Laboratory Magnetoplasmas as Stellar-like Environment for ⁷Be β-Decay Investigations Within the PANDORA Project

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

The manuscript presented by Naselli and Collaborators describes the expected outcome of the measurements of the decay probability of ionized 7Be in a plasma environment to be realized with PANDORA, a B minimum ion trap under construction.
The proposed measurement and methodology is of great interest and, if successful, will provide first of its kind experimental information.
The publication of the manuscript is therefore of great relevance in view of the expected consequences in many fields, especially in Nuclear Astrophysics.
The plasma trap is extensively presented in Section 2 and some other information is provided in Section 3. The Authors may take advantage of the many papers already present in the literature, mostly authored by the Authors of the present manuscript, to tighten this part and make the paper more effective towards the case of 7Be.
The paper is well written, however some redundancies are present throughout the text. In my opinion the symbols could be used more consistently across the different sections.

However, before I can recommend the paper for publication, I have some major observations, and more of minor relevance and suggestions, listed in detail below, that the Authors may consider to take into account.

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Major comments:

1 - Line 312: "Particle-in-Cell (PIC) codes which can generate 3D maps of electron density ne and energy density E_e consistent with the electromagnetic (EM) field of the injected microwaves [47-48]" I suggest the Authors to add a comment about the dependence of the RF power on the element forming the plasma. This information is in my view needed, since it connects with the estimates of equations 2-4, that assume the total power is not influenced by the plasma composition and thus the concentration c of the ion of interest with respect to the buffer element.

2 - Line 351: "For n_e < 10^{28} m^{-3}, p_i is density-independent", is it really 10^{28} m^{-3} or there is a typo? If 10^{28} m^{-3} is actually intended, it is unclear why the grid calculation had to be performed at different densities being p_i independent of the values considered in the present work.

3 - Lines 379-388: A gross indication of the fraction of 7Be ions in the different charge states would help the reader to get a more quantitative idea of the simulated processes. An explicit comment on the 1+ charge state (negligible? not calculated?) would also be a useful addition. The neutral charge state is discussed later, but a reference might be given here. 
Also a quantitative statement on which fraction of the ions lies outside of the plasmoid region would strengthen the Authors statements. The "by eye" evaluation from Figure 4 subplots is rather difficult, also in consideration of the different color scale maxima used. (see also comment on lines 433-434)

4 - Line 412: "A total of 4.1x10^9 events were simulated" it is unclear which is the chosen distribution of the events within the chamber volume. This information has to be provided by the Authors.

5 - Lines 433-434: "the detection regards especially the γ-emission occurring the in plasma core, where we expect to have larger densities and temperatures", this statement apparently conflicts with the observation about the distribution of the 7Be^4+ ions at lines 387-388. The addition of the above requested information (comment to lines 379-388) would be very helpful also in this view.

6 - Lines 527-529: "This design choice stems from the strategic placement of apertures for the γ-ray detectors, which were carefully positioned to avoid the so-called magnetic branches. These branches represent regions within the magnetic trap where the magnetic field lines are more intense. In such areas, background radiation due to intense bremsstrahlung X-rays – arising from axial and radial electron losses impacting on the plasma chamber walls - is expected to be significantly higher", it is unclear whether the X-ray background is included in the Geant4 simulations and thus is difficult to appreciate the effectiveness of the careful positioning of the detectors. The Authors may anticipate the results presented later in Table 4, possibly in terms of absolute efficiency (although convoluted with the expected 7Be concentration distributions) rather than in terms of counting rates.

7 - Lines 538-548: The role of the environmental radioactivity (gamma-rays from the 40K and 238U, 232Th decay chains) is not considered at all in the discussion of the expected background. Some quantitative estimates regarding this component must be provided.

8 - Lines 566-567: "the total volumetric detection efficiency
(e_Tot = 0.0013) previously estimated in [43]", I could not find this number in Ref. [43] of the manuscript, although compatible with some of the data presented in figure 9 of [43]. If I understand correctly this efficiency is what one should get by integrating, over the chamber volume, the data presented in Figure 6. However, taking the numbers given in subsection 3.2 (lines 412-424), I  get to a significantly lower value (~an order of magnitude). The Authors may comment on this.

9 - Lines 649-656: "[...] "non-plasmizated" contribution[s] [...] are being neglected in the computation of the overall background", although the argument brought by the Authors that the detection is optimised towards the plasmoid appears to be valid, I understand from line 649 that in the plasmoid volume is expected only 1% of the total activity. In this view it is worth noting that in the optimistic assumption of a 5cm lead shielding, the expected reduction of the flux of 0.5MeV energy gamma rays, is in the order of 1E-5, that in turn for a 555MBq source means 5.5kBq outside the shielding, that is a figure comparable with the ~2kBq plasmoid activity reported in Table 4. Therefore I expect that the details of the detection of decays from "non-plasmizated" 7Be might be relevant and may potentially affect the conclusions driven by the Authors on the possibility of quantifying the difference in decay rate, and thus the "in-plasma" decay probability.

10 - Section 4: In this section the error budget is extensively described. However, the uncertainty on the overall gamma-ray detection efficiency is not discussed, and therefore is not accounted for. While the Geant4 simulations are certainly of help, besides the statistical uncertainty due to the number of simulated events, many other aspects have to be accounted for usually through validation measurements. The Authors may add a comment on the expected overall uncertainty and the planned validation of the simulation, if any.

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Minor observations and suggestions

11 - Reference [7]:
In Phys. Rev. 71 (147) page 274 is reported the abstract of the paper presented by E. Segrè at the 276th meeting of the American Physical Society held on January third and fourth, 1947. If the Authors intend to refer to this content they should correct the page number in the reference.
Possibly, the Authors intend to refer to the published paper E. Segrè and C.E. Wiegard "Experiments on the Effect of Atomic Electrons on the Decay Constant of Be7" Phys. Rev. 75, 39(1949) reporting the results of the experimental efforts in detecting the 7Be decay constant variation.

12 - Lines 60-62: reference to relevant literature is needed.

13 - Line 80: LTE is defined only at line 131, would be better to do it here as well.

14 - Line 81: Possibly one among "benchmark" and "study" is not needed.

15 - Lines 89-90: "The decay rates (expected to change dramatically as a function of the ion ionization state in the PANDORA plasma environment)" at this stage of the text it is not clear on what such an expectation is based, and to which rates, among the several mentioned in the preceding text, this applies.

16 - Line 102: "and as a test radiation for Archaeometry", possibly some words are missing here?

17 - Line 104: "scientific relevance" is a very broad concept, the Authors may narrow it for the cases under discussion.

18 - Line 112: "we focus on a novel physical case for PANDORA", the phrasing might be misleading. Since PANDORA is an experimental  facility yet to come, one would assume that all cases are novel until they will be actually investigated.

19 - Line 114: Reference [24] does not appear to be the most appropriate here.

20 - Line 115: "7Li abundance by", possibly " 7Li abundance predicted by" is more appropriate.

21 - Line 120: Most likely Reference 29 does not deal with 7Be EC, 7Be will be discovered only 15 years later.  

22 - Lines 234-235: "operating at INFN and ATOMKI- laboratories in Hungary", to be rephrased since, as written, one gets the wrong impression that INFN laboratory is in Hungary.

23 - Line 236: "the background", I assume it is intended "in the HPGe detectors", that is not readily clear since just above "[a]ll the devices" are referred to.

24 - Line 237: "e.m.", the later definition as EM (line 311) might be done here.

25 - Line 240-241: "the cones of view created in its structure", it's unclear what the Authors mean here.

26 - Lines 245-246: "Two- Close-Frequency-Heating (TCFH)" a reference to relevant literature would be useful here.

27 - Line 303: possibly "behind" is not the most appropriate term here.

28 - Line 309: "the INFN-LNS and LNL groups", its unclear to what the Authors refer to 

29 - Lines 313-331: Although is kind of obvious, it might still be useful to specify that the plots in panels a, b, c, (and correspondingly d-f) correspond to planes at z=0, y=0, x=0, respectively.

30 - Line 325: possibly "transport" is not the most appropriate term here.

31 - Lines 335-349: For a given cell the Authors assume a Maxwell distribution for the electrons that in turn allows to estimate the local temperature as E_e=3/2T_e, that should be equivalent to the LTE assumption for the cell (line 335). The Authors may add a few words to make clear why in the use of the FLYCHK code the non-LTE case has to be considered. 

32 - Lines 351-352: since the plot it is not presented, it is sufficient to simply state that the results are fitted as a function of k_BT_e.

33 - Line 376: It would be appropriate to mention also in Figure 4 caption the value of the concentration c.

34 - Lines 399-405 and Figure 5: the choice of labels as [1] etc., is rather unfortunate since it collides with the style of the bibliographic references of the Journal.

35 - Lines 406-409: This statement appears to be somewhat redundant.

36 - Lines 640-641: "The expected activity ranges from tens of GBq (for a concentration of 5×10-4) to hundreds of MBq (for a concentration of 10-6)", this statement does not represent the values reported in Table 4.

37 - Lines 683-685: "After irradiation, shirt-lived isotopes dec ay over several days, enhancing the lithium-to-beryllium ratio for subsequent applications", correct the "shirt" typo. In addition, 7Be decays into 7Li, therefore after irradiation the actual lithium-to-beryllium ratio can only increase (although on the short term in negligible amount with respect to the initial stoichiometric value).

38 - Line 736: Equation 19 contains the definition of F and the definition of lambda^*, this second expression is not used further. The lambda_i^* are actually not defined in the text, I assume they are the same as the lambda_i appearing in Equation 5. If this is the case then, according to Equation 5, the expression 
     lambda^* = \sum_i=1^4 F_i lambda_i^* 
should hold.
It should be noted however, that the choice of the Authors to in dicate the sum of the number of Be ions in the different charge states as N_0^{Be^{i+}} is somewhat confusing.

39 - Line 926: "The European Physical Journal" has to be changed in "The European Physical Journal Special Topics"

40 - Lines 937-938: Author should read "Vincent B.". In addition the ": Plasma Physics" does not appear in the citation as per https://theses.hal.science/tel-02466976v4

Author Response

Please see the attachment.

Author Response File: Author Response.pdf

Reviewer 2 Report

Comments and Suggestions for Authors

This article proposes a new experimental facility PANDORA aimed at studying the changes in nuclear decay in laboratory electron cyclotron resonance (ECR) plasma, which is significantly innovative. The PANDORA facility combines advanced plasma generation technology, multi-diagnostic systems, and gamma ray detection systems, opening up new avenues for research in nuclear astrophysics and nuclear physics.

‌This article provides a detailed description of the conceptual design, experimental methods, numerical simulation, and Monte Carlo simulation process of the PANDORA facility. Through particle-in-cell (PIC) simulation and collision-radiation model, the authors evaluated the ionization and atomic excitation states of 7Be in plasma, as well as its impact on electron capture decay rates. In addition, GEANT4 simulation was used to determine the efficiency of the gamma ray detection system.

The research findings not only contribute to solving the lithium problem in cosmology, but may also have significant implications for solar neutrino physics. In addition, the PANDORA facility can also be applied in multiple fields such as plasma physics, magnetic confinement fusion technology, and archaeological metrology, demonstrating its broad application prospects.

The experimental design considers various factors, including the spatial distribution of plasma, the emission and detection efficiency of gamma rays, and the influence of background radiation. Through virtual experiment running, the author evaluated the sensitivity of the experiment and determined the experimental running time required to achieve statistical significance.

Although this article has the above advantages, currently it is mainly based on numerical simulation and Monte Carlo simulation, lacking actual experimental data and verification. Of course, simulation results can provide a theoretical basis for experiments, but real experimental results may be influenced by various unknown factors. This issue needs further discussion.

Although the analysis of uncertainty in the article is comprehensive, it still falls short in certain aspects. For example, the uncertainties in online monitoring accuracy of plasma parameters such as electron density and temperature, as well as the stability of gamma ray detection systems, have not been discussed in detail. This also needs further discussion.

At the same time, achieving the experimental conditions described by PANDORA facilities faces technical challenges. For example, the generation and injection of highly charged ions, long-term stable maintenance of plasma, and effective suppression of background radiation all require highly specialized technologies and equipment. These technological challenges should also be further discussed.

Based on the above opinions, I think that this article has high academic value and innovation, and can provide new ideas and methods for the research of nuclear astrophysics and nuclear physics. Despite some drawbacks and challenges, they can all be addressed through further discussion. Therefore, I believe that this article can be published after appropriate modifications and improvements.

Author Response

Please see the attachment.

Author Response File: Author Response.pdf

Round 2

Reviewer 1 Report

Comments and Suggestions for Authors

Dear Editor,

I have read the response of the Authors and the revised version of the manuscript. 

All the concerns that I have raised in my previous report have been clarified and implemented in the text, where appropriate.
In my opinion the manuscript in its present form reports with sufficient detail and clarity all the relevant information about the expected outcome of the measurements of the decay probability of ionized 7Be in the B minimum ion trap PANDORA, currently under construction.

Therefore I recommend the manuscript to be published in Universe.