggestion that meteorite material – due to the inclusions – behaves like a\ncomposite has already been made in Mulford et al.\nThe structure of the manuscript was reorganized to facilitate a clearer distinction between the\neffects and improve overall comprehensibility.\n14) Fig.5: The meaning of the color bar is unclear, specifically the normalization “per bin of 1 cm3” is\nsometimes used for energy but not usually for temperature. Should the units instead be “K/pulse?\nOr this normalization should be described.\nReply: Thank you for this helpful comment. Figure 1 and Figure 5 are based on two separate\nMonte Carlo simulations. Figure 1 presents the simulated local energy deposition profile in\nJ/cm³, while Figure 5 shows the corresponding local temperature increase derived from a\ndedicated simulation focusing on temperature development. Based on the reviewer’s comment,\nwe conducted an additional Monte Carlo simulation using COMSOL and GEANT4 with higher\nspatial resolution over the full meteorite cylinder volume to obtain a more detailed temperature\ndevelopment. In the revised manuscript, we replaced Fig. 5 with the new high-resolution\nGEANT4/COMSOL simulation, which now provides a more precise spatial representation of\nthe local temperature increase. The color scale indicates the temperature increase per pulse, in\nunits of K/pulse. We updated the figure caption and methods section accordingly to clarify this\nnormalization. The main purpose remains to demonstrate that, even at the highest beam\nintensities, the temperature increase remains far below phase transition thresholds of the\nmaterial.\n15) Line 301-303: It does not seem correct to say “the PT100 sensor measured roughly the same amount\nof temperature increase as for the oscillating diagrams” because the diagrams do not measure\ntemperature. Or the method behind this inference should be explained more fully.\nReply: Thank you for this remark. We agree that the original wording was not precise, as the\noscillatory diagrams obtained by Laser Doppler Vibrometry do not measure temperature\ndirectly. We have therefore revised the sentence to: “The PT100 sensor measured roughly the\nsame amount of temperature increase as for the beam shots characterized by oscillatory\nbehavior.” This wording more accurately reflects that the comparison refers to beam shots\nassociated with oscillatory response, not to temperature measurements derived from the LDV\ndata itself.\n16) Line 324-325: Why was this weighting performed? Does it imply a systematic error in the model?\nReply: Thank you for this important question. We added a more structured explanation in the\nMethods section capturing the following: The weighting was performed because a simple\nhomogeneous integration of the measurement data, taken at z = 5 cm (middle of the cylinder),\nwould not properly reflect the fact that the energy deposition is strongly position-dependent\nalong the longitudinal (z-) axis of the cylinder, as shown by the FLUKA simulation. The\nweighting compensates for this effect by scaling the LDV-derived local energy with the ratio\nof simulated temperature at each position to the PT100 reference, thus providing a more\naccurate estimate of the total energy deposited into plastic deformation across the entire\nsample volume. Of course, performing LDV measurements at multiple longitudinal positions\nwould be preferable, but this was not feasible due to experimental limitations at CERN related\nto equipment access restrictions in high-radiation zones.\n17) Line 329-330: The values (with units) when used in (2) do not appear to give units of energy; they\ngive units of force. Also, it is unclear how the dislocation density was calculated from (2).\nReply: First, we estimated the energy loss in the oscillatory LDV signals by comparing the\nenergy content during oscillatory, i.e. elastic (low-amplitude) and non-oscillatory, i.e. plastic\n(suppressed amplitude) phases, summing across all beam shots. The total plastic deformation\nenergy was determined to be 𝐸 = 360 𝜇J. This value was corrected for spatial distribution\nplastic\nusing Monte Carlo thermal simulations (FLUKA), normalized to the PT100 temperature sensor\ndata.\nAssuming that this energy is fully stored in newly formed dislocations, we used the relation\n𝐸 = ½ G b2 with G=75 GPa, and b = 1.44 Å to obtain a dislocation line energy of\ndisloc\n7.78×10−10 J/m. This corresponds to a calculated dislocation density increase of 6.1×1010 m−2,\nconsistent with prior studies on Kamacite which show that significant hardening can occur at\nrelatively low increases in dislocation density compared to typical metals (Osuch et al).\nFollowing the empirical relation between yield strength and dislocation density (approximately\nthe square root of the dislocation density), this would translate into a hardening of Kamacite\nfrom an initial yield strength of ~350 MPa (as obtained by nanoindentation measurements\n\\cite{ueki2021excellent}) to ~875 MPa. Again, based on this comment and others addressing\nthe hardening process and underlying calculations, we reorganized the manuscript, particularly\nin the Discussion and Methods section."}, {"round": 2, "reviewer_comments": {"reviewer_1": "The edits and thoughtful responses provided by the authors have addressed all of my comments/concerns about the paper from the first revision. There are some very minor issues that remain that I have detailed below:\n1. Citation 1 (Miles et al) is probably not the best citation for general Planetary Defense, including references to Z-machine experiments. I would suggest either citing the Dearborn and Miller for a general overview of Planetary Defense and early work by Remo on Z-machine experiments.\n2. Line 176 has a colon like it is going to provide a definition - I think it should be a period.", "reviewer_2": "All the comments provided by this reviewer have been carefully addressed and fully incorporated, leading to a substantial improvement in the overall quality of the manuscript. Therefore, the article is now deemed suitable for publication.", "reviewer_3": "The authors have substantially improved both the rigor and clarity of this work. Several issues still remain as outlined below.\nMajor comments\n1. The temperature map (Fig.6), based on revised, higher-resolution simulations, shows substantially higher peak temperatures than before. Because the heating is nearly instantaneous (250 ps per pulse), one can use the Grüneisen parameter to estimate local pressure of several GPa in the region of maximum energy deposition, which is an order-of-magnitude higher than the peak stress estimated by the authors using the method of Bertarelli based on the response of the entire rod. This reintroduces the question of localized, solid-solid phase transition contributing to the energy dissipation. The authors cite two papers on the high-pressure phase behavior of iron (Jain, Anderson); however, there has been more recent work suggesting Fe and Fe/Ni alloys may undergo fcc to hcp transition under conditions of a few hundred Kelvin temperature rise and a few GPa pressure (as an example only, see Torchio 2020, DOI:10.1029/2020GL088169). Given present uncertainties in phase behavior in this regime, more discussion or analysis on this point seems necessary to distinguish between solid-solid phase transition and the proposed defect production.\n2. Following the above, the authors should consider if the response measured with LDV should be contextualized as a volumetrically-averaged result or similar, and the potential influence (or not) of localized heating and stress may need to be discussed.\nMinor comments\n1. Fig.1b is still missing a scale bar for the inset at upper right, which is necessary for interpretating the image.\n2. Abstract, first sentence: “dynamic response” is vague, which makes the statement “an effect that has not been captured until now” not particularly meaningful.\n3. Fig.6, fonts are very small and difficult to read on the color bar and elsewhere.\n4. Line 293: As a point of style only, “worldwide” seems overly emphatic and unnecessary."}, "author_response": "17 October 2025\nDear Reviewers,\nWe would like to thank you for taking the time to consider the revised version of our manuscript\nentitled “Dynamical development of strength and stability of asteroid material under 440 GeV proton\nbeam irradiation” (Manuscript ID: NCOMMS-24-76790). We are grateful for your detailed and\nvaluable feedback, which has significantly helped us to strengthen and clarify our study.\nIn this second revision, we have addressed the remaining points raised in the previous round and\nincluded additional work to further consolidate our findings. The main updates concern:\n• Application of the Grüneisen parameter to derive local pressure values from the higher-\nresolution temperature profile simulations, offering an independent and quantitative\nconsistency check for our interpretation of the observed material response.\n• Expanded discussion of these results taking into account more recent work on high-pressure\nphase behavior of Fe–Ni alloys and a comparison between the Bertarelli thermal-stress model\nand the local peak pressures derived via the Grüneisen approach.\n• Explicit clarification that the LDV measurements represent volumetrically averaged\nresponses.\n• Besides we modified wording, replaced or added relevant references and polished two figures\nfor better clarity.\nIn addition to the revised manuscript, we have uploaded a version with all textual changes highlighted\nin blue (figures omitted for improved readability). We believe that these additions further strengthen\nthe robustness of our conclusions and improve the overall clarity and readability of the paper.\nThank you again for your constructive evaluation and consideration of our work.\nSincerely,\nMelanie Bochmann (on the behalf of all co-authors)\nReviewer #1 (Remarks to the Author):\nThe edits and thoughtful responses provided by the authors have addressed all of my\ncomments/concerns about the paper from the first revision. There are some very minor issues that\nremain that I have detailed below:\n1) Citation 1 (Miles et al) is probably not the best citation for general Planetary Defense, including\nreferences to Z-machine experiments. I would suggest either citing the Dearborn and Miller for a\ngeneral overview of Planetary Defense and early work by Remo on Z-machine experiments.\nReply: Thank you for this suggestion. We fully agree and have cited Dearborn & Miller for the\ngeneral overview of Planetary Defense in the first paragraph of the introduction. In addition, we\nincluded Remo’s early Z-machine studies as a more relevant reference for laboratory-scale\nsimulations.\n2) Line 176 has a colon like it is going to provide a definition - I think it should be a period.\nReply: Thank you for noting this. We agree — the colon at the end of line 176 was unintended\nand was replaced by a period in the revised version.\nReviewer #2 (Remarks to the Author):\nAll the comments provided by this reviewer have been carefully addressed and fully incorporated,\nleading to a substantial improvement in the overall quality of the manuscript. Therefore, the article is\nnow deemed suitable for publication.\nReviewer #3 (Remarks to the Author):\nThe authors have substantially improved both the rigor and clarity of this work. Several issues still\nremain as outlined below.\nMAJOR COMMENTS\n1) The temperature map (Fig.6), based on revised, higher-resolution simulations, shows substantially\nhigher peak temperatures than before. Because the heating is nearly instantaneous (250 ps per\npulse), one can use the Grüneisen parameter to estimate local pressure of several GPa in the region\nof maximum energy deposition, which is an order-of-magnitude higher than the peak stress\nestimated by the authors using the method of Bertarelli based on the response of the entire rod. This\nreintroduces the question of localized, solid-solid phase transition contributing to the energy\ndissipation. The authors cite two papers on the high-pressure /Ni alloys may undergo fcc to\nhcp transition under conditions of a few hundred Kelvin temperature rise and a few GPa pressure\n(as an example only, see Torchio 2020, DOI:10.1029/2020GL088169). Given present uncertainties\nin phase behavior in this regime, more discussion or analysis on this point seems necessary to\ndistinguish between solid-solid phase transition and the proposed defect production.\nReply: We thank the reviewer for the valuable suggestion to use the Grüneisen approach for\nestimating the instantaneous thermal pressure under ultrafast (≈250 ps) isochoric heating.\nWe calculated the Grüneisen parameter γ using the relationship 𝛾 =\n𝛼𝑉 ∙𝐾𝑇,\nusing the\n𝜌 ∙𝑐𝑣\nthermophysical parameters for Fe-Ni in the dominating kamacite phase:\nProperty Value Unit Reference\nThermal expansivity, α 11.1 ∙ 10-6 K-1 [27]\nYoung s modulus, E 240 GPa [24]\nPoisson ratio, ν 0.3 [28]\nDensity, ρ 8060 kg/m3 [18]\nSpecific heat coefficient, c 461 J/kg K [25,26]\np\nDerived properties\nBulk modulus, K 200 GPa K = E/(1-2v)\nT T\nVolumetric thermal expansivity α 11.1 ∙ 10-6 K-1 α =3α\nV V\nThese values yield a Grüneisen parameter of 𝛾 ~ 1.8. Applying p ≈ γ∙ ρ∙c ∙ΔT to the peak\nv\ntemperature rises from the revised, higher-resolution simulation yields local thermal pressures\nbetween 2.2 and 3.0 GPa (details are in the table below).\n∆T [K] V [mm3] p [GPa]\nthreshold heated local\n300 4.0897 2.2\n350 1.3216 2.5\n400 0.1364 2.8\n430 0.0056 2.9\n435 0.0015 2.9\n440 0.0002 2.9\nAs the reviewer correctly notes, these local pressures are approximately an order of magnitude\nhigher than the meteorite cylinder rod-averaged thermal peak stress using the thermal stress\nmodel by Bertarelli et al.\nFor comparison, Torchio et al. (2020) report that in Fe–Ni alloys the bcc → hcp (α → ε)\ntransition starts at pressures above ≈ 12 GPa for Ni ≈ 20 wt %, and completes at 17 GPa, shifting\nto even higher pressures (> 100 GPa) with increasing Ni content. The average Ni concentration\nin our iron meteorite sample is significantly lower (≈ 6.15 wt % overall, ≈ 5.5 wt % for the\ndominant bcc kamacite phase). Consequently, the 2–3 GPa local pressures estimated here lie\nwell below any known equilibrium phase-transition thresholds, and we therefore do not expect\nsolid–solid phase transitions under these conditions.\nWe have included this additional consistency check in the summary part of the Discussion\nsection (line 191) and added a dedicated paragraph in the Methods section (line 363) providing\nfurther details of the calculations.\n2) Following the above, the authors should consider if the response measured with LDV should be\ncontextualized as a volumetrically-averaged result or similar, and the potential influence (or not) of\nlocalized heating and stress may need to be discussed.\nReply: Correct, LDV is only volumetrically averaged result as it is discussed, will be included\nexplicitly in the manuscript. The localized hot zone (ΔT ≥ 300 K) determined from the revised\nsimulation corresponds to only ~0.7 % of the total cylinder volume, while the thermal stress\nwave generated there propagates throughout the full sample. An additional explanatory sentence\nand disclaimer have been included in the corresponding Methods section to clarify this\ninterpretation (line 389).\nMINOR COMMENTS\n1) Fig.1b is still missing a scale bar for the inset at upper right, which is necessary for interpretating\nthe image.\nReply: Thank you for pointing this out. We have replaced the previous image with a simplified top-\nview photograph to avoid perspective distortion. The new version includes explicit x- and y-\ndimensions in the caption (21.4 cm × 14.3 cm), which provides a clear spatial reference.\nThis photograph was added.\n2) Abstract, first sentence: “dynamic response” is vague, which makes the statement “an effect that\nhas not been captured until now” not particularly meaningful.\nReply: We agree that “dynamic response” was too general. We have revised the opening sentence\nto specify the physical process investigated, clarifying the novelty of the experimental observation.\nIn addition, we modified other text sections accordingly (e.g. in the introduction).\n3) Fig.6, fonts are very small and difficult to read on the color bar and elsewhere.\nReply: Thank you for noting this. We have increased the overall figure size and adjusted the font\nsettings, including those on the color bar, to ensure readability in the revised version.\n4) Line 293: As a point of style only, “worldwide” seems overly emphatic and unnecessary.\nReply: Thank you for this stylistic suggestion. We agree that “worldwide” is unnecessary and have\nremoved it in the revised version for a more concise phrasing."}, {"round": 3, "reviewer_comments": {"reviewer_3": "The authors have addressed all of my concerns, and I recommend publication of this manuscript. I would like to point out, however, that the thermal expansion coefficient stated on line 213 is inconsistent with the value stated in the Methods, Table I. I assume this is a typographical error."}, "author_response": ""}]

Decision letter