Title: Simulation Study of Plasma Boundary in HT-6M Tokamak

using Extended Two-Point Model

Author: Rungsin Kongkerd, Apiwat Wisitsorasak

The referee’s comments appear in black color, the author’s response appears in blue color, the changes made to paper appear in green color.

1. (Introduction) Paragraph 1 Line 2-3: Please check reference --> [Wesson]The mistake about the reference has been corrected.

2. In formula (1)-(3), Please define parameter that you use in the formula (e.g. n, T) We add the definition of T and n as follow “where T and n represent plasma temperature and plasma density, respectively.

3. Figure 2 shows the plot of momentum loss fraction (need a space) (fmom), also in Figure 2’s caption. The mistake at figure 2 has been corrected.

4. Forgot “full stop” before Here the SOL width δ generally depends…. 5. Forgot “full stop” after “the total area of LCFS.” Sorry for my errors, I already add the “full stop” after those sentences.

6. where ki and kcx refer to rate of ionization and charge exchange (W-->w).The mistake on this sentence has been corrected as your suggestions. And we also added more description about the calculation as followed

7. Please check the sentences “Equations 1, 5, and 7 form a complete set of equations of the two-point model.”We try to clarify the sentence by changing it as follow “Equations 1, 5, and 7 form a set of equations that relates the density and temperature at the upstream (Tu, nu) to these at the downstream (Tt, nt).”

8. Last paragraph in section 3.1 “figures 4.”--> “figure 4.” Thank you, that error has been corrected on the update version.

9. Last paragraph in section 3.1 “Based on the comparison(no space), (with space) our prediction … The mistake on this sentence has been corrected as your suggestions.

10. plasma major radius , plasma minor radius --> plasma major radius and plasma minor radius? The mistake on this sentence has been corrected as your suggestions.

11. Please add the last line (under “snapshot 7 …”) for table 1. Thank you for your comment, a line was added as your suggestion.

12. Figure 3, Tt and Tu are not subscript and in Figure 5 both of them are italic. The mistakes at figure 3 has been corrected. About the figure 5, I have to inform you that all variables in my proceeding were write in italic.

13. Figure 5 show the upstream and target temperatures as a function of the upstream density,and figures 6 --> Figure 5 show(s) the upstream and target temperatures as a function of the upstream density, (with space) and figure( no s) 6 plots … The mistake on this sentence has been corrected as your suggestions.

14. Please check the sentences “the temperatures at the upstream are target are approximately equal”. We already fixed that mistake by changing a word “are” to “and”.

15. The particle flux show(s) a maximum value … That grammatically error has been corrected.

16. You didn’t mention figure 7. Thank you for the suggestion. We already added the explanation of figure 7 as follow“The parallel heat flux reaching the target also decreases with increasing of upstream density due to radiative cooling effect, see figure 7.”

17. In section 3.2 unit ‘m^-3’ are in italic but in conclusion are in normal, please check.Thank you for leaving the comment, we already changed all ‘m^-3’ in this proceeding from italic to normal character.

Reviewer 2: The paper entitled “Simulation Study of Plasma Boundary in HT-6M Tokamak using Extended TwoPoint Model” described the behavior of particle and heat exhausted from the core to

the limiter in SOL region. I would recommend for publication only after the following points have been clarified and corrected: Major comments: 1. In introduction, authors mentioned that one of the major concerns for fusion device is plasma contamination by atoms from the solid materials. However, this work does not appear to investigate such phenomena. Instead, this works investigates the behavior in SOL region using the source coming from plasma source and ending at the Limiter. No interactions between these particles/heat and the plasma wall is included in the model. In addition, no particles coming from the wall going back to the plasma is considered. We already removed the topics of plasma contamination by atoms from the solid materials to prevent the confusion and changed to the sentence below.“On the other hand, a limiter which is a solid object that protrudes into the plasma for limiting the plasma in the core and preventing direct contact between the hot plasma and the wall. However, this can create an area of open magnetic field line which exhibit some physical differences with plasma core. Understanding the plasma behaviour in this region is thus significantly important as it is a boundary for the core plasma.”

2. Normally, the tokamak plasma can be considered quite symmetric around the magnetic axis, it doesn’t make much sense to assume that there is only one point that heat and particles are coming out. Authors need to justify their assumption that the source coming out of the plasma only at the midplane. I would imagine the prediction being more accurate if authors consider that effect. “The precise locations where the fluxes enter the SOL are still under investigated. Experimental results [11] and simulations [12, 13] suggest that there is the ballooned transport at the edge of the plasma. The transport is found to be localized at the outer mid plane and can enhance the radial transport in the SOL. Therefore, this work assumes that the particle flux enters the SOL at the outer mid plane only.”

3. The two-point model used in this work is derived based on fluid description in the steady state. However, in most current fusion

device, especially in HT-6M, where the discharge is rather short. The plasma may still only be in transient phase. Please comment on this.In HT-6M and future Thailand Tokamak, the pulse length is shorter than 300 ms so we agree that the equilibrium state may not be occur. However, in the future the machine might be upgraded to have longer discharge time so that the steady state can be finally obtained. we noted this comment in the main text as follows “We note that the discharge time of HT-6M tokamak is rather short (∼300 ms) and the plasma may only be in the transient phase. In this work, however it is assumed that the plasma in the steady state can be for obtained for TT1 tokamak.”

4. There are a lot of grammar mistakes, please see minor comments for some suggestions and please read thoroughly again before submitting your revision. Minor comments:

1. In tokamaks, this boundary layer can be established by divertors and limiters [1] [wesson]. The mistake about the reference has been corrected.

2. However, this can result in plasma contamination of plasma by atoms … --> However, this can result in plasma contamination by atoms…The mistake on this sentence has been corrected as your suggestions. 3. …this thin region of the SOL may provide more informative. --> …provide more information. The mistake on this sentence has also been corrected.

4. …and SD1D model, This work…--> …and SD1D model. This work

Thank you, the mistake has been corrected.

5. Can you justify your assumption that parallel velocity along the SOL can be neglected?

Due to the effect of sheath potential, the parallel velocities of particles at the upstream and SOL are much smaller compared to those near the limiter. We clarified this assumption in the main text as follows“In order to derived a set of equations that relates the temperatures and densities at the two points, the parallel viscosity of the plasma is considered negligible along the SOL. The particles have a non-negligible parallel velocity in a thin region in front of the target due to the sheath potential [1].”

6. How do you calculate the reaction rate of ionization and charge exchange processes? Thank you for the comments, we have added the description about calculation of reaction rate of ionization and charge exchange processes as followed.

7. Authors explained “As the temperature decreased, the plasma will significantly loss momentum since the ionization and charge exchange occur more often”. This contradicts with figure 2 where the loss seems to be increased with temperature. The momentum loss fraction fmom presents momentum fraction that can transfer from midplane to the limiter. Thus if value of fmom is 1, there is no momentum loss.

8. For the sake of simplicity, it can be approximate by … --> …it can be approximated by … That grammatically error has been corrected.

9. One of the drawbacks of bisection method is that if there are more than one solutions close to each other, the method fails to distinguish them. Please comment on this. In this study, we already plot the function over this range (nu ~10^18-10^20 m3) and found that there is only one solution. Other calculation techniques such as Newton method can also be used to solved this set of equations as well.

10. In this section, We first validate… --> In this section, we first validate… The mistake on this sentence has been corrected as your suggestions.

11. Results of figure 3 (also figure 5) shows that the upstream and target temperatures reduce as the upstream density is increased. Authors explained that it’s because the conservation of pressure along the field line. However, at some point the trend at upstream temperature switch. Please explain what happens. Does the minimum point have significance? This is relating to the the decreasing of target density at high upstream density.

12. Snapshot No. used in table 1 (1-7) and shot number used in figure 4 (0-6) are not the same. Also, the numeric of figure 4 can be added as extra column in table 1. I do not see the necessity to plot it as histrogram. We already removed the histogram and put it in the table 1. as your suggestion.

13. HT-6M was operated with plasma density around 10e19 at plasma center. In addition, in J. Promping et al (2018), the similar plasma density was predicted. Why do authors use such a high density for upstream in this work? In this work, we attempt to investigate a wide range of density as much as possible. Therefore, the upstream density is varied between 0.1 x 10e19 to 3.5 x 10e19. This may provide useful information for tokamak operations in the future.

14. In figure 3, the x-axis was labeled as n_s but the description used n_u The mistake on those figure has been corrected as your suggestions.

15. Figure 7 was included but was never mentioned or discussed about in the text. Thank you for the suggestion. We already added the explanation of figure 7 as follow“The parallel heat flux reaching the target also decreases with increasing of upstream density due to radiative cooling effect, see figure 7.”

16. Can you explain why at low upstream density, the upstream and target temperatures are almost the same? Thank you for your comment. We have added the explanation of this question in the main text as followed“At the low density, the particle convection dominates the particle transport. The plasma temperature in the SOL is also high so that the heat conduction which is proportional to T5/2 is large. Thus the variation of the temperatures along the SOL is negligible.”

17. Can you describe in more detailed why the decreasing of the particle flux would imply plasma detachment? Does the result in figure 8 implies that we should operate plasma with such high density in order for plasma detachment to occur?We describe the plasma detachment in the main text as follows.“The detached regime can be occurred in this high density regime since the temperature at the target becomes very low. The neutral

particles that are coming from the target are less probably ionized at this low temperature. Therefore, the ionization front moves away from the target, and the particle and heat fluxes decreases [1].”

The result suggests that one method to achieve the detached state is by raising the density.