An excellent and very clear article. The only corrections I have to suggest are minor typos: (1) 5th line after eq. 4, 'othwerwise' (2) first line of caption to figure 3 is missing something. (3) in 2nd last line or article: 'the the'
Very clear and concise review. I have only the following comments or suggestions:
1. "Plasma" might be a better word for a gas containing mobile electrical charges. So the first sentence could be like this: "Gases containing mobile electrical charges, or plasmas..." There are other places where "plasma" could be used instead of "gas".
2. The simple physical picture illustrated by Fig.1 does not reveal the importance of increasing angular momentum with R. So the expression "...but the angular momentum of the lower orbits is smaller than that of the higher orbits." could be deleted. Or maybe there is a better way to incorporate this element into the simple picture?
3. "to" is missing in the sentence right under Fig.1 "....must fall to a lower orbit of corresponding TO smaller angular momentum."
4. In the first line of the paragraph after Eq.(4), it might be better to write (1/R^3)[d(R^4\Omega^2)/dR] to be clearer.
5. It is not so clear why a week K in Eq.(5) can destabilize the system. Is it possible to add some steps to illustrate this point?
6. "motion" is misspelled right after Eq.(7).
7. The reference of "Liu et al." should be referred to "Phys. Rev. E" not "Phys. Rev. Lett.".
I thank the reviewers for their very helpful comments.
I have followed almost all the suggestions, though after some careful thought, I have in some places elected to keep my original formulation for reasons that I hope are compelling.
My detailed response to reviewer B is as follows:
1. I would prefer to leave the description as is, though the reviewer is of course perfectly correct in referring to a gas with mobile charges as a plasma. The reason that I prefer the current description is that the analysis applies in principle to both gases and metal liquids, and to have keep referring plasmas and liquids separately would detract from the flow of the writing, while adding little of substance to the article.
2. I have added a sentence to the caption of figure (1) to emphasize that the angular momentum is increasing outward.
3. The sentence has been rewritten correctly.
4. Again, I would prefer to leave the writing as is, introducing the alternative formula for \kappa^2 a few sentences after equation (4). I believe that the development and the flow is more natural as written.
5. A few sentences after equation (5) have been added to explain why small K leads to instability.
6. & 7. Typos corrected. Thank You!
I am glad that my comments were helpful. Maybe the author has some misunderstandings about my point No.2, so I would like to repeat again here: what I meant there is that the simple physical mechanism illustrated by Fig.1 seems to work as long as Omega is a decreasing function of R, regardless the angular momentum profile. So mentioning that the angular momentum increases with R seems unnecessary to me. Maybe I am wrong? Otherwise I am perfectly fine.
Author : Magnetorotational Instability
Response to reviewer B:
In fact it is important that the angular momentum increase outward in understanding the mechanism of the MRI. This is why, in the example, the outer element rises when it acquires angular momentum, and the inner element falls when it loses angular momentum. So it is good to emphasize this in the caption---as prompted by the initial comment, even if it involved a misunderstanding!
The reviewer is correct when he points out that if the angular velocity decreases outwards, the rotation is unstable whether or not the angular momentum increases outwards. But the physical mechanisms are very different. If the angular momentum decreases outward, the flow is Rayleigh unstable, a process very distinct from the MRI.
So I hope the reviewer will be content to accept the presentation as written.
I understand and appreciate the further clarifications from the author. I agree that the rotation is unstable when the angular momentum decreases outwards due to the Rayleigh mechanism that lowers the total mechanical energy. Having a spring in this case can obviously further promote the instability, which I interpret it as a help by the MRI mechanism. Thus, the MRI mechanism works regardless the angular momentum increases or decreases outwards, as long as the angular velocity decreases outwards as implied by Fig.1. But in the case when the angular momentum increases outwards, only the MRI mechanism can destabilize the rotation, and that's the whole point!
Of course I am happily accept the article!