Attosecond Pulses from Ionization Injection Wakefield Accelerators

Round 1

Reviewer 1 Report

See the attached response.

Comments for author File: Comments.pdf

I would like to suggest further checks to find some possible mistake or typo in the text

Author Response

We thank the Referee for the very detailed comments and the suggested
amendments to the text.
In Fig. 2 (now Fig. 3 in the revised manuscript), the predictions of the model (orange line) were plotted along with outcomes from a set of q-3D simulations with the ReMPI setup. The physical and numerical parameters of ReMPI simulations were reported in Sect. 2 and we included this information in the text. The error bars were estimated by considering the discrepancy between the rms value obtained with three distinct methods, i.e direct evaluation of the variance from the particles positions, equivalent rms from Absolute Mean Deviation (robust analysis) and gaussian fit of the longitudinal position distribution.   The central point was obtained by averaging the three outcomes and the error bars are the dispersion values. We also included this information in the text and we thank the Referee for pointing this out. 

Reviewer 2 Report

The manuscript titled "Attosecond pulses from Ionization Injection Wake Field Accelerators" presents a study on the generation of attosecond electron beams using the resonant multi-pulse ionization injection (ReMPI) scheme. Ionization injection is a commonly employed method in Laser plasma accelerators (LPA) experiments. In this work, the authors investigate the relationship between the electron bunch length and the delay of the ionization pulse from the accelerating gradient node. The paper introduces a practical concept, but there are some issues that require clarification and revision. I recommend addressing the following points to enhance the paper:

 

1.  The statement in the first paragraph of page 2, which reads, "the electric field generated by electron beams driving large amplitude plasma waves are usually much lower than the ones in equally driving laser pulses," appears to be incomplete or unclear. To ensure accuracy and clarity, it is recommended to revise this statement to better convey the underlying physics.

2.  Provide more details about the ionization region of Ar^(8+->9+)of the ionization pulse used in the simulation. It would be valuable to include a graphical representation displaying the laser fields of the ionization pulse, making the ionization region explicit.

3.  Please provide a detailed explanation of the physical insights behind achieving the minimum beam duration, as depicted in Figure 2. Specifically, clarify the reasons for obtaining this minimum duration concerning the minimum delay of the ionization pulse position relative to the node of the accelerating field.

4.      The paper lacks information regarding the energy and energy spread of the bunch, which is crucial for assessing bunch quality. To enhance the understanding of the bunch characteristics, it is advisable to include the information about beam energy.

Additionally, there is a need to address whether the laser propagates to the dephasing position in the setup.

5.  On page 4, in the first paragraph, specify the direction for the normalized emittance.

6.   In the Results section, specify the plasma length utilized in the simulation. It would be helpful if you could specify the distance at which electrons with a charge of Q=5.5 pC is obtained.

7.   In the first paragraph of Section 1, there is a repetition of the word “amplitude”.

Comments for author File: Comments.pdf

Author Response

We wish to thank the Referee for his/her suggestions which have strongly improved the manuscript.

1 The statement in the first paragraph of page 2, which reads, "the electric field generated by electron beams driving large amplitude plasma waves are usually much lower than the ones in equally driving laser pulses," appears to be incomplete or unclear. To ensure accuracy and clarity, it is recommended to revise this statement to better convey the underlying physics.

Re: We fully agree that the sentence is somewhat obscure. We wanted to point out that in both the laser or beam-driven options the wakefield amplitude should exceed the trapping threshold, but the electric field of the driver for the beam-driven case is much lower than that for the laser-driven. We clarified this in the text.

2  Provide more details about the ionization region of Ar(8+->9+)of the ionization pulse used in the simulation. It would be valuable to include a graphical representation displaying the laser fields of the ionization pulse, making the ionization region explicit

Re: We added a figure with information about the extracted electrons' positions and the residual rms transverse momentum. The active ionization process is $Ar 9\rightarrow 10$ here, as the driver already extracted all the available $Ar 8+$ electrons.  

3 Please provide a detailed explanation of the physical insights behind achieving the minimum beam duration, as depicted in Figure 2. Specifically, clarify the reasons for obtaining this minimum duration concerning the minimum delay of the ionization pulse position relative to the node of the accelerating field.

Re: We added a more detailed explanation of the reason why the shortest trapped beam length is reached when the ionization pulse is placed on the node of the accelerating gradient.

4    The paper lacks information regarding the energy and energy spread of the bunch, which is crucial for assessing bunch quality. To enhance the understanding of the bunch characteristics, it is advisable to include the information about beam energy.

Additionally, there is a need to address whether the laser propagates to the dephasing position in the setup.

Re: The aim of the paper is to provide insights and a usable model to predict (and eventually minimize)  the beam length with advanced ionization injection schemes. The model can be employed in two-color, ReMPI and PWFA (trojan horse) schemes and each of them has its own limitation and optimised working points. In the paper, we included an example of beam extraction and trapping in the ReMPI scheme and this is because we have the highest experience there, but we stress again that the model can be fruitfully used in any of the mentioned schemes. We decided not to include in the manuscript the further steps of the acceleration process because that would be the focus of another, more specific, paper devoted to the generation of high-brightness GeV-scale attosecond long electron beams. We hope the Referee will understand our point here. 

About the laser (ionization) pulse longitudinal propagation, we added a dedicated paragraph in Sect. 2.

5  On page 4, in the first paragraph, specify the direction for the normalized emittance.

Re: We added the requested sentence.

6  In the Results section, specify the plasma length utilized in the simulation. It would be helpful if you could specify the distance at which electrons with a charge of Q=5.5 pC is obtained.

Re: We added the requested information.

Round 2

Reviewer 1 Report

The answers to the questions appearing in the previous referee report were satisfactory. The modifications made for the revised version were also satisfactory.

Reviewer 2 Report

The authors have duly addressed my comments. The paper now seems suitable for publication.