RF Characterization and Beam Measurements with Additively Manufactured Fast Faraday Cups

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

Line - Comment 

30 - beta < 1 should be used instead of <100% 

48 - repetition of "tapered" 

66 - why not continue the notation using beta? beta = 0.15 instead of v_b 

113-141 - Field plots or SE trajectories may help the reader keep track of the scenarios described - Discussion of SE should be condensed for better readability. Too much focus on the negative bias case, which would not be employed anyways. 

165-168 - Field plots / SE trajectories should be used here to clarify the improvement over the ACFFC geometry 

210-211 - clarify, that "drill hole" is in collector here not sentence after 

236-237 - s_pen indices are too long, sentence works without s=, only stating values 

Figure 7 - Missing reference (??) 

355-357 - Misleading statement. AM parts performed better due to geometrical deviations between the parts (as stated). This is not an inherent property of the AM parts making them better. It is fine to focus on the AM parts, but not "because" they performed better. 

512-515 - Misleading statement. "Better" rf performance seems to be solely due to geometrical differences changing the impedance matching of the FFC.  It can not be concluded that they are inherently better. Machined ones with same dimensions might perform the same or better. Nonetheless the paper shows, that AM parts can successfully be used for this use case.  Authors should highlight the feasibility of AM structures for diagnostics.   

Overall comments:

• Further visual aids, especially highlighting the field enhancements etc. of the TRCFFC would greatly improve the readability of the paper.
• Authors should be careful about claims that highlight the improved performance of the AM parts if the reason is, as was also stated in the paper most likely due to differences in geometry.  
• Another possible benefit of AM could be discussed: Lower SEY due to higher surface roughness?   
• Title: "RF CHARACTERIZATION AND BEAM MEASUREMENTS WITH 3D PRINTED FAST FARADAY CUPS" Comment: Using "Additive Manufacturing" instead of "3D printing" would be advised.   

Overall suitable for publication once the above comments are addressed

Author Response

Response to reviewer’s comments and recommendations for the manuscript

instruments-3833241

29.10.2025

Dear Reviewer,

we greatly appreciate your thorough evaluation and thoughtful feedback on our manuscript. Your comments were very helpful and contributed decisively to improving the quality and presentation of our work. We have carefully considered each of your concerns and revised the manuscript accordingly. Please find detailed responses to your remarks below. We hope these improvements meet your expectations and contribute to the manuscript’s overall quality. In addition to this response, we provide a marked-up version of the manuscript highlighting all changes, with line numbers to locate each change efficiently.

Line – Comment:

• “30 - beta < 1 should be used instead of <100%”

Thank you for pointing that out. You are right, we mixed the notation of beta in decimal and percentage style. We standardized it to the more usual convention in accelerator physics and replaced it to  < 1 (line 29 to 30).

• “48 - repetition of "tapered"”

Thank you very much for the suggestion to improve the wording and style. The repetition occurred due to first glossary appearance of TRCFFC. We removed the second text “tapered” in line 54 to 55.

• “66 - why not continue the notation using beta? beta = 0.15 instead of v_b”

Thank you very much for indicating the bad notation. It was a leftover from an early stage of the paper. We removed  and replaced with beta. It is the only occurrence this way and all other occurrences have been beta already. (lines 73-74)

• “113-141 - Field plots or SE trajectories may help the reader keep track of the scenarios described - Discussion of SE should be condensed for better readability. Too much focus on the negative bias case, which would not be employed anyways.”

&

“165-168 - Field plots / SE trajectories should be used here to clarify the improvement over the ACFFC geometry”

Thank you very much for this extremely valuable suggestion and for offering a solution, so that the reader keeps track of the scenarios.

Based on your suggestion we simulated trajectories with the particle tracking solver of CST Particle Studio and created images with both, the trajectories together with the electrical field created by the bias voltage applied to the collector for all three geometries for different bias settings (see Fig. 3 and 7). We shortened the description of the first regime discussed to make it less repetitive (lines 132 to 139). The improvement towards the ACFFC is the combination of bias and geometrical suppression, which delays the signal of the SE and reduces the amount of SE contributing to the output signal significantly. (Lines186 to 193)

• “210-211 - clarify, that "drill hole" is in collector here not sentence after”

Thank you for your valuable comment. You are right that this part was not clearly stated and less understandable. For a significant improvement, we rephrased it (lines 243-247) and added labels to the geometry plot in Fig 6 to give more explanation references, e.g. heat shield, glass pins, heat shield bracket and collector, also. The first mentioned drill hole was referring to the chassis drift passage, not the collector. But still the collectors drill hole (sentence after) needs to be even larger than the drift passage due to the space charge-blow-up of the bunch. The ions shall not hit anywhere else but inside the drill hole of the collector, so that no SEs are generated anywhere else without the separation time diluting the shape of the bunch.

• “236-237 - s_pen indices are too long, sentence works without s=, only stating values”

Thank you very much for this hint. We removed  with long indices and refer to numbers only in the text. (line 272)

• “Figure 7 - Missing reference (??)”

We thank you for pointing out the incorrect link in the manuscript.
Reference link was mismatching and is now linking correctly to the figure. We have corrected it accordingly. (See Fig. 8)

• “355-357 - Misleading statement. AM parts performed better due to geometrical deviations between the parts (as stated). This is not an inherent property of the AM parts making them better. It is fine to focus on the AM parts, but not "because" they performed better.”

Thank you for the valuable comment. We have revised the manuscript (lines 415–418) to clarify that the selection of the additive manufacturing (AM) part was based on its ability to achieve the required geometric precision in this specific case, rather than implying an inherent superiority of AM parts in general.
In consultation with the workshop team, it was highlighted that conventional machining of the collector presents significant challenges due to its geometry, especially the lack of sufficiently large straight sections and the difficulty in accurately drilling opposing tapers. These constraints increase the risk of part deformation or vibration during processing, making conventional machining more prone to geometric deviations in this case. While not impossible, machining the collector conventionally demands more careful handling and set-up to mitigate these challenges. This context motivated our preference for the AM part in this study.

• “512-515 - Misleading statement. "Better" rf performance seems to be solely due to geometrical differences changing the impedance matching of the FFC. It can not be concluded that they are inherently better. Machined ones with same dimensions might perform the same or better. Nonetheless the paper shows, that AM parts can successfully be used for this use case. Authors should highlight the feasibility of AM structures for diagnostics.”

Thank you for the insightful comment. We have amended the manuscript by removing the phrase “surpassing conventionally machined ones” to avoid implying inherent superiority of AM parts based solely on this study’s results (line 584). As noted, the improved RF performance is attributed to geometric differences affecting impedance matching rather than an intrinsic advantage of AM manufacturing. To emphasize the practical significance of AM technology, we also expanded the paragraph in the conclusions (lines 583–591) discussing the broader feasibility and benefits of using additive manufacturing for accelerator diagnostics and related applications in a more general manner. This highlight AM as a promising fabrication approach capable of producing components meeting stringent geometric and functional requirements, thereby broadening design flexibility and reducing manufacturing complexity.

 

Overall comments:

• “Further visual aids, especially highlighting the field enhancements etc. of the TRCFFC would greatly improve the readability of the paper.”

We appreciate the suggestion to include further visual aids to improve the paper’s readability. We have added detailed plots illustrating the field configurations for all three geometries (Figs. 3 and 7). To clarify, the improved secondary electron suppression of the TRCFFC compared to the RCFFC does not result from a fundamentally different field configuration, but rather from the optimized geometrical suppression. The TRCFFC generates significantly fewer secondary electrons that require mitigation by the bias field compared to the RCFFC. Only the SE being capable of leaving the collector drill hole must be handled by the bias field. Additionally, the delay of the secondary electron signal in the TRCFFC is longer, resulting in less distortion of the actual ion signal. The bias field of the TRCFFC is slightly weaker than the one for the RCFFC, which is a direct consequence of the larger gap between collector and chassis.

• “Authors should be careful about claims that highlight the improved performance of the AM parts if the reason is, as was also stated in the paper most likely due to differences in geometry.”

Thank you for your comment regarding the claims on the improved performance of the additive manufacturing (AM) parts. We have revised the manuscript to provide a fair comparison regarding the use of the different techniques, especially for our task. In this particular application, the geometric precision towards the CAD model is critical in determining device quality. Therefore, any manufacturing method that minimizes deviations from the intended geometry is advantageous. However, the manufacturing technique itself is not inherently relevant, provided that the required precision is achieved. In our study, the AM process yielded components with tighter dimensional accuracy than the conventionally machined parts we used.
It was not our intention to claim that AM can inherently be manufactured more precisely. We apologize if it was interpreted that way. We have revised the argument so that it no longer implies that AM is inherently more precise.

• “Another possible benefit of AM could be discussed: Lower SEY due to higher surface roughness? “

Thank you for the suggestion regarding the potential benefit of AM related to SEY and surface roughness. This is indeed an interesting aspect that we had not previously explored. Following your recommendation, we have added a paragraph discussing studies on the influence of surface roughness on SEY (lines 370-381). These studies generally indicate that rougher surfaces, above a certain value, tend to produce fewer secondary electrons. However, the available data do not cover the surface roughness of our AM produced collectors. Consequently, we included a statement in the conclusions section (lines 590-591) acknowledging the need for further research on this topic. A comprehensive analysis of the impact of surface roughness on SEY in the context of AM parts for rougher surfaces would require a dedicated study beyond the scope of the current paper. This addition aims to highlight the potential significance of this effect while maintaining scientific caution.

• “Title: "RF CHARACTERIZATION AND BEAM MEASUREMENTS WITH 3D PRINTED FAST FARADAY CUPS" Comment: Using "Additive Manufacturing" instead of "3D printing" would be advised. “

Using “Additive Manufacturing” instead of “3D Printing” in the title is definitely the better choice for a scientific publication. “Additive Manufacturing” is the established, formal term recognized in academic and technical communities rather than the casual “3D printing”. We changed the title to:

RF CHARACTERIZATION AND BEAM MEASUREMENTS WITH ADDITIVELY MANUFACTURED FAST FARADAY CUPS

 

In addition, we also replaced other occurrences of “3D printed” from section headings and the text throughout the manuscript.

Reviewer 2 Report

Comments and Suggestions for Authors

Some comments and recommendations for the manuscript

instruments-3833241

27. Aug. 2025

 

This manuscript is an article on Fast Faraday Cups (FFCs), for which especially, TRCFFC has been newly designed and fabricated with 3D printed technique from the viewpoint of the precise bunch-length measurement with considering a higher SE suppression design.

The fundamental principle and detection method were in detail described. The mechanical fabrication results based on the 3D printed technique were in detail evaluated. The rf characterization and beam tests were carried out in comparison with an old-type RCFFC at the end of the UNILAC of GSI. The measurement results were in detail analyzed and it was found that the obtained results were successfully estimated and consistent with simulations.

The obtained results show that the developed FFCs can be clearly applied to a precise bunch-length diagnostics in various ion accelerators. I believe that this article gives an important step to fundamental designs of FFCs in many applications.

This article is described by a clear discussion and plain English. However, I will give following questions and some minor comments as a reader of the interesting article, although this article is very interesting. I recommend this article to publish in Instruments (MDPI) after revisions.

 

Major suggested points

• In the discussions of section 1.1, the result of Fig.2 shows that the pulse width and pulse area (or absolute charges) are strongly dependent on the bias voltage. Even for the stationary pulses with suitable bias voltages greater than 250 V, the obtained pulse waveform is far from that of I_b, which is an original bunch waveform. Thus, it seems that the ACFFC is not applicable to beam diagnostics from a viewpoint of both the bunch width and charge measurements, because there may be no suitable corrections to them. Is this understanding correct, because there are no discussions in terms of the validity on the bunch width and charge measurement? It should be clarified.
• In the 109^th to 111st lines of section 1.1, you mention that “the pre-field of the bunch is shielded by a grid, …..”. Based on this explanation, it may give no clear explanation, because there are two ways to understand it from the viewpoint of the cancellation of the pre-field with a grid. One is that the pre-field cancellation is not depending on the bias voltages, and the cancellation effect is a few ps before the actual charges reach the collecting surface. The second is that the pre-field cancellation is depending on the bias voltages, and however, the cancellation effect is only a few ps at maximum. It may be better to add some explanation to these understandings.
• In the discussions of section 1.2, the working principle of RCFFC is described in detail. Based on the RCFFC’s principle, it seems that the bunch waveforms can be reproduced by adjusting the bias voltage, and however, there are no discussions in terms of the absolute charge measurement by using the RCFFC. It seems that it may be difficult to measure the absolute charges, because the aperture hole size for incident ions is very limited. Thus, the RCFFC may be applicable to only the bunch width measurements. Is this understanding correct, because there are no discussions in terms of the validity on the charge measurement? If so, the RCFFC is a developed version to the ACFFC in terms of not a bunch-charge but a bunch-width measurement. If so, how can we understand an inherent diagnostics function to fundamental FCs, that is, absolute charge measurement. It should be clarified.
• In the 151st line of section 1.2, you mention that “… is shielded by a \phi 0.8 mm pinhole in “the heat shield”, ….”. After section 1.2, the word “the heat shield” is often used, and however, it is difficult to understand it without any descriptions. What is the heat shield and the purpose, etc.? Which area does it indicate? It should be clarified in Fig.1.
• In the 244th to 257^th line of section 2.1, you discussed on the detailed mechanical design for the connection between the collector and connector. It is important to design from the viewpoint of the impedance matching in terms of proper signal propagation from the collector to the connector. In simulation results as shown in Fig.7, does any impedance matching effect be considered? There are no discussions on it because the impedance matching affect to the pulse waveform. It should be clarified.
• In Fig.11 of section 2.2 (and also in Fig.13), it is not clear what “\Delta 2 CAD model (\mu m)” in the horizontal and “Area (mm^2)” in the vertical axis mean. The meaning of them is not clear. It may be better to give the corresponding clear definitions.
• In Tables 1 and 2 of section 2.3, the temporal resolution (ps) is specified, and however, its definition is not specified anywhere. It should clearly be specified.
• In Fig.15a and 15b of section 2.3, it is difficult to understand the significant differences in the frequency distributions for the RCFFC and TRCFFC in the simulation results. What are the main reasons to derive such results? It may be better to add the reasons and discuss them.

 

Minor suggested points

(1) In Fig.1 of section 1, it may be better to specify a unit in geometrical dimension of the mechanical drawings in the figure caption, and also to specify materials for the main components in the figures.

(2) In the 77^th line of section 1, it may be better to be revised to “with the square of the incident ion’s charge state Z, the number of incident ions N_{ion}, and the target electron density …”.

(3) In the figure caption of Fig.2 of section 1, it may be better to be revised to “CST PIC simulation ….. the ACFFC (Fig. 1a) …”.

(4) In the figure caption of Fig.3 of section 1, it may be better to be revised to “CST PIC simulations ….. the RCFFC (Fig. 1b) …”.

(5) In Fig.3b of section 1, some data points are hidden by a legend. All the data points should clearly be displayed without being covered by any legends. It may be better to contract the scale of legend.

(6) In Fig.2 and Fig.3 of section 1, it is difficult to discriminate NO SEE points from other points. it may be better to use, for example, open circles.

(7) In the 148^th line of section 1.2, you mention that “… a radially drilled hole with a diameter of 2 mm and a depth of 2.5 mm.”. However, it seems that the diameter of the drilled hole may be 1 mm from Fig.1b. Please check it. It may better to directly add these parameters in Fig.1b.

(8) In the 153rd line of section 1.2, you mention that “Around the drill hole, … to further reduce the critical distance to 2 mm.”. It is not clear which length is indicated for the critical distance. It should clearly be specified in Fig.1b.

(9) In the 207^th to eq.(6) lines of section 2.1, it may be better to be revised to “The projected gain is reduced … the transverse bunch shape. The projected gain f_{gain} is given by

f_{gain}=erf()/erf(),   (6)

where erf is the Gauss error function. Assuming a transversal beam …”.

(10) In Fig.5 of section 2.1, it may be better to specify a unit for geometrical dimension of the mechanical drawing, and also to specify materials for the main components with colored hatched lines in the figure caption.

(11) In the 212^nd line of section 2.1, it may be better to be revised to “… than the drift passage width to prevent …”.

(12) In the figure caption of Fig.7 of section 2.1, it may be better to be revised to “… and (b) …”.

(13) In the 253rd to 255^th lines of section 2.1, you mention that “… glass pins are added (see Fig.5) …”. However, it is difficult to see the glass pins in Fig.5, and thus, it may be better to clearly indicate them in Fig.5.

(14) In the 272nd line of section 2.2, it may be better to be revised to “… (see section 2.1)”.

(15) In the 281st line of section 2.2, it may be better to add a non-abbreviation for the word “Cu-ETP”.

(16) In the 304th line of section 2.2, it may be better to be revised to “… (see section 2.3)”.

(17) In eq.(9) of section 2.3, it seems that \sigma’ is represented for the conductivity because we cannot see whether or not “ ’ ” means a simple comma or \sigma’. It should be clarified.

(18) In the 382nd line of section 2.3, it may be better to clearly define the distance L in Fig.5 because there is no definition on it.

(19) In Fig.17b of section 2.4, S12 is indicated in the vertical axis, and however, in the figure caption, S21 is indicated. Please check it.

(20) In Fig.18 of section 2.4, some data points are hidden by a legend. All the data points should clearly be displayed without being covered by any legends. It may be appropriate to put the legends outside of graphs.

(21) In Fig.20b of section 2.4, it can clearly be seen that another waterfall around the time of 9 ns appeared, and however, there are no discussions on it. It may be better to give some explanation on it.

(22) In the 522^nd line of Summary, a misprint for “an insufficient SE …” is found. Please check it.

Comments for author File: Comments.pdf

Author Response

Response to reviewer’s comments and recommendations for the manuscript

instruments-3833241

Oct. 29 2025

Dear Reviewer,

we sincerely thank you for your valuable time and constructive comments on our manuscript. Your insightful suggestions have greatly helped us improve the clarity and quality of the work. We have carefully considered all points raised and incorporated them in the new revision of the paper. We believe the manuscript is now significantly strengthened as a result. Please find detailed responses to your remarks below. We hope these improvements meet your expectations and contribute to the manuscript’s overall quality. In addition to this response, we provide a marked-up version of the manuscript highlighting all changes, with line numbers to locate each change efficiently.

Major suggested points:

• “In the discussions of section 1.1, the result of Fig.2 shows that the pulse width and pulse area (or absolute charges) are strongly dependent on the bias voltage. Even for the stationary pulses with suitable bias voltages greater than 250 V, the obtained pulse waveform is far from that of I_b, which is an original bunch waveform. Thus, it seems that the ACFFC is not applicable to beam diagnostics from a viewpoint of both the bunch width and charge measurements, because there may be no suitable corrections to them. Is this understanding correct, because there are no discussions in terms of the validity on the bunch width and charge measurement? It should be clarified.”

Thank you for this valuable observation. The following clarifications address the question regarding the capability of measuring the bunch shape with the ACFFC, which may be caused by the different scaling of left and right axis. The signal  is not normalized to the measured output voltage signal. The scale is set such that the data fit within 95 % of the scale range. Consequently, the altered voltage signals exhibit much higher amplitudes than the reference “No SEE” scenario and thus also the  signal, which obscures the similarity in temporal shape between those two. The reference case for comparison is the “No SEE” scenario, which shows the output signal with the secondary-electron yield (SEY) deactivated, representing the unaltered achievable output. For high bias voltages , the effect of secondary electrons is well suppressed, and the signal with activated SEY approaches the “No SEE” case, which is the best achievable result. The difference compared to the plots of the RCFFC is that the maximum voltage signal is much higher due to less effective secondary-electron suppression.
We have adjusted Fig. 2 to be consistent with the RCFFC plots, so that it behaves as if normalized to the “No SEE” case without being actually normalized by adjusting the y-axis span. The “No SEE” case was made more prominent and easier to distinguish from  to highlight their similar behavior. The scaling for the RCFFC and TRCFFC plots have been changed to match peak of “NO SEE” and , also (see Fig. 4 and 8) to be consistent in the presentation of the simulation data. Normalizing the plots would conceal that the signal amplitude is halved due to the two-ports. Therefore, normalization was avoided. (see line 118 to 130)

 

• “In the 109th to 111st lines of section 1.1, you mention that “the pre-field of the bunch is shielded by a grid, …..”. Based on this explanation, it may give no clear explanation, because there are two ways to understand it from the viewpoint of the cancellation of the pre-field with a grid. One is that the pre-field cancellation is not depending on the bias voltages, and the cancellation effect is a few ps before the actual charges reach the collecting surface. The second is that the pre-field cancellation is depending on the bias voltages, and however, the cancellation effect is only a few ps at maximum.
  It may be better to add some explanation to these understandings.”

We are grateful for your detailed observation and provide clarification below. We re-plotted the cross-section of the ACFFC, highlighting the grid position with blue dots and adding a label and distance scale for clarity (see Fig. 1a). The grid is kept at ground potential, so its effect does not depend on the applied bias voltage. Biasing the collector positively or the grid negatively produces the same suppression behavior. Since the collectors of the radial-coupled FFCs are positively biased, we adopted the same scheme for the ACFFC. As a result, the grid shields the pre-field independently of the biasing conditions, preventing the bunch’s electric field from being detected a few picoseconds before the charges arrive at the collector. In addition, we rephrased the section (line 118-130) to be more descriptive what the grid is used for trying to emphasis the importance of a proper bias.

 

• “In the discussions of section 1.2, the working principle of RCFFC is described in detail. Based on the RCFFC’s principle, it seems that the bunch waveforms can be reproduced by adjusting the bias voltage, and however, there are no discussions in terms of the absolute charge measurement by using the RCFFC. It seems that it may be difficult to measure the absolute charges, because the aperture hole size for incident ions is very limited. Thus, the RCFFC may be applicable to only the bunch width measurements. Is this understanding correct, because there are no discussions in terms of the validity on the charge measurement? If so, the RCFFC is a developed version to the ACFFC in terms of not a bunch-charge but a bunch-width measurement. If so, how can we understand an inherent diagnostics function to fundamental FCs, that is, absolute charge measurement. It should be clarified.”

We appreciate your insightful question regarding the measurement capabilities of the RCFFC and TRCFFC. The purpose of the RCFFC and TRCFFC is to measure the bunch shape, not the absolute bunch charge. As you correctly noted, due to the limited beam fraction passing through the pinhole aperture, the absolute charge cannot be measured. For this reason, charge measurement is not discussed in our work. The main focus is to demonstrate that radially coupled FFCs can measure the bunch shape on a bunch-by-bunch resolution rather than only as an average, allowing them to observe changes within a bunch train in a straightforward manner. A short paragraph has been added to the introduction to clarify and motivate the focus on bunch shape measurements only (line 45-52).

 

• “In the 151st line of section 1.2, you mention that “… is shielded by a \phi 0.8 mm pinhole in “the heat shield”, ….”. After section 1.2, the word “the heat shield” is often used, and however, it is difficult to understand it without any descriptions. What is the heat shield and the purpose, etc.? Which area does it indicate? It should be clarified in Fig.1.”

Thank you very much for this valuable information. While writing the paper, we unfortunately paid too little attention to this detail and we are very sorry for this.

In response to your remark, we have improved the visualization and description of the heat shield for clarity. A label and distinct color were added to indicate the heat shield in Fig. 1 for the RCFFC. The heat shield is made of tantalum and serves to absorb the portion of the beam power that does not pass through the pinhole. In the RCFFC, the full beam power could possibly damage the thin collector. For high-power applications, the heat shield should be actively cooled to prevent excessive heating, and the pinhole transmission must be limited so that the power reaching the copper collector remains below its melting threshold. In our case at GSI, active cooling is not required. The section text was also revised to describe the function of the heat shield and how it contributes to stable and accurate measurements (lines 171-176).

 

• “In the 244th to 257th line of section 2.1, you discussed on the detailed mechanical design for the connection between the collector and connector. It is important to design from the viewpoint of the impedance matching in terms of proper signal propagation from the collector to the connector. In simulation results as shown in Fig.7, does any impedance matching effect be considered? There are no discussions on it because the impedance matching affect to the pulse waveform. It should be clarified.”

Thank you for bringing attention to this fundamental aspect of the mechanical and electrical design. The TRCFFC is designed to maintain a 50 Ω impedance throughout its geometry, from the collector through the full taper down to the SMA connectors. The ratio of inner to outer diameter remains constant during the taper to match the diameter of the SMA pins while preserving 50 Ω impedance. The main deviations from this ideal geometry occur at the collector hole (used for ion measurements) and at the positions of the glass pins, which introduce a different permittivity. The effect of the glass pins is discussed in detail and only significantly impacts frequencies above 6 GHz (see Fig. 14).

 

 

 

Another source of possible mismatch is the transition at the interface between the TRCFFC and the SMA connector due to the change from vacuum to PTFE insulation. This creates small steps in the inner and outer conductor diameters being different in the SMA and the FFC, leading to very minor signal reflections. To quantify this, the most significant reflection is below 1% in the HFTD simulation data. This reflection occurs at the inner radius step, which is larger by a factor of 8.5 compared to the outer radius step. Both sides of the transition preserve 50 Ω impedance, making these edge effects the only substantial source of potential reflections. By design, the reflection at the outer radius step - the relevant one for the particle signal - is estimated by simulations to be below 0.1%.

No signal reflection from these transitions is observed in the “No SEE” PIC simulation, nor in temporal resolution PIC simulations (with pulse-width sigma down to 1 ps and beta up to 0.999). Any reflection remains below the noise level. For this reason, we did not perform a full TDR analysis but instead relied on S-parameter evaluation to evaluate impedance matching, as it inherently covers both reflections and transition characteristics. We added a paragraph to the text discussing the mentioned details above (line 293-303).

• “In Fig.11 of section 2.2 (and also in Fig.13), it is not clear what “\Delta 2 CAD model (\mu m)” in the horizontal and “Area (mm^2)” in the vertical axis mean. The meaning of them is not clear. It may be better to give the corresponding clear definitions.”

Thank you very much for the important note. We had not realized that this part is misleading. We have revised both the illustration (Fig. 12 and 14) and its caption to provide clear definitions. The second plot next to Figures 11 and 13 is a histogram showing the measured deviations between the constructed part and the CAD model. Both the left (color map) and right (histogram) images display the same information in different formats. The left side indicates the spatial position of the deviations, while the right side (histogram) shows the distribution of these deviations to quantify the e.g. average discrepancy. “Δ to CAD” refers to the difference between the measured value and the nominal value from the CAD model. The x-axis marks this deviation (in μm), while the count or area on the y-axis reflects either the number of points (pixels) or - for the measurements done by Fraunhofer IWS (Institut für Werkstoff und Strahltechnik) - the corresponding surface area (in mm²) exhibiting a given deviation. The data from Fraunhofer IWS are normalized to the scanned surface area, while the other histogram is given by the pixel (point) count for each deviation bin.
To increase clarity, the label was changed to “Difference to the CAD (μm),” and the figure caption was expanded to be more descriptive what the histogram represents.

 

• “In Tables 1 and 2 of section 2.3, the temporal resolution (ps) is specified, and however, its definition is not specified anywhere. It should clearly be specified.”

Thank you for this remark. It is correct that the definition of temporal resolution should be specified more clearly. We have now addressed this in the manuscript. The equation is the same as for  (see Eq. 11). From the simulation, the original Gaussian is known () and the simulated output signal is also Gaussian-like (within the design region, though it can be altered if outside of specifications). We extract the corresponding  from the simulation output signal. Now knowing the input and output, we can deconvolve similarly to Eq. 11 to determine the intrinsic temporal resolution. The relation is . We added this to the text (line 453-454). The symbol  has also been added to the table headings.

 

• “In Fig.15a and 15b of section 2.3, it is difficult to understand the significant differences in the frequency distributions for the RCFFC and TRCFFC in the simulation results. What are the main reasons to derive such results? It may be better to add the reasons and discuss them.”

We thank the reviewer for this perceptive question regarding the differences observed in the frequency distributions. We hope that the following explanation clarifies the main reasons behind these results and their interpretation. These two plots show the output signals of the RCFFC and TRCFFC for two different bunch velocities, 5% and 15% of the speed of light, which correspond to the lower and upper bounds of the design goal. In these simulations, the bunch length is much shorter (10 ps) compared to the design criteria >100 ps. The signals are not identical; for example, in Fig. 15a, the RCFFC displays a short straight section similar to that of the TRCFFC in Fig. 15a, but this feature is not present in Fig. 15b. This straight section creates the impression that the RCFFC peak is tilted to the right. The time scales of the two plots also differ. These plots complement the FFT plots below by providing the time-domain basis for the frequency analysis.
The temporal resolution of this type of FFC is velocity-dependent, making it important to visualize this dependency to understand how beam velocity affects temporal resolution. To further clarify, we reordered the plots to better show their connection and updated the caption accordingly. Also, we added the used beta to the left-hand plots. Additionally, we expanded the discussion (line 473-486).

Minor suggested points:

• “In Fig.1 of section 1, it may be better to specify a unit in geometrical dimension of the mechanical drawings in the figure caption, and also to specify materials for the main components in the figures.”
  Thank you for this valuable hint. In Germany there is a rule that all dimensions     are given in mm unless otherwise stated. It was not clear to us that there is no           worldwide rule that prescribes which unit of measurement is used for        technical drawings. We are very sorry for this misunderstanding.

As a result, all materials have been added to the components and labeled directly in the graphic. Names of the main components are now included in the figure. The units in the mechanical drawings have been standardized by replacing decimal commas (German standard) with international decimal points. Decimal precision has been reduced to one digit, which is sufficient for accuracy while making the figure less cluttered. In Fig. 1a, the shielding grid was made more prominent and clearly labeled. In Fig. 1b, dimensions for the drill hole depth in the collector and the minimum distance between the collector and chassis in the reduced diameter section of the chassis were also added. (See Fig. 1)

• “In the 77th line of section 1, it may be better to be revised to “with the square of the incident ion’s charge state Z, the number of incident ions N_{ion}, and the target electron density …”. “

We appreciate the reviewer’s careful suggestion to improve the clarity of this sentence. We have revised the text accordingly and added “, the number of       incident ions ” to ensure that all relevant parameters are explicitly          mentioned for completeness and precision. (see line 85)

 

• “In the figure caption of Fig.2 of section 1, it may be better to be revised to “CST PIC simulation ….. the ACFFC (Fig. 1a) …”. “
  We thank the reviewer for this helpful comment. We have added “Fig.~” before the reference to ensure that the caption clearly and formally refers to          another figure within the paper. This change improves readability and           consistency in figure referencing. (See Fig. 2)
  
  
• “In the figure caption of Fig.3 of section 1, it may be better to be revised to “CST PIC simulations ….. the RCFFC (Fig. 1b) …”. “
  We are grateful for the reviewer’s attention to detail. Following this                         suggestion, we have added “Fig.~” to make the reference clear and      This enhances the figure caption’s accuracy and aligns             with best         practices for professional figure labeling and cross-referencing in scientific          manuscripts. (See Fig. 4)
  
  
• “In Fig.3b of section 1, some data points are hidden by a legend. All the data points should clearly be displayed without being covered by any legends. It may be better to contract the scale of legend. “

Thank you for your comment. We reduced the size of the legend for Fig.3a and b to present all data. (See Fig. 4)

 

• “In Fig.2 and Fig.3 of section 1, it is difficult to discriminate NO SEE points from other points. it may be better to use, for example, open circles. “

We are grateful for your suggestion to improve the figures. We changed “NO SEE” to dotted line with open circle markers in red and  easier to compare. “NO SEE” shows the unaltered output signal of the FFCs while  shows the actual emitted current of the source.

 

• “In the 148th line of section 1.2, you mention that “… a radially drilled hole with a diameter of 2 mm and a depth of 2.5 mm.”. However, it seems that the diameter of the drilled hole may be 1 mm from Fig.1b. Please check it. It may better to directly add these parameters in Fig.1b. “

Thank you for pointing out this discrepancy. It is an error in the manuscript. 1mm diameter is correct as stated in the image Fig1b. (line 168)

 

• “In the 153rd line of section 1.2, you mention that “Around the drill hole, … to further reduce the critical distance to 2 mm.”. It is not clear which length is indicated for the critical distance. It should clearly be specified in Fig.1b.”

Thank you for this hint. We added a measure in cross section plot in Fig 1b. also made it more precise to 2.1mm. (See line 176)

 

• “In the 207th to eq.(6) lines of section 2.1, it may be better to be revised to “The projected gain is reduced … the transverse bunch shape. The projected gain f_{gain} is given by f_{gain}=erf()/erf(), (6) where erf is the Gauss error function. Assuming a transversal beam …”.”

Thank you for your valuable suggestion. We have expanded the relevant section accordingly. Specifically, we defined erf correctly as Gauss error function and added a factor of 2 to account for the fact that diameters, rather than radii, were used in the previous calculation. The original estimation using the error function is valid for essentially one-dimensional cases, such as a beam that is wide in one plane and narrow in the other. To address more general scenarios, we have included a two-dimensional estimation for symmetric beams by calculating the integrated charge density of a Gaussian distribution limited by different hole sizes. This addition allows the approach to cover a wider range of beam geometries and improves the accuracy of our model. We believe these revisions enhance the clarity and completeness of the presentation. (line 233 to 247)

 

• “In Fig.5 of section 2.1, it may be better to specify a unit for geometrical dimension of the mechanical drawing, and also to specify materials for the main components with colored hatched lines in the figure caption. “

Thank you for your helpful suggestion. We have updated the figure by adding the materials corresponding to the colored parts in the caption to clarify the composition shown. Additionally, we included more labels, making it easier for readers to identify precisely which parts are being referred to in the text. To further enhance clarity, we also included a sentence in the caption specifying the dimensions used in the figure. These additions help ensure that the figure can be understood independently. (See Fig. 6)

 

• “In the 212nd line of section 2.1, it may be better to be revised to “… than the drift passage width to prevent …”. “

Thank you for your helpful suggestion. We added the word “width” into this sentence. (line 243)

 

• “In the figure caption of Fig.7 of section 2.1, it may be better to be revised to “… and (b) …”. “

Thank you for pointing us on this broken reference. The reference label was unintentionally still in pre-submission form such that is was compiled to (??) instead of (b). (See Fig. 8)

 

• “In the 253rd to 255th lines of section 2.1, you mention that “… glass pins are added (see Fig.5) …”. However, it is difficult to see the glass pins in Fig.5, and thus, it may be better to clearly indicate them in Fig.5. “

Thank you very much for the valuable suggestion to enhance the readability of the paper. We have labeled the glass pins and all other major components in the figure to clarify their positions within the cross section. The labels are color-coded to match the corresponding parts making it easier to identify each element. (See Fig. 6)

 

• “In the 272nd line of section 2.2, it may be better to be revised to “… (see section 2.1)”. “

Thank you, we added the word “section” to clarify the reference. (See line 297)

 

• “In the 281st line of section 2.2, it may be better to add a non-abbreviation for the word “Cu-ETP”. “

Thank you for your comment. We have added that CU-ETP stands for "electrolytic tough pitch copper," a common high-purity copper grade used in electrical applications. (See lines 327-328)

 

• “In the 304th line of section 2.2, it may be better to be revised to “… (see section 2.3)”.“

Thank you for your suggestion. We have added the word “section” to clarify the reference, making it more precise and easier for readers to locate the cited part in the manuscript. (See lines 318-319)

 

• “In eq.(9) of section 2.3, it seems that \sigma’ is represented for the conductivity because we cannot see whether or not “ ’ ” means a simple comma or \sigma’. It should be clarified.”

Thank you for your comment. We clarified the sentence by adding a space after the equation to indicate that the comma belongs to the sentence, not to the equation itself. (See Eq. 10)

 

• “In the 382nd line of section 2.3, it may be better to clearly define the distance L in Fig.5 because there is no definition on it.”

Thank you for your suggestion. We have added the distance L to the figure for clarity. Additionally, we colorized the labels to correspond with their respective parts, which improves readability and helps the reader quickly identify each component in the figure.
(See Fig. 6)

 

• “In Fig.17b of section 2.4, S12 is indicated in the vertical axis, and however, in the figure caption, S21 is indicated. Please check it. “

Thank you for your comment. We corrected it to show the transition of S21 correctly. (See Fig. 18b)

 

• “In Fig.18 of section 2.4, some data points are hidden by a legend. All the data points should clearly be displayed without being covered by any legends. It may be appropriate to put the legends outside of graphs. “

Thank you for your suggestion. We rescaled the plot so all data points are below the legend and brought the FFC results to the front for better visibility. These changes make the figure clearer and easier to interpret. (See Fig. 19)

 

• “In Fig.20b of section 2.4, it can clearly be seen that another waterfall around the time of 9 ns appeared, and however, there are no discussions on it. It may be better to give some explanation on it. “

Thank you very much for this valuable comment regarding the missing discussion of part of the measurement results. For us, the signal was outside the time range of interest and thus we did not discuss it. However, you are completely right that this result should also be discussed to get a complete view of the measurement results. For this reason, we have carried out an analysis.

The waterfall around the time of 9ns is a reflection outside the FFC. It is visible in Fig 20b only for the source of the reflection is closer to the TRCFFC output than for the RCFFC. Both FFCs are in series. This can be seen clearly in Fig 21a and b where the reflection is at 16ns for the RCFFC and 13.5ns for the TRCFFC. So, the waterfall plot shows also this reflection 2.5ns later but it is outside the time window of Fig. 20a.

To make this more prominent we shifted the 0 of the timescales of all those plots to be on peak of the measured signal. This way it is easier to compare the results also between the different views and settings. In addition we expanded the discussion of the measurement results to include the reflections in lines 549 to 554.

• “In the 522nd line of Summary, a misprint for “an insufficient SE …” is found. Please check it. “

Thank you for your comment. We corrected the spelling mistake. (line 596)

Author Response File: Author Response.docx

Round 2

Reviewer 1 Report

Comments and Suggestions for Authors

The authors have provided significant improvements to the manuscript and adressed all comments. Overall an excellent paper. 

Author Response

Dear reviewer,
we sincerely thank you for your positive feedback and for acknowledging the improvements made in the revised manuscript. We are grateful for your constructive input throughout the review process, which has greatly contributed to enhancing the quality of our work.

Reviewer 2 Report

Comments and Suggestions for Authors

Some comments and recommendations for the manuscript instruments-3833241

8. Nov. 2025

 

After reading the revised article, I think that it has been revised in a quite satisfactory way because the argument has become clearer than that of the previous one. This report is very interesting because it is in detail described by discussing more sophisticated versions of FFCs step by step with starting from fundamental ACFFC design. The final version, TRFFC, is also in detail discussed based on detailed simulations and measurements, and finally the experimental validation was performed in terms of the two types of FFCs. The obtained results may help another modified design of various FCs in future beam instrumentation and diagnostic technologies in wider accelerators.

I believe that this paper gives an important step to wider applications in accelerators and other disciplines. I strongly recommend this article to publish in Instruments.

Finally, I point out a few minor revisions to be revised before publication.

• In the 140^th - 161^th lines of p. 4-5 of section 1.1, you use SE and SEs in contexts. It seems that you make a distinction for the SE and SEs. If so, for example, in the 140^th line, it should be that the fast SEs (or SE) mainly increase (increases) the total signal intensity, ….. It may be better to take care of the distinction for the use of singular and plural form. Please check it.
• In the caption of Fig.11, it seems that the figure labels (b) and (c) may be character corrupted, while the label (a) is right. Please check it.
• In the 480^th line of section 2.3, it may be better to describe “the bandwidth is 6.064 GHz (TRCFFC 2.685 GHz), which corresponds ….”, because in this context, it is not clear to which bandwidth is for TRCFFC (or RCFFC). Please check it.

Comments for author File: Comments.pdf

Author Response

Response to reviewer’s comments and recommendations for the manuscript

instruments-3833241

Nov. 10 2025

Dear Reviewer,

we sincerely thank you for your continued time and effort in reviewing our manuscript. We appreciate your careful reading and the valuable feedback provided in this second round. The three minor comments were addressed in full, and corresponding changes have been incorporated into the revised version of the paper. We believe these refinements further improve the clarity and consistency of the manuscript. Please find our detailed point-by-point responses below:

Minor revisions:

• “In the 140th - 161th lines of p. 4-5 of section 1.1, you use SE and SEs in contexts. It seems that you make a distinction for the SE and SEs. If so, for example, in the 140th line, it should be that the fast SEs (or SE) mainly increase (increases) the total signal intensity, ….. It may be better to take care of the distinction for the use of singular and plural form. Please check it.”

Thank you for this valuable observation. In general, the plural form is appropriate, as all described effects refer to groups of secondary electrons. We revised the full manuscript accordingly.

• “In the caption of Fig.11, it seems that the figure labels (b) and (c) may be character corrupted, while the label (a) is right. Please check it.”

Thank you very much for pointing out the possible label issue. We carefully checked the manuscript and found no error in the original LaTeX file. After recompiling it using a different LaTeX installation, the labels were displayed correctly. We therefore believe this was an uncommon compilation error, as all other hyperlinks and references were compiled properly.

• “In the 480th line of section 2.3, it may be better to describe “the bandwidth is 6.064 GHz (TRCFFC 2.685 GHz), which corresponds ….”, because in this context, it is not clear to which bandwidth is for TRCFFC (or RCFFC). Please check it.”

Thank you for bringing this ambiguity to our attention. We have revised the sentence to state explicitly that the main value refers to the RCFFC, with the corresponding value for the TRCFFC given in parentheses. The updated version is as follows:

The bandwidth of the RCFFC at β = 5 % (see Fig. 16a) is 2.432 GHz (TRCFFC 0.953 GHz) and in the case of β = 15 %, the bandwidth is 6.064 GHz (TRCFFC 2.685 GHz), which corresponds to a factor of 2.5 to 2.25 between the bandwidths of both devices. (line 477 to 479)

Author Response File: Author Response.docx