SciPost Submission Page
Classification of magnetohydrodynamic transportat strong magnetic field
by Bartosz Benenowski, Napat Poovuttikul
|As Contributors:||Bartosz Benenowski · N Poovuttikul|
|Date submitted:||2020-05-21 02:00|
|Submitted by:||Poovuttikul, N|
|Submitted to:||SciPost Physics|
|Subject area:||Fluid Dynamics|
Magnetohydrodynamics is a theory of long-lived, gapless excitations in plasmas. It was argued from the point of view of fluid with higher-form symmetry that magnetohydrodynamics remains a consistent, non-dissipative theory even in the limit where temperature is negligible compared to the magnetic field. In this limit, leading-order corrections to the ideal magnetohydrodynamics arise at the second order in the gradient expansion of relevant fields, not at the first order as in the standard hydrodynamic theory of dissipative fluids and plasmas. In this paper, we classify the non-dissipative second-order transport by constructing the appropriate non-linear effective action. We find that the theory has eleven independent charge and parity invariant transport coefficients for which we derive a set of Kubo formulae. The relation between hydrodynamics with higher-form symmetry and the theory of force-free electrodynamics,which has recently been shown to correspond to the zero-temperature limit of the ideal magnetohydrodynamics, as well as simple astrophysical applications are also discussed.
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Anonymous Report 1 on 2020-9-14 Invited Report
This work is a technically impressive, relevant, timely and important addition to the field of magnetohydrodynamics, which was recently reformulated in the language of higher-form symmetries by Ref. . It was only through this new machinery that it became clear how the zero temperature (or, in other words, the extremely strong magnetic field) limit of MHD could be understood and that this limit was connected to a previously widely studied theory called force-free electrodynamics.
What is interesting about this zero temperature limit is that a consistent truncation of MHD exists which is non-dissipative and, yet, it retains the structure of an infinite gradient expansion series with higher-and-higher derivatives. It is believed that a non-dissipative limit is impossible in standard neutral hydrodynamics, which makes MHD special.
Since the limit is non-dissipative, the leading-order corrections to ideal MHD come from second-order hydrodynamics (the MHD equivalent of the full BRSSS theory). A few of these terms were studied previously (in  and then in , ...) and their phenomenology discussed. However, this is the first paper that completely classifies all of them. In a sense, this work is equivalent to finding all possible “viscosities” in Navier-Stokes hydrodynamics, which are the leading-order corrections to ideal hydrodynamics. The number in the Navier-Stokes theory is 2, here it is 11. Whatever the full second-order MHD theory is, it should reduce to the results of this paper in the limit of extremely strong magnetic field. Moreover, this paper teaches us how force-free electrodynamics needs to be corrected away from the ideal limit at zero temperature.
One issue with papers that are of this nature, that are this technical and delve into the complexity of classifying higher-order hydrodynamics, is that it is pretty much impossible to know whether the classification presented here is completely correct. It is even harder to determine whether it is optimal (it contains the smallest possible number of terms). This is not a criticism of this paper, only a warning to the community that such classifications require independent verification.
The paper would be even stronger if the authors managed to find a direct new physical consequence of their second-order terms. Naturally, this is very difficult and any such success easily warrants a separate publication.
Taking all this into account, I believe that the paper is certainly of high enough quality, novelty and relevance to warrant publication in SciPost.
I do not think that any major changes are necessary. The list of smaller suggestions follows.
At the end of section 3, I suggest that the authors add a complete list of all transport coefficients and show how they can be computed out of two- and three-point function Kubo formulae; i.e., a list of all transport coefficients expressed purely in terms of hydrodynamic n-point functions.
I suggest a thorough read through the text to eliminate typos and grammatical errors.
Above eq. 2.11a, the authors talk about the conservation law 2.4. I would not call 2.4 a conservation law. Those are diffeomorphisms and gauge transformations.
Below eq. 2.30, it should say “break down” not “breakdown”.
Regarding these additional gapped modes, the authors say that they cannot be removed by a frame choice (above eq. 2.37). Below eq. 3.9, they then say that it is also possible that this mode can be removed upon the field redefinition. Can it be removed or not? I have found the discussion of these extra modes a bit confusing in places and it would be nice if this could be clarified, possibly with a summary in a single location in the text (maybe in the discussion). Some interesting sounding comments are also added at the beginning of page 19, but the full meaning of that paragraph and the physical significance of such modes in the cited references in not completely clear.