Optimal Conditions for the Generation of Runaway Electrons in High-Pressure Gases

Round 1

Reviewer 1 Report

In the work a 'review' is presented covering mostly previous work of the two very respected authors. However the work contains hardly any new material nor does it put the work in perspective with the work of contempory authors. Even the theoretical an experimental sections of the present work contain too few cross links to make the work interesting.

For this reason I recommend to add a section where the theoretical predictions on the RAEB process are compared with actual data concerning the energy distribution of electrons and other experimental observable quantities for a few experiments. 

Author Response

Comments and Suggestions for Authors

In the work a 'review' is presented covering mostly previous work of the two very respected authors. However the work contains hardly any new material nor does it put the work in perspective with the work of contempory authors. Even the theoretical an experimental sections of the present work contain too few cross links to make the work interesting.

For this reason I recommend to add a section where the theoretical predictions on the RAEB process are compared with actual data concerning the energy distribution of electrons and other experimental observable quantities for a few experiments. 

Indeed, in this manuscript, the content (experimental, theoretical and graphic materials) is presented only by the author’s data. We believe that our research group has generated original data on all aspects of the review topic to fully outline all modern research methods and the level of understanding of the phenomenon of electron runaway. We have tried to reflect in this context the results of other research groups, as we understand it. We admit that we might have missed someone, and we would be grateful to the Reviewer if he would provide such examples. We have added new comments to the Conclusion section on the analysis of theoretical simulations and comparisons with experiments. Several new items in the list of citations have also been added.

Corrections and additions made to the text are marked in yellow.

Reviewer 2 Report

This is an interesting review on a not so well known aspect of plasma physics, namely the generation of runaway electrons at atmospheric pressure. Thus, I think that the paper deserves publication, after a minor review according to the following points:

1) Line 89: I do not understand how this paragraph describes different phenomena from the previous one. Aren't we anyway talking about runaway electrons in a high pressure gas? Please, clarify.

2) Line 127: What is RSIEP? It does not seem to have been defined before.

3) Line 170: I do not understand the words "thereby limiting plasma heating". The problem with runaway electrons in fusion devices is mainly their capability of damaging plasma-facing components, and even punching holes in the vacuum chamber. The connection with heating is not apparent to me.

4) Line 234: "Liquid" is incorrect, it should probably be "fluid".

5) Line 253: "Rezerford" should probably be "Rutherford".

6) Line 296: Please clarify the different meaning of the two terms on the RHS of equation 5. Isn't the second one equal to the current density, when ion motion is neglected?

7)  Figure 3: These figure (especially the top frame) show the presence of two peaks in the distribution function, corresponding to electron moving in opposite directions. The authors claim that the one at negative velocities corresponds to scattered electrons. However, it is not so obvious why the scattered electrons should retain such a coherence in velocity space, that is why they appear as a narrow peak. Can the authors elaborate on this?

8) It seems to me that all the figures correspond to results obtained by the authors' research groups, since nowhere is given a statement about them being reproduced from another publication. If this is correct, it is quite unusual for a review. Can the authors comment on this?

The English language seems of acceptable quality

Author Response

Comments and Suggestions for Authors

This is an interesting review on a not so well known aspect of plasma physics, namely the generation of runaway electrons at atmospheric pressure. Thus, I think that the paper deserves publication, after a minor review according to the following points:

Thank you for your positive assessment of our work.

1) Line 89: I do not understand how this paragraph describes different phenomena from the previous one. Aren't we anyway talking about runaway electrons in a high pressure gas? Please, clarify.

Additional clarification has been inserted into this paragraph. Corrections and additions made to the text are marked in yellow.

X-ray radiation in gas discharges is generated under the influence of runaway electrons, but due to its higher penetrating ability, X-ray quanta are much easier to register. Therefore, the registration of X-ray radiation in such discharges carries, although indirect, important quantitative information about the number and energy spectrum of runaway electrons. The number of publications on X-ray radiation is greater than on electron detection. Therefore, we considered it necessary to provide references to these works in the review. We added another article in the additional discussion: S. Yatom, D. Levko, J. Z. Gleizer, V. Vekselman, and Ya. E. Krasik. X-ray diagnostics of runaway electrons generated during nanosecond discharge in gas at elevated pressures // APPLIED PHYSICS LETTERS 100, 024101 (2012)

2) Line 127: What is RSIEP? It does not seem to have been defined before.

In the manuscript, full information about the organization RSRIEP (Russian Scientific and Research Institute of Experimental Physics) is given on page 2, line 67 (version of the article before correction).

3) Line 170: I do not understand the words "thereby limiting plasma heating". The problem with runaway electrons in fusion devices is mainly their capability of damaging plasma-facing components, and even punching holes in the vacuum chamber. The connection with heating is not apparent to me.

Indeed, fast electrons damage the walls of the chamber. But even before this moment, they take energy from the electric field, thereby reducing the power of energy input into the ion component of the thermonuclear plasma. When runaway electrons impact the walls of the chamber, they evaporate; accordingly, they contaminate the plasma and particles of heavy elements limit the heating of the plasma. Thus, the harmful effect of runaway electrons is complex. Additional clarification has been inserted into this paragraph.

4) Line 234: "Liquid" is incorrect, it should probably be "fluid".

We replaced: "Liquid" with "fluid".

5) Line 253: "Rezerford" should probably be "Rutherford".

We replaced: "Rezerford" на "Rutherford".

6) Line 296: Please clarify the different meaning of the two terms on the RHS of equation 5. Isn't the second one equal to the current density, when ion motion is neglected?

Indeed, on the right side of equation (5), the second term describes the current of free electrons. We completely neglect the ion current in this model (taking into account the ion current would add a third term to the right side). The first term describes the scalar current flowing in the electrical circuit of the discharge; we find it from the Kirchhoff equation for the circuit, as explained below in strings 308-311 (version of the article before correction). We do not write this equation here, since it is determined by the specific type of electrical power circuit and may look different.

 
7)  Figure 3: These figure (especially the top frame) show the presence of two peaks in the distribution function, corresponding to electron moving in opposite directions. The authors claim that the one at negative velocities corresponds to scattered electrons. However, it is not so obvious why the scattered electrons should retain such a coherence in velocity space, that is why they appear as a narrow peak. Can the authors elaborate on this?

This is the forward-backward approach effect reflected in formula (6) of our scattering model. Backscattered electrons have the same energy as forward electrons. Therefore, the peak width of “forward and reverse” electrons is the same.

8) It seems to me that all the figures correspond to results obtained by the authors' research groups, since nowhere is given a statement about them being reproduced from another publication. If this is correct, it is quite unusual for a review. Can the authors comment on this?

Yes, indeed, this review contains figures only from the articles of the review authors. We considered this justified since we have a large array of our own data on the entire range of issues in this work: from theoretical models with the results of numerical calculations to accurate measurements of both electrical parameters of discharges and modern diagnostics of picosecond electron beams.

In our experimental work, which was carried out after the pioneering work [14], the parameters of the runaway electron beams were significantly improved and in direct measurements of the beam current using specially created collectors, the main dependencies on the magnitude and duration of the runaway electron beam current, as well as on the distribution of electrons, were obtained by energies and their spatial distribution. In this case, modern oscilloscopes with subnanosecond and picosecond time resolution were used, see the works [Tarasenko, V.F., Rybka, D.V., Burachenko, A.G., Lomaev, M.I. and Balzovsky, E.V., 2012. Note: Measurement of extreme-short current pulse duration of runaway electron beam in atmospheric pressure air. Review of Scientific Instruments, 83(8).], [Tarasenko, V.F. and Rybka, D.V., 2016. Methods for recording the time profile of single ultrashort pulses of electron beams and discharge currents in real-time mode. High voltage, 1(1), pp.43-51.] and [119]. Due to Editorial restrictions on the number of self-citations, we have provided links to only some of our works.

Reviewer 3 Report

This paper is a review of the efforts, primarily those of the authors and their colleagues, to obtain pulsed bunches of high-energy runaway electrons in dense gases and to understand the underlying physics. Being the major contributors to the original research on this topic, the authors are uniquely qualified to write such a review. The review is written reasonably well, and the physics is explained clearly. The results are very interesting and useful to researchers interested in this field. I recommend publication of this paper.

Please correct the spelling of the name of the great scientist from Rezerford to Rutherford.

Author Response

Comments and Suggestions for Authors

This paper is a review of the efforts, primarily those of the authors and their colleagues, to obtain pulsed bunches of high-energy runaway electrons in dense gases and to understand the underlying physics. Being the major contributors to the original research on this topic, the authors are uniquely qualified to write such a review. The review is written reasonably well, and the physics is explained clearly. The results are very interesting and useful to researchers interested in this field. I recommend publication of this paper.

Thank you for your positive assessment of our work.

Comments on the Quality of English Language

Please correct the spelling of the name of the great scientist from Rezerford to Rutherford.

We have replaced "Rutherford" with "Rutherford".

Reviewer 4 Report

The review entitled “Optimal Conditions for Generation of Runaway Electrons in High Pressure Gases” by Andrey Kozyrev and Victor Tarasenko is well presented and provides an overview of experimental and analytical  studies focussed  on runaway electrons in gases. It will be beneficial if the authors will address the following aspects:

“who focused on running electrons initiated by high-energy electrons” - could you please clarify this statement

Figure 3 - Please  specify in the figure legend  what is “mc”

“the Maxwell bias current” – please clarify this term in the context of the developed model

“ ionized the gas tin the entire gap,”   should be “ionized the gas in the entire gap”

Figure 9/Figure 10  – please comment on uncertainties  in these experimental data, there are no error bars in these experimental graphs.

In the Conclusion section the authors state: “The RAEB amplitudes of ~100 A have already been reached in air at atmospheric pressure [31] and can be further increased”. However, in their modelling part the authors state that “Under conditions of so fast breakdown, the Maxwell bias current may constitute a significant (and sometimes even main) part of the total current flowing in the discharge circuit. So, at time 200 ps (the top frame in Fig. 3), even the runaway electrons have no 350 time to reach the anode, but the current in the circuit reaches 250 A”

How does  this model support the statement in the conclusion section ? The authors do not discuss the main outcome from  the modelling section in their Conclusion, it would be beneficial to provide conclusions based on all parts discussed in this paper.   

Author Response

Comments and Suggestions for Authors

The review entitled “Optimal Conditions for Generation of Runaway Electrons in High Pressure Gases” by Andrey Kozyrev and Victor Tarasenko is well presented and provides an overview of experimental and analytical studies focussed on runaway electrons in gases. It will be beneficial if the authors will address the following aspects:

 “who focused on running electrons initiated by high-energy electrons” - could you please clarify this statement

This is string 42. We have corrected this phrase to the correct one: “…who focused on running electrons initiated by high-energy cosmic ray particles”

Figure 3 - Please specify in the figure legend  what is “mc”

Here m is the mass of the electron, c is the speed of light. The momentum on the ordinate scale of Figure 3 is given in relative units. We have added this explanation in the figure caption.

“the Maxwell bias current” – please clarify this term in the context of the developed model

This is string 352. We have corrected this term to the correct one: “…Maxwell displacement current”

 “ ionized the gas tin the entire gap,”   should be “ionized the gas in the entire gap”

This is a typo, we accept the correction.

Figure 9/Figure 10  – please comment on uncertainties  in these experimental data, there are no error bars in these experimental graphs.

These curves are taken from articles, see [28], [Tarasenko, V.F., Baksht, E.H., Burachenko, A.G., Kostyrya, I.D., Lomaev, M.I. and Rybka, D.V., 2008. Supershort avalanche electron beam generation in gases. Laser and Particle Beams, 26(4), pp.605-617.] and, [117], which were published. The spread of the measured parameters of the beam current after training the cathode in the single-pulse mode did not exceed 10-20%. 

In the Conclusion section the authors state: “The RAEB amplitudes of ~100 A have already been reached in air at atmospheric pressure [31] and can be further increased”. However, in their modelling part the authors state that “Under conditions of so fast breakdown, the Maxwell bias current may constitute a significant (and sometimes even main) part of the total current flowing in the discharge circuit. So, at time 200 ps (the top frame in Fig. 3), even the runaway electrons have no 350 time to reach the anode, but the current in the circuit reaches 250 A”

Figure 2 shows the current in the discharge circuit. It appears as soon as electrons begin to move in the gap. By the 200th picosecond, the electrons have not yet reached the anode, but the current in the circuit is already large (~300 A). Near the anode, where there are still no electrons, the current density is determined by the Maxwell displacement current. The maximum current of the runaway electron beam is observed at approximately the 250th picosecond (middle frame in Fig. 3 and 250ps curve in Fig. 4); the amplitude of the fast electron current pulse behind the anode foil was approximately 1 A.

The authors of the review specifically experimentally investigated the issue of the influence of the bias (displacement) current on the magnitude of the discharge current in the gap and the current from the collector behind the foil, see the works [Andreev, Y.A., Kostyrya, I.D., Koshelev, V.I. and Tarasenko, V.F., 2006. Electromagnetic radiation of a nanosecond discharge in an open gas-filled diode. Technical physics, 51, pp.637-643.], [Kostyrya, I.D. and Tarasenko, V.F., 2006. Effect of insulating films on the current of an electron beam from gas-filled diodes exposed to voltage pulses with a nanosecond rise time. Technical physics, 51, pp.1512-1516], [28], and it was shown that when metal foils are used to extract a beam, the bias current (we call it dynamic bias (displacement) current [44]) does not affect the collector readings. Moreover, based on the research carried out in [28], errors in measurements of the current of a beam of runaway electrons were reported in [Maltsev, A.N., 2006. Dense gas discharge with runaway electrons as a new plasma source for surface modification and treatment. IEEE transactions on plasma science, 34(4), pp.1166-1174.], which erroneously stated that a runaway electron beam current with an amplitude of 2 kA was detected in air at atmospheric pressure. At the same time, the bias current was measured; in this work, a device with a high inductance gas diode was used, in which dielectric films were installed. When receiving a runaway electron beam current with an amplitude of 100 A [Kostyrya, I.D., Rybka, D.V. and Tarasenko, V.F., 2012. The amplitude and current pulse duration of a supershort avalanche electron beam in air at atmospheric pressure. Instruments and Experimental Techniques, 55, pp.72-77.], [Tarasenko, V.F., 2011. Parameters of a supershort avalanche electron beam generated in atmospheric-pressure air. Plasma Physics Reports, 37, pp.409-421.] its registration was carried out behind an Al foil with a thickness of 10 microns, which was reinforced with a grid with a transparency of 90% on the side of the collector. The discharge current under these conditions exceeded 2 kA. This trend is consistent with the calculations presented in Fig. 3.

How does this model support the statement in the conclusion section ? The authors do not discuss the main outcome from the modelling section in their Conclusion, it would be beneficial to provide conclusions based on all parts discussed in this paper.  

Discussion of theoretical results added to Conclusion. Corrections and additions made to the text are marked in yellow.

Round 2

Reviewer 1 Report

The authors have added a section discussing the absense or a clear link between experiments and theory for this subject, just as I asked for in my previous report.

Additionally a few more minor corrections have been made to improve the work.

The paper is thus acceptable for publication.