Physical Processes That Occur in Self-Organized Tokamak Plasma

Round 1

Reviewer 1 Report

The text is so badly written that it is not possible to follow the thoughts of the authors. The reviewer has the vague feeling that the content of the paper might be OK for publishing, but in its present form the paper in unsuitable even for judging the content.

I suggest that the authors rethink and completely rewrite their paper, befor resubmission to any journal.

To be honest, the English of the paper is of such a low quality that it hinders the reader from properly understand the physics argumentation. Not only the English needs to be brushed up, but alingside the complete chain of argumentation.

Author Response

Manuscript ID: plasma-2349873
Type of manuscript: Review
Title: Physical Processes to be Occurred in the Self-Organized Tokamak Plasma
Authors: Ksenia A. Razumova, Sergey Lysenko *

Referee 1

The text is so badly written that it is not possible to follow the thoughts of the authors. The reviewer has the vague feeling that the content of the paper might be OK for publishing, but in its present form the paper in unsuitable even for judging the content.

I suggest that the authors rethink and completely rewrite their paper, before resubmission to any journal.

Comments on the Quality of English Language

To be honest, the English of the paper is of such a low quality that it hinders the reader from properly understand the physics argumentation. Not only the English needs to be brushed up, but alingside the complete chain of argumentation.

We are very sorry for the bad translation and we try to correct this serious shortcoming. However, we cannot change the logic of our arguments, since the essence of this article is the alternative considering the processes occurring in the plasma. We encourage readers to note to a fundamentally different approach to the problem, associated with the process of self-organization, rarely taken into account before.

Author Response File: Author Response.docx

Reviewer 2 Report

Dear Authors,

I have read your manuscript with much interest: the ideas you present are fascinating and in my opinion may have a great impact in the field. However, I would like to see them better exposed and motivated. Therefore, before suggesting acceptance, I have some questions and remarks.

• Beside of some specific sentence, which I suggest you to revise (see below, my comments on the quality of English language), there is some check I would suggest about Eqs.(2)-(3) and about the definition of the quantities appearing therein.  I note that Q of Eq. (2) is not defined, in the text, and I wonder if is there any misprint in the sign of the first or second equality in Eq. (3): as the pressure is always positively defined, it seems to me that there is an inconsistency in the signs of the terms at the right hand side of the first and of the second equality.

• Then, I have some questions and clarification to ask you, related to the physics that you discuss.

line 44: “the turbulent temperature”. Could you please clarify better, both to me and in the manuscript, this expression? Why do you call it that way? Moreover, since you stress the out-of-equilibrium condition of the plasma, do you mean this temperature to be meant in the usual thermodynamical sense of the zeroth principle of thermodynamics (i.e., it corresponds to a Maxwellian distribution of the particle velocities) or is there here some other implication related to the condition of turbulence, which you highlight?

Lines 94-97: Maybe I misunderstood something, but it seems to me there is a misprint in the sign of the exponent of the temperature and then in the subsequent proportionality relations between temperature and density: since Spitzer's resistivity scales like T^{-3/2}, I would say that Ohmic heating scales with the same negative power of temperature, rather than with a positive power of it. If do you agree, corrections in the subsequent sentences should follow accordingly.

Lines 104-105: “Such requirements… coefficient $\chi_0$”. I agree with this sentence, per se, but I do not find as evident the logical “necessity” of the generation of a magnetic island. I mean: in the light of the discussion which follows, in which you relate the level of turbulence fluctuations to the possibility of generating a magnetic islands or not, which does not seem to me to be generally evident, I would appreciate some more clarification about the way this occurs. Do you mean that a configuration with a magnetic island is the “only” configuration expected to fulfill the required conditions? If so, can you please expand the paragraph by better explaining why/how is it so?

Line 113:  “then $F$ increases”. Why? Can you please clarify this point, by expanding the sentence also in the manuscript?

Line 232: “Thus we may conclude.. same phenomenon”. This is  both a quite strong statement and a fascinating perspective. I am not refusing it (besides, you stress the experimental evidence of the correlation between transport barriers and magnetic islands) but due to its implications, I would like to see this concept better argued in your manuscript.         It seems to me that this remark goes together with my remark above, related to lines 104-105. For example, an implication, of what you argue seems to me that studies of the generation of transport barriers in tokamak turbulence should not be modelled in the electrostatic limit, which neglects the way electrostatic fluctuations affect the amplification of magnetic perturbations up to the point that magnetic islands are generated. Although several published studies exist (and I note, you have not quoted many), which have discussed the connection between, e.g., ITG turbulence and magnetic reconnection, this subject seems to me to be still under investigation to give it as “granted”. What I mean is that, while, on the one hand, the strength and beauty of your argument seems to me to be in the “global”, complex-system type approach, with which you interpret the occurrence of the two phenomena (generation of transport barriers and of magnetic island) in a unified way based on self-organization arguments, on the other hand I do not fully appreciate the actual “causal” mechanism with which the formation of transport barriers is connected to that of magnetic islands or not.  Can say something more on this point and, in case, may expand this subject in the conclusions?

• The English requires some serious improvement (almost everywhere there are misprints, and several sentences require, in my opinion, to be rephrased) and some more care in the editing would have been appreciated (e.g., some sentences at lines 142-148 are a verbatim cut and paste of sentences at lines 129-136). I note in particular some expressions which should be clarified, since they convey an unclear message to the reader. I note them here, since I think the apparent disagreement I have with these sentence is probably due to some misunderstanding of mine, because of wording issues:

lines 53-54:  "it is always self-organized".  Do you really mean that any plasma state display self-organization properties, or rather that it can always undergo some self-organization process? Personally I think the second statement to be correct (and also in agreement with what you say later in the manuscript, it seems to me) so.. please, either rephrase this sentence or motivate better your point of view, if it is different from mine and you literally mean what you wrote.

Lines 114-115: “Thus” and “the island cannot be”. I guess this is another problem of wording, but honestly in this sentence I have not been able to follow the logic of your argument. What I have not understood is if you mean that a neoclassical tearing mode can not form, in first instance, or if it can not grow above a certain threshold because of the turbulence, or if do you mean something else. Can you please better explain your point by rephrasing this sentence? 

lines 129 and 141: "inconsistently". It is not clear, here, what do you mean with this word. Did you mean, maybe, "independently", or something else? Please rephrase it.

Author Response

Manuscript ID: plasma-2349873
Type of manuscript: Review
Title: Physical Processes to be Occurred in the Self-Organized Tokamak Plasma
Authors: Ksenia A. Razumova, Sergey Lysenko *
Referee 2

Dear Authors,

I have read your manuscript with much interest: the ideas you present are fascinating and in my opinion may have a great impact in the field. However, I would like to see them better exposed and motivated. Therefore, before suggesting acceptance, I have some questions and remarks.

    Beside of some specific sentence, which I suggest you to revise (see below, my comments on the quality of English language), there is some check I would suggest about Eqs.(2)-(3) and about the definition of the quantities appearing therein.  I note that Q of Eq. (2) is not defined, in the text,

Thank you. We define Q and other variables in (2) (3).

and I wonder if is there any misprint in the sign of the first or second equality in Eq. (3): as the pressure is always positively defined, it seems to me that there is an inconsistency in the signs of the terms at the right hand side of the first and of the second equality.

Now we use the absolute values!

Then, I have some questions and clarification to ask you, related to the physics that you discuss.

line 44: “the turbulent temperature”. Could you please clarify better, both to me and in the manuscript, this expression? Why do you call it that way? Moreover, since you stress the out-of-equilibrium condition of the plasma, do you mean this temperature to be meant in the usual thermodynamical sense of the zeroth principle of thermodynamics (i.e., it corresponds to a Maxwellian distribution of the particle velocities) or is there here some other implication related to the condition of turbulence, which you highlight?

We use the equations offered to us by the classics of self-organization. As far as we understood them, non-equilibrium thermodynamics deals with fluctuations and transferring something from the standard thermodynamics is not easy.

Here q takes the place of temperature in the equation. We will change this phrase in the text:

…and θ is the equivalent of thermodynamical temperature. J.B. Taylor called it as ‘magnetic temperature’.

Additional reference:

Taylor J.B. Relaxation of toroidal plasma and generation of reverse magnetic fields. Phys. Rev. Lett. 1974, 33, 1139-1141.

Lines 94-97: Maybe I misunderstood something, but it seems to me there is a misprint in the sign of the exponent of the temperature and then in the subsequent proportionality relations between temperature and density: since Spitzer's resistivity scales like T^{-3/2}, I would say that Ohmic heating scales with the same negative power of temperature, rather than with a positive power of it. If do you agree, corrections in the subsequent sentences should follow accordingly.

The electric field E=jR, the power P= j² R; where j is the current density (E= const), R is resistivity. If T_e is peaked, j is peaked more steeply µTe^3/2 and R µT^-3/2 ; so P µT^3/2

Lines 104-105: “Such requirements… coefficient $\chi_0$”. I agree with this sentence, per se, but I do not find as evident the logical “necessity” of the generation of a magnetic island. I mean: in the light of the discussion which follows, in which you relate the level of turbulence fluctuations to the possibility of generating a magnetic islands or not, which does not seem to me to be generally evident, I would appreciate some more clarification about the way this occurs. Do you mean that a configuration with a magnetic island is the “only” configuration expected to fulfill the required conditions? If so, can you please expand the paragraph by better explaining why/how is it so?

We cannot analyse all processes in a turbulent background. In is a “black box” for us (really KSTAR can receive some information). We know that the result of its activity must be F_min (free energy) for the residual MHD configuration. Do you know something else except island? Let us try to use this arguments.

Line 113:  “then $F$ increases”. Why? Can you please clarify this point, by expanding the sentence also in the manuscript?

Flattening of the current profile in the island leads to the change of the pressure profile and violates the condition F = F_min. This activates the turbulent background, which maintains the current and pressure profiles in the island.

Line 232: “Thus we may conclude..same phenomenon”. This is both a quite strong statement and a fascinating perspective. I am not refusing it (besides, you stress the experimental evidence of the correlation between transport barriers and magnetic islands) but due to its implications, I would like to see this concept better argued in your manuscript. It seems to me that this remark goes together with my remark above, related to lines 104-105. For example, an implication, of what you argue seems to me that studies of the generation of transport barriers in tokamak turbulence should not be modelled in the electrostatic limit, which neglects the way electrostatic fluctuations affect the amplification of magnetic perturbations up to the point that magnetic islands are generated. Although several published studies exist (and I note, you have not quoted many), which have discussed the connection between, e.g., ITG turbulence and magnetic reconnection, this subject seems to me to be still under investigation to give it as “granted”. What I mean is that, while, on the one hand, the strength and beauty of your argument seems to me to be in the “global”, complex-system type approach, with which you interpret the occurrence of the two phenomena (generation of transport barriers and of magnetic island) in a unified way based on self-organization arguments, on the other hand I do not fully appreciate the actual “causal” mechanism with which the formation of transport barriers is connected to that of magnetic islands or not. Can say something more on this point and, in case, may expand this subject in the conclusions?

When you speak about ITG or other instability, you try to analyze processes inside a ‘black box’ (background). In our approach, we try to analyze the result of its work only. All electrostatic models do not take into account the self-organization, but plasma physics begins from this position!

Our colleagues prefer to explain each phenomenon by the separate way, but the self-organization take place in the whole system, and all processes have to be interconnected.

In experiments there are some cases of small barriers without islands. In this case, islands have high m numbers, which difficult (but possible) to measure. We never see the island without ITB, but its width may be narrow, about< 0.5 cm, when the island is large. The barrier q=1 is called as a ‘mixing zone’.

Comments on the Quality of English Language

The English requires some serious improvement (almost everywhere there are misprints, and several sentences require, in my opinion, to be rephrased) and some more care in the editing would have been appreciated (e.g., some sentences at lines 142-148 are a verbatim cut and paste of sentences at lines 129-136). I note in particular some expressions which should be clarified, since they convey an unclear message to the reader. I note them here, since I think the apparent disagreement I have with these sentence is probably due to some misunderstanding of mine, because of wording issues:

The text is changed

lines 53-54:  "it is always self-organized".  Do you really mean that any plasma state display self-organization properties

YES!

Or rather that it can always undergo some self-organization process? Personally I think the second statement to be correct (and also in agreement with what you say later in the manuscript, it seems to me) so, please, either rephrase this sentence or motivate better your point of view, if it is different from mine and you literally mean what you wrote.

Amendment: …if the time is greater than the time of the turbulent relaxation. This process is inevitable as the equilibrium establishing

Lines 114-115: “Thus” and “the island cannot be”. I guess this is another problem of wording, but honestly in this sentence I have not been able to follow the logic of your argument. What I have not understood is if you mean that a neoclassical tearing mode can not form, in first instance, or if it can not grow above a certain threshold because of the turbulence, or if do you mean something else. Can you please better explain your point by rephrasing this sentence?

I suspect that tearing mode theory is valid only during time less than the time of the turbulent relaxation.

Also see the new text

lines 129 and 141: "inconsistently". It is not clear, here, what do you mean with this word. Did you mean, maybe, "independently", or something else? Please rephrase it.

 Heating power P(r) has to be input just in accordance with self-consistent pressure profile p_c(r), then the condition F=Fmin remains to be valid. In the other case, new structures will be created by the turbulent background. From this point of view, additional heating always inconsistent with p_c(r).

Thanks to Referee for interesting comments

Author Response File: Author Response.docx

Reviewer 3 Report

"Minor revision" mainly means to fix a few bugs - like repetitions on page 4

Please also see comments in the attached file.

The paper presents a review that describes the processes associated with the plasma self-organization in tokamaks. The paper is well-written, although English could be slightly improved, presented scientific results are clear so I will strongly recommend publishing this manuscript. I have several comments and suggestions, but they are mainly to fix bugs and improve readability. My comments on the content of the article should be taken as an advice, not as a request.

Page 2, line 44. “entropy and … is the t” => Missing ? .

Page 2, line 44. “turbulent temperature” => please explain

Page 2, line 65. “since it smoothest the gradient that feeds it” => this is correct for gradient driven instabilities, not for all

Page 2 formula (2) => will be useful to explain here for clarity: Г is … p_c is …

Page 3 line 87. “The modern spherical tokamaks ST40 [11] and Globus-M2 [12] allow” => better to say “may allow”

Fig.3 line 115. “pressure profile inside the island cannot be” => please re-write. “cannot exist”? But we know that NTMs do exist.

Page 4 from line 141. This is repetition of what is said at page 3 from line 129.  Also lines from 138 and 149 are identical. Please fix.

Page 4  line 155 “ internal transport barrier occurs.” => “may occur”. We know that ITB can be created and sustained without islands.

Page 5 line 173. “neoclassical flux, which is negligible for normal tokamak” => correct but not for all cases. Low collisionality, spherical tokamaks etc have significant neoclassical fluxes. So better to specify what “normal tokamak” exactly means.

Page 5 line 182. “Typically, in tokamaks it is about 2 mm.” => in some tokamaks. Depending, for example, on TF. Also, there are fast ions.

Page 5 line 185. “island m = 20–25” => maybe useful to say that this is for MTMs

Page 5 line 200. Formula (3) Also comments are needed.

Page 6 line 206. “In many experiments, where the formation of barriers and islands have been studied, 206 an unexpected result has been found: barriers and islands always formed together.” => better to say “in some experiments” and give references. In many experiments, like DIIID, JET or MAST this is not always the case

Page 6 Fig 5a. I would not say that the width of ITB in this shot was 2 cm. It is much wider. Feature marked as ITB is an island, but more likely 3/2 or even 2/1. Flattening of profile may be either due to a sawtooth (which on MAST is typically at q~08, not 1) or due to other reasons. Were there sawteeth in this pulse?

Page 7 line 233. “formation of the barrier and the island are two aspects of the same phenomenon” => better to say “in some cases” or “may be to aspects”

Page 7 line 239. “at various” => in various

Page 7 line 241. Was KSTAR regime claimed to be hybrid? Please check specific point in Fig.8. FIRE mode and H-mode were more often. “highest discharges” => “highest performance discharges”

Page 8 line 263. “after the disruption,” => after the minor disruption, or “internal disruption”

Page 9 line 276. “Such modes are called “advanced tokamak” or “hybrid” regimes,” => “advanced tokamak” and  “hybrid” regimes are different regimes, at least on JET.

Comments for author File: Comments.pdf

Please fix a few bugs - like repetitions on page 4 and some suggestions to improve English.

Author Response

Manuscript ID: plasma-2349873
Type of manuscript: Review
Title: Physical Processes to be Occurred in the Self-Organized Tokamak Plasma
Authors: Ksenia A. Razumova, Sergey Lysenko *
Referee 3

"Minor revision" mainly means to fix a few bugs - like repetitions on page 4

Corrected

Please also see comments in the attached file.

The paper presents a review that describes the processes associated with the plasma self-organization in tokamaks. The paper is well-written, although English could be slightly improved, presented scientific results are clear so I will strongly recommend publishing this manuscript. I have several comments and suggestions, but they are mainly to fix bugs and improve readability. My comments on the content of the article should be taken as an advice, not as a request.

Page 2, line 44. “entropy and … is the t” => Missing ? .

Corrected

Page 2, line 44. “turbulent temperature” => please explain

…and θ is the equivalent of thermodynamical temperature. J.B. Taylor called it as ‘magnetic temperature’.

Additional reference:

Taylor J.B. Relaxation of toroidal plasma and generation of reverse magnetic fields. Phys. Rev. Lett. 1974, 33, 1139-1141.

Page 2, line 65. “since it smoothest the gradient that feeds it” => this is correct for gradient driven instabilities, not for all

Corrected as:  depletes the source (e.g. gradient)

Page 2 formula (2) => will be useful to explain here for clarity: Г is … pc is …

We defined all variables in Eqs (2-3)

 Page 3 line 87. “The modern spherical tokamaks ST40 [11] and Globus-M2 [12] allow” => better to say “may allow”

Corrected

Fig.3 line 115. “pressure profile inside the island cannot be” => please re-write. “cannot exist”? But we know that NTMs do exist.

No! It may be the incorrect interpretation of experiment. As it is shown in fig. 1, flattening of the total pressure profile does not mean the flattening of the profile in the island (you have to subtract the self-consistent profile from the curve to obtain the profile in the island).

We add the sentence : Thus, the Neoclassical Tearing Mode (NTM) – the mode with flattened pressure profile inside the island cannot exist at times longer than the time of turbulent relaxation.

Page 4 from line 141. This is repetition of what is said at page 3 from line 129.  Also lines from 138 and 149 are identical. Please fix.

Corrected

Page 4  line 155 “ internal transport barrier occurs.” => “may occur”. We know that ITB can be created and sustained without islands.

No, should occur.

In experiments, where the time and space resolution is quite good, the islands are visible. For small barriers, the islands have a high number m and they are not registered without a special technique.

If the islands are large, (q=1) the dependence of m on the rebuilding the barrier between disruptions is well seen, see fig.9.

Page 5 line 173. “neoclassical flux, which is negligible for normal tokamak” => correct but not for all cases. Low collisionality, spherical tokamaks etc have significant neoclassical fluxes. So better to specify what “normal tokamak” exactly means.

Thank you.  but not for all cases.

Low-collisionality spherical tokamaks etc have significant neoclassical fluxes

See text

Page 5 line 182. “Typically, in tokamaks it is about 2 mm.” => in some tokamaks. Depending, for example, on TF. Also, there are fast ions.

Thank you.

Amendment: thermal ions

Amedment: In some tokamaks as TEXTOR and T-10

Page 5 line 185. “island m = 20–25” =>maybe useful to say that this is for MTMs

No, they are usual MHD islands

Page 5 line 200. Formula (3) Also comments are needed.

This expression is defined in section 2.2, lines 94-95

We rewrite it in-line

Page 6 line 206. “In many experiments, where the formation of barriers and islands have been studied, 206 an unexpected result has been found: barriers and islands always formed together.” =>better to say “in some experiments” and give references. In many experiments, like DIIID, JET or MAST this is not always the case.

The main point of the paper: barriers and islands are together, but insufficient resolution of diagnostics sometimes does not allow to detect them.

We amend this sentence in section 3.2.

Amendment to section 3.3.:

…during rebuilding the barrier.

Page 6 Fig 5a. I would not say that the width of ITB in this shot was 2 cm. It is much wider. Feature marked as ITB is an island, but more likely 3/2 or even 2/1. Flattening of profile may be either due to a sawtooth (which on MAST is typically at q~08, not 1) or due to other reasons. Were there sawteeth in this pulse?

You are absolutely right. The width of the barrier depends on the phase of sawtooth, which change m in the flow Г1 and, accordingly, the calculated width of the gap. However, only authors of the experiment can conduct quantitative calculations. The initial profile is rather asymmetrical, but the ASTRA code symmetrize it with possible distortions. Some experimental information may be unavailable for us. This figure is presented as illustration and for rough estimations. It is very useful to learn how to register islands with high m (harmonics).

Page 7 line 233. “formation of the barrier and the island are two aspects of the same phenomenon” => better to say “in some cases” or “may be to aspects”

We use ‘obviously’

Amendment:

The increased pressure gradient (barrier) results in abootstrap current. The F_min condition requires fragmentation of the bootstrap current layer into the local islands, similarly to layer of mercury, owing to a high surface tension,

Page 7 line 239. “at various” => in various

Corrected

Page 7 line 241. Was KSTAR regime claimed to be hybrid? Please check specific point in

We believe that in all experiments with advanced confinement it is important to obtain a sufficiently wide zone with a low dq/dr. The method of programming the q(r) profile is not essential, that is why we call all these modes "advanced tokamak regimes".

Fig.8. FIRE mode and H-mode were more often. “highest discharges” => “highest performance discharges”

‘performance’ is inserted

Page 8 line 263. “after the disruption,” => after the minor disruption, or “internal disruption”

after the “internal disruption”

Page 9 line 276. “Such modes are called “advanced tokamak” or “hybrid” regimes,” => “advanced tokamak” and  “hybrid” regimes are different regimes, at least on JET

No, there is the same physics –to interrupt of contact between the islands in the flux Г1.

The method of obtaining a wide area with low dq/dr is not so important

Amendment to Conclusion:

Self-organization radically changes the pattern of processes occurring in plasma. The small instabilities, eddies, waves and flows that we tried to make responsible for the energy confinement, turned out to be connected only by the fact that to minimize the level of their activity, creating the most compact MHD configurations in plasma, corresponding to the minimum of free energy, that is, a minimum of turbulent activity.

The resulting MHD system responds to external impacts by forming new subsystems, new islands or a chain of small islands, which, interacting, can increase the radial flux of energy. Our task is to have a self-consistent plasma with minimal distortion of the pressure profile. Under certain conditions, islands can contribute to obtaining the best confinement.

The best possible confinement for a given parameters can be calculated simply and reliably: no scailings or models are needed for this.

Our goal is to reliably obtain this regime, why is it necessary to understand the physical processes that control the behavior of such a system.

Thanks to Referee for interesting comments.

Author Response File: Author Response.docx

Round 2

Reviewer 1 Report

Paper fine, can go on.

Reviewer 2 Report

I thank you for your detailed replies and amendments to the text, which I find now clearer. You have addressed all my previous points and you have exhaustively answered to all my questions. It is therefore with pleasure that I recommend your interesting work for publication.

I have just one suggestion, which I leave however as an optional choice to you - that is, in any case I do not ask the see the manuscript again and, in case you want to implement my suggestion, the corresponding minor change in the text can in my opinion directly arranged during the proof correction, so to speed up the possible publication process:

thanks to your reply to my remark about previous lines 94-97, I got your point and why you wrote that the Ohmic heating scales like T^{3/2}. In this regard,  I realized that the "ingredient" of your argument, which I was missing, is the fact that the electric field E is assumed to be constant, in this estimate. Maybe reminding this in the text -e.g., by just writing something like " E=jR with E = const" in between parentheses- could  help the reader. 

The English of the amended text seems to me considerably better than before.

I think to have noticed just some minor misprints and some sentence, which probably could be reworded differently, so to improve the reading, but I think that any amendment in this sense could be successfully done during the possible proof reading stage of the manuscript.