Femtoscopy for the NAno-Plasmonic Laser Inertial Fusion Experiments (NAPLIFE) Project

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

The draft is informative and interesting. The authors apply the Hanbury-Brown and Twiss analysis and got important information on scattered Deuterium and Hellium. The paper would be easier for readers if the authors consider the following: (1) To show the abbreviation of NAPLIFE (NAno-Plasmonic, Laser Inertial Fusion Experiments ?), (2) page 1, 36th line, "wavelenght", "wave length" ?

 

Comments on the Quality of English Language

The quality of English is fine, although I am not a native speaker and can not judge.

Author Response

The draft is informative and interesting. The authors apply the Hanbury-Brown and Twiss analysis and got important information on scattered Deuterium and Helium. The paper would be easier for readers if the authors consider the following: (1) To show the abbreviation of NAPLIFE (NAno-Plasmonic, Laser Inertial Fusion Experiments?), (2) page 1, 36th line, "wavelength", "wave length”? Response: We highly appreciate the referee’s positive opinion. (1) The abbreviation is now shown in the title of the manuscript. (2) Wavelength is correct in that sentence, because we refer to the resonant length of the wave. Comments on the Quality of English Language The quality of English is fine, although I am not a native speaker and can not judge. Response: We highly appreciate the referee’s positive opinion.

Reviewer 2 Report

Comments and Suggestions for Authors

See the attached Word-file.

Comments for author File: Comments.pdf

Author Response

The paper “Femtoscopy for the NAPLIFE Nano-Fusion Project” by L.P.  Csernai et al.  considers a possibility to use momentum correlations of identical light nuclei to determine the spacetime extent of their production in a target irradiated by a laser beam. The paper represents a minireview and its understanding requires a careful reading of a number of references.

 

The subject is quite novel and interesting.  It would be certainly worth of publishing in Universe if clarifying two principal questions related with the femtoscopic momentum correlations applied to deuterons with momenta 10-100 MeV/c emitted by a source of radius r ~10 μm and lifetime
 τ ~10-100  fs  [7].

Response: We highly appreciate the referee’s summary and positive opinion.

 

First, such a large spacetime extent of the source requires to measure the momentum difference q  ~  l/r  ~  20  MeV/c  with  a  precision  of  several  MeV/c  at  least,  i.e.  with unrealistic relative precision better than 10^-10.

Response:  The anticipated width of the momentum distribution is  ~ 1- 2 MeV (see Fig.6 of ref.  [28].) The argument of the Reviewer is that for a source of about r= 10 micrometers,

the with of the correlation function can be estimated as hbar/ r = 10**(-8) MeV, so indeed a relative precision of about 10**(-8) is needed, if we want to measure the extent of the hot zone where fusion is expected to happen.

 

However, with a realistic relative momentum resolution of q = a few keV, source sizes of about hbar/q ~ 10**(-10) m can be achieved. This is similar to the atomic scales.

Micrometer length scales can likely be studied by observing the reaction with ordinary microscopes and femtoscopic methods can be utilized to study the dynamics on the scales of relevant atomic physics reactions like the formation of deuterium atoms from electrons and deuterons.

 

The picture is somewhat like core-halo type of systems. These are relavant not only in astrophysical observations, as noted by G. Baym in his nucl-th/9804026 , Fig. 7 c, but also in high energy particle and nuclear physics, as noted in ref.  Z.Phys.C 71 (1996) 491-497 e-Print: hep-ph/9411307 [hep-ph] Thus a large halo surrounding a hot center effectively suppresses the strength of the correlation function, depending on the ratio of intensities coming from the core and from the halo part of the source. This way the proposed method can likely be utilized to see small hot spots in the extended domain of the hot fusion volume.

We thank the Referee for this comment and note that a more detailed feasibility study for a detailed experimental proposal will be necessary if such an experimental setup is proposed. The topic of the current manuscript is more like  a conceptual consideration of the application of femtoscopic methods in a new project, laser induced fusion and the scope of the manuscript is limited to the results presented by L. P. Csernai at the ISMD 2023 conference in Gyöngyös, Hungary. We thank Reviewer 2 for stressing this point. We cannot predict the future limits of experimental progress and in the last 30 years of femtoscopic studies the improvement of resolution and detector techniques exceeded all earlier expectations. So we propose to include this remark of the Reviewer to the manuscript, noting the current precision level of momentum resolution for momentum measurements of deuterons.

Second, at q ~ l/r, the Coulomb repulsion exponentially suppresses deuteron pairs already at q < l/r : 7 MeV/e (a  = 28 fm is the Bohr radius of a deuteron pair) thus making these pairs unobservable. Unfortunately, even the time separation τ = 100 fs is insufficient to switch off the Coulomb repulsion; its absence would require τ >> Mr² :  3 ms (M is the deuteron mass) [see,  e.g., arXiv nucl-th/0501065].

Response: Our initial irradiation volume is about 10 μm and the observed final crater volume exceeds 100 μm, thus, our source size during ignition and burning is much larger than the Bohr radius. The reviewer is correct that Coulomb repulsion may suppress the Bose-Einstein correlation function of deuterons if the burning process lasts only for τ = 100 fs and the lifetime of the source should be increased to the order of few ms to be able to detect their correlation function. This would require a factor of 10**(10) increase in the lifetime of burning. We note this limitation too in the revised manuscript and suggest that for future, concrete measurement proposals these limitations must be evaluated and considered. Note that similar feasibility studies and test measurements were performed already at the time of the start of stellar interferometry by Hanbury Brown and Twiss.  See e.g. R. Hanbury Brown: Boffin: a personal story of the early days of radar, radio astronomy and quantum optics (CRC Press, 1991).

 

As for the spacetime HBT correlations, besides. Astronomy, they can be used to measure the energy momentum spread of the emitted quanta also in laboratory. E.g., the linewidth of ~ 4  μeV,  corresponding  to  ~  2  ns  width  of the  time  delay  distribution,  was  measured  from  a  mercury  discharge  lamp  [Phys.  Rev.  153 (1967) l13].  This technique is however inapplicable in case of the deuteron energy spread of keV or MeV, corresponding to unrealistic time delay distribution width of 10^-18 s or 10^-21 s.  in fact, the HBT technique is not required since the deuteron energies in keV or Mev range can be measured directly.

Response: Our intention is not to measure the linewidth of the deuteron or alpha emission. Reviewer 2 states, this can be measured directly, and the spread of these distributions is very large. Thus, the extremely short time delay is not relevant for us. The laser irradiation time is as long as the light penetration time across the target, and the particle emission time is even longer. 

      For us the HBT method is used to determine the size (or shape) of the emitting source, when this is not measurable by other methods. This is also the case sometimes in astronomy, but most of the time in high energy heavy ion reactions. In ICF reactions the ignition and burning size is not directly measured. The present problem is that after initial ignition of a central spot of an extremely compressed target the expansion is faster than the spread of the burning and so the whole fuel target is not burned.

 

Thus, the determination of ignition and burning size is essential, as the energy of a single deuteron is not sufficient to determine the size of the source. We add to the conclusions of this manuscript that so far, we have considered conceptual questions and the need to apply novel methods (also added to manuscript at line 110):  So far, the application of femtoscopic methods to measure the sizes of deuteron sources is on the level of a conceptual proposal, that should be followed up with a more detailed, technical design report that includes a concrete technical setup proposal as well.

 

In short, we thank Reviewer 2 for considering the important limitations of our proposed method. We hope to explore these limitations in greater detail in a follow-up manuscript and detailed technical design report.

Reviewer 3 Report

Comments and Suggestions for Authors

In this short paper the authors summarize the contribution of L.P. Csernai at the 52.nd International Symposium on Multiparticle Dynamics held at 24.8. 20223 in Hungary.

The authors describe briefly the NAPLIFE laser-fusion project, which exploit laser wake field acceleration to obtain the emission  of particles (p, d, He) with multi-MeV energies from gold nanorod antennas. 

Due to the shortness of this manuscript its content as well as the physics behind can only be understood and appreciated by those experts who actually participated in the symposium.

Which bosons are meant in the 2nd paragraph of the introduction?

Several sentences  in the manuscript appear to be incomplete? ... is the same, fluctuating following..., ...laser fusion studies highly structured detector systems...

The method of analysis is not explained. Also no results for the correlation function are presented.

Why should eq.(2), the difference of two thermal Boltzmann distributions with the same temperature T, be adequate for for out-of equilibrium situations.

In summary, due to numerous deficiencies, this manuscript cannot be recommended for publication in MDPI journal UNIVERSE.

 

 

Comments on the Quality of English Language

Some corrections of the english language is necessary.

Author Response

Comments and Suggestions for Authors

In this short paper the authors summarize the contribution of L.P. Csernai at the 52. nd International Symposium on Multiparticle Dynamics held at 24.8. 2023 in Hungary.

The authors describe briefly the NAPLIFE laser-fusion project, which exploits laser wake field acceleration to obtain the emission of particles (p, d, He) with multi-MeV energies from gold nanorod antennas.

Due to the shortness of this manuscript its content as well as the physics behind can only be understood and appreciated by those experts who actually participated in the symposium.

Response: We highly appreciate the referee’s correct and positive summary. The more extended version, with detailed mathematical presentation is given in the last reference of the manuscript, no. [26]

 

Which bosons are meant in the 2nd paragraph of the introduction?

Response:  The method is applicable for bosons emitted during the ignition and burning of fusion fuel, i.e. Deuterium and Helium as mentioned in the abstract.

Several sentences in the manuscript appear to be incomplete? ... is the same, fluctuating following..., ...laser fusion studies highly structured detector systems...

Response:  The sentence: “The acceleration is the same, fluctuating following the direction of E.” is changed to “The direction of acceleration is the same.”  The sentence: “In the present, limited budget NAPLIFE laser fusion studies highly structured detector systems are not available, but one or two detectors are available.” is changed to “In the present, limited budget of the NAPLIFE laser fusion project, highly structured detector systems are not available, but one or two detectors are accessible.”

 

The method of analysis is not explained. Also, no results for the correlation function are presented.

Response: The kinetic modeling is done by the open-source EPOCH code mentioned in the figure caption of Figure 1. As mentioned in the abstract we only propose how to adopt this method. The presented EPOCH simulation applies to a single nanorod only, which in itself is not an experimentally realizable situation. Thus, calculating a correlation function for this case would not provide any useful information.

 

Why should eq. (2), the difference of two thermal Boltzmann distributions with the same temperature T, be adequate for out-of equilibrium situations.

Response: We realize that the presentation of cancelling Jüttner distribution was not sufficient in this brief article, thus in front of eq. (2), we inserted the extended explanation in the revised manuscript:

The particles emitted from the surface of the target are not represented well with the Jüttner (relativistic Boltzmann) distribution because this includes particles emitted backwards into the target also. This is also the situation at the hadronization and “freeze out” in ultra-relativistic heavy ion reactions. Bugaev remedied this problem [24-pre] by introducing the “Cut-Jüttner” distribution with a step function, Θ(x) or Θ(p_μdσ^μ), to remove the particles moving back into the source. The discontinuity of this distribution is removed by adding the negative mirror image of the Jüttner distribution on the opposite side of the surface. The distribution created this way, the “Cancelling-Jüttner” distribution [24], is now smoothly goes to zero at the surface.  The negative part is cancelled by the step function.

[24-pre] K.A. Bugaev, Shock-like freeze-out in relativistic hydrodynamics, Nucl. Phys. A606 (1996) 559

 

Round 2

Reviewer 2 Report

Comments and Suggestions for Authors

See the attached file.

Comments for author File: Comments.pdf

Author Response

Enclosed please find our response

Author Response File: Author Response.docx

Reviewer 3 Report

Comments and Suggestions for Authors

The authors have made corrections and they added further clarifying statements to their manuscript, such that this short paper could now be recommeded for publication in Universe. 

Comments on the Quality of English Language

Minor editing of English language required.

Author Response

Enclosed please find our response

Author Response File: Author Response.docx