Optimization of Tungsten Anode Target Design for High-Energy Microfocus X-Ray Sources via Geant4 Monte Carlo Simulation

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

The anode target is a bottleneck for the performance of the micro-focus X-ray source, and its optimized design is crucial for improving micro-focus X-ray sources. This paper investigates the optimal thickness of transmission and reflection target , along with the effects of electron beam incidence angles, beryllium window thickness, and filter materials on the energy spectra and spatial distributions and so on, it is obviously benefit to improve the micro-focus X-ray source design.

There are some parts of the paper that need to be discussed.

1. In fact，flat panel detector is more used than annular detector. Thus，annular detectormodel for Geant4 is established in the fig.1 maybe get different result from practice.
2. The thermal loading of the target is also key factor of the target design, but it is regrettable that there is little discussion of this in this paper.
3. It should be clarifiedthat the relationship between the X ray energy and that of the impinging electron beam.  It obviously that the X ray energy can’t be more than that of the impinging e-beam. In figures 2 and 3, it is clearly not true that the X ray energy is much greater than that of the electron beam.
4. The simulation results and conclusions in this paper should be verified by experiments.
5. There is a edit error on line 303.

Author Response

We sincerely thank the referees for their time, careful reading, and constructive comments on our manuscript. We have thoroughly revised the manuscript in accordance with their suggestions. Below we provide our point‐by‐point responses to all comments, along with details of how we have modified the text or figures.

 

Referee 1:

The anode target is a bottleneck for the performance of the micro-focus X-ray source, and its optimized design is crucial for improving micro-focus X-ray sources. This paper investigates the optimal thickness of transmission and reflection target , along with the effects of electron beam incidence angles, beryllium window thickness, and filter materials on the energy spectra and spatial distributions and so on, it is obviously benefit to improve the micro-focus X-ray source design.

There are some parts of the paper that need to be discussed.

Response: We thank referee 1 for the positive assessment and insightful suggestions. We address each of the questions and concerns below:

1. In fact, flat panel detector is more used than annular detector. Thus, annular detector model for Geant4 is established in the fig.1 maybe get different result from practice.

Response: We agree with the referee regarding the common use of flat-panel detectors. The annular detector in our simulation was a computational choice to enable uniform angular sampling and efficient energy–angle-resolved analysis within the Geant4 framework, rather than to model a specific commercial setup. To clarify this, we have added the following sentence to the Methods section (Page 3, Lines 132–134): “Although flat-panel detectors are widely used in practice, an annular detector geometry was adopted in the simulation to ensure uniform angular sampling and facilitate energy–angle-resolved analysis.”

 

2. The thermal loading of the target is also key factor of the target design, but it is regrettable that there is little discussion of this in this paper.

Response: We fully agree that thermal loading is a critical factor for long‐term target stability and design. Our current study focuses on radiation generation efficiency and spectral optimization under various geometric and beam‐energy conditions, assuming steady‐state thermal management akin to commercial micro‐focus tubes. A coupled thermo-mechanical analysis will be the subject of future investigation. To acknowledge this important aspect and guide future work, we have added the following statement to Section 3.2 (Page 8, Lines 292–295): “It is acknowledged that temperature rise and associated stress at the tungsten–copper interface are paramount for operational stability and lifetime. Future work will incorporate coupled thermo‐mechanical analysis to quantitatively evaluate these effects under realistic operating conditions.”

3. It should be clarified that the relationship between the X ray energy and that of the impinging electron beam. It obviously that the X ray energy can’t be more than that of the impinging e-beam. In figures 2 and 3, it is clearly not true that the X ray energy is much greater than that of the electron beam.

Response: We thank the reviewer for highlighting this potential source of confusion. The apparent discrepancy arises because the vertical axes in Figures 2(a-c) and 3(a-c) represent the total X-ray energy recorded per detector pixel (the sum of all photon energies passing through that pixel during the simulation), rather than the energy of an individual photon. Since the simulation uses 10⁸ incident electrons, the integrated X-ray energy can exceed the energy of a single electron, while each photon remains below the incident‐electron energy. To eliminate confusion, we have revised the y-axis labels in Figures 2(a-c) and 3(a-c) from “Energy (keV)” to “Total X-ray Energy (keV)”, which more accurately represents the integrated photon energy recorded per detector pixel. This adjustment eliminates possible confusion without altering the underlying data or results.

 

 

4. The simulation results and conclusions in this paper should be verified by experiments.

Response: We agree that experimental validation is a crucial next step. The fabrication and characterization of high-energy microfocus targets with precisely controlled micron-scale thicknesses is technically challenging and requires specialized facilities beyond our current scope. This study aims to establish a foundational theoretical framework to guide such future experimental efforts. We have added the following statement to the Conclusions section (Page 10, Lines 347–349): “Future work will prioritize the experimental validation of these simulation results through the fabrication of optimized anode targets and the characterization of their emission properties.”

 

5. There is an edit error on line 303.

Response: We thank the referee for their careful reading. This error has been corrected in the revised manuscript.

 

Reviewer 2 Report

Comments and Suggestions for Authors

This work optimizes the tungsten anode target of a high-energy microfocus X-ray source operating in the 100-300keV range by using Geant4. The results are primarily based on simulations using existing tools, and lack original methods or experimental verification. The model constructed in the simulation is reasonable, and the parameters that need to be optimized are discussed through simulation. It can provide theoretical guidance for the design of high-energy micro focal spot X-ray sources, and may contribute to detector calibration, flatness correction, beam hardening correction, and radiation shielding design. Several issues should be addressed prior to publication.

 

1. How should we interpret the(energy) bar on the left side of Figure 2(a) and Figure 3(a)?
2. Please clarify the correspondence between the observation angles discussed in lines 205, 208, 212 and those indicated in Figure 3(a).
3. The error sentence in line 303 needs to be corrected.
4. To simplify the simulation, the electron beam was treated as perfectly monochromatic in energy and strictly collimated along the +Z axis, with zero angular divergence. Have you considered the influence of the electron incidence velocity and angle?

Author Response

We sincerely thank the referees for their time, careful reading, and constructive comments on our manuscript. We have thoroughly revised the manuscript in accordance with their suggestions. Below we provide our point‐by‐point responses to all comments, along with details of how we have modified the text or figures.

Referee 2:

This work optimizes the tungsten anode target of a high-energy microfocus X-ray source operating in the 100-300keV range by using Geant4. The results are primarily based on simulations using existing tools, and lack original methods or experimental verification. The model constructed in the simulation is reasonable, and the parameters that need to be optimized are discussed through simulation. It can provide theoretical guidance for the design of high-energy micro focal spot X-ray sources, and may contribute to detector calibration, flatness correction, beam hardening correction, and radiation shielding design. Several issues should be addressed prior to publication.

Response: We appreciate Reviewer 2’s positive assessment that our simulation model is reasonable and that this study can provide theoretical guidance for micro‐focus X-ray source design. Below are our responses to specific points.

1. How should we interpret the(energy) bar on the left side of Figure 2(a) and Figure 3(a)?

Response: We thank the reviewer for this question. The scalebar labeled “Energy (keV)” in Figures 2(a) and 3(a) refers to the total X-ray energy recorded by each detector pixel, i.e., the sum of the energies of all photons passing through that pixel. We have updated the figures and captions accordingly, changing the label to "Total X-ray Energy (keV)" to ensure clarity.

 

2. Please clarify the correspondence between the observation angles discussed in lines 205, 208, 212 and those indicated in Figure 3(a).

Response: We thank the referee for pointing this out. The angles cited in the text (0°, 15°, 30°, etc.) correspond directly to the detector pixel centers shown in Figure 3(a). To avoid ambiguity, we have revised the caption of Figure 3 and the relevant sentences in Section 3.2 (red color in main text) to explicitly note this correspondence.

 

3. The error sentence in laine 303 needs to be corrected.

Response: We thank the referee for their careful reading. The error at line 303 has been corrected in the revised manuscript.

 

4. To simplify the simulation, the electron beam was treated as perfectly monochromatic in energy and strictly collimated along the +Z axis, with zero angular divergence. Have you considered the influence of the electron incidence velocity and angle?

Response: We appreciate the reviewer’s thoughtful question. We deliberately modelled the beam as monoenergetic and perfectly collimated to isolate the effects of target geometry and material interactions. We acknowledge that a real beam with energy spread and divergence would slightly broaden the angular distribution and smooth spectral features. However, we do not expect this to alter the core optimization trends identified in this study. We have added a note to Section 2.1 (line 101-103) to this effect: “The influence of finite beam divergence and energy spread is expected to slightly smooth the spectra but not alter the presented optimization trends.”

 

 

Author Response File: Author Response.pdf

Reviewer 3 Report

Comments and Suggestions for Authors

This manuscript presents a Monte Carlo simulation study using the Geant4 toolkit to optimize the design of tungsten anode targets for high-energy (100–300 keV) microfocus X-ray sources. The authors systematically investigate both transmission and reflection target geometries, evaluating the influence of target thickness, electron incidence angle, beryllium window thickness, and filter materials on the X-ray output.

Several points require clarification and revision to enhance the scientific rigor before it can be accepted for publication. Here are my suggestions:

1.    The manuscript states that Geant4 (version 11.0.3) was used with its physics models for electromagnetic interactions (lines 88-90). In order for the Monte Carlo study to be reproducible, it is necessary to specify the exact physics option that was employed. Geant4 offers several standard electromagnetic physics options (e.g., G4EmStandardPhysics_option4, G4EmLivermorePhysics, and etc.), each with different models and accuracy ranges, particularly for low-energy electron and photon transport relevant to this work.

2.  There is a broken cross-reference in the text on line 303, the text reads "...and Error! Reference source not found.". This is a critical formatting error that must be corrected.

3.  The finding that the optimal reflection target thickness decreases with increasing electron energy (Figure 3d) is one of the most interesting and counter-intuitive results of the study. The discussion of this phenomenon (lines 258-276) is somewhat superficial. The authors correctly note the ambiguity at lower energies due to a broad plateau but do not provide a deep physical explanation for the downward trend at higher energies

Author Response

We sincerely thank the referees for their time, careful reading, and constructive comments on our manuscript. We have thoroughly revised the manuscript in accordance with their suggestions. Below we provide our point‐by‐point responses to all comments, along with details of how we have modified the text or figures.

Referee 3:

This manuscript presents a Monte Carlo simulation study using the Geant4 toolkit to optimize the design of tungsten anode targets for high-energy (100–300 keV) microfocus X-ray sources. The authors systematically investigate both transmission and reflection target geometries, evaluating the influence of target thickness, electron incidence angle, beryllium window thickness, and filter materials on the X-ray output. Several points require clarification and revision to enhance the scientific rigor before it can be accepted for publication. Here are my suggestions:

Response: We sincerely thank the referee 3 for the detailed review and constructive suggestions that have enhanced the rigor of our work. We have carefully addressed each comment, clarified missing information, and made corresponding revisions to the manuscript as detailed below:

1. The manuscript states that Geant4 (version 11.0.3) was used with its physics models for electromagnetic interactions (lines 88-90). In order for the Monte Carlo study to be reproducible, it is necessary to specify the exact physics option that was employed. Geant4 offers several standard electromagnetic physics options (e.g., G4EmStandardPhysics_option4, G4EmLivermorePhysics, and etc.), each with different models and accuracy ranges, particularly for low-energy electron and photon transport relevant to this work.

Response: We thank the reviewer for this important point regarding reproducibility. We have now specified the physics option in the revised Methods section (Page 3, Lines 88–90): “and we used the G4EmStandardPhysics_option4 package, which provides detailed low‐energy electromagnetic models suitable for electron–photon transport in the 100–300 keV range.”

 

2. There is a broken cross-reference in the text on line 303, the text reads "...and Error! Reference source not found.". This is a critical formatting error that must be corrected.

 

Response: We thank the referee’s comment. The broken cross-reference was caused by a corrupted figure link during the Word-to-PDF conversion. It has been corrected in the revised manuscript, and all figure and table references have been rechecked for consistency.

 

3. The finding that the optimal reflection target thickness decreases with increasing electron energy (Figure 3d) is one of the most interesting and counter-intuitive results of the study. The discussion of this phenomenon (lines 258-276) is somewhat superficial. The authors correctly note the ambiguity at lower energies due to a broad plateau but do not provide a deep physical explanation for the downward trend at higher energies

Response: We thank the referee for highlighting the importance of this result. To improve understanding of the observed inverse correlation, we have substantially expanded the discussion in Section 3.2 (Page 8, Lines 273–279) to provide a deeper physical explanation: “At higher incident energies, electrons penetrate deeper into tungsten, shifting the bremsstrahlung‐generation region further below the surface. As the path length for photon re-absorption increases with depth, thicker targets produce stronger internal attenuation of high‐energy photons. Therefore, thinner reflection‐geometry targets become more efficient at higher energies by minimizing internal self‐absorption while still providing sufficient electron stopping length. This behavior reflects the competing influences of increasing electron penetration depth and photon attenuation.”

Author Response File: Author Response.pdf

Round 2

Reviewer 1 Report

Comments and Suggestions for Authors

1. In figures 2 and 3, Vertical axis unit may be“X ray intensity” not” X ray energy” .
2. There is still a edit error on line 322.

Author Response

1. In figures 2 and 3, Vertical axis unit may be “X ray intensity” not” X ray energy” 

Response: We have clarified the presentation by changing the y-axis labels in Figures 2(a-c) and 3(a-c) to "Normalized X-ray Intensity" and have adjusted the data accordingly. This revision more accurately represents the relative intensity distribution recorded by the detector, effectively preventing any misunderstanding without altering the underlying trends or conclusions of the data.

2. There is still a edit error on line 322.

Response: We thank the referee for their careful reading. This error has been corrected in the revised manuscript.

Author Response File: Author Response.pdf