Hi Anvar,
Many thanks for your second set of comments. Below first some responses
to your latest ones and then to your earlier ones. If you have further
comments regarding the pages after p.20, let me know.

Regarding Bx and By being independent, we now write "uncoupled from
each other". In alpha effect dynamos, as we explain below, Bx and By
are coupled.

On page 14, you commented about kinetic helicity; we just wanted to
explain when the incoherent alpha-shear dynamo can be important.
I think you where thinking about something else.

Regarding Kazantsev 1968, it says May 1968 for JETP, and November 1967
for Zh Eksp Teor Fiz, but we refer to the former.

Regarding "earlier references" (still on page 14), we meant Batchelor
1950, but have now rephrased and shortened it.

Regarding "nonmagnetic Kolmogorov turbulence doesn't exist", yes, its
meant as a statement. There hardly are examples where astrophysical
turbulence is nonmagnetic, right?

Regarding the peak spreading to smaller k, this is only true of the
nonlinear case. This paragraph is about the kinematic case. The new Fig.4;
see http://norlx65.nordita.org/~brandenb/tmp/Galactic-Dynamos/paper.pdf
now has 2 panels (page 14).

Regarding more references, we are only allowed to use 200, so that's
why we have to be selective. Kulsrud & Anderson (1992), who never seem
to have heard about Kazantsev, present the case very clearly, so it is
worth re-reading. But we do now refer to the Almighty Chance book,
which I definitely find worth reading.

Regarding your comment about imposed field, we have now said earlier
that B_0 is an imposed field (and not a mean field).

Regarding your comment that <a.b> can vary in space, we now say
"$\overline{\aaaa\cdot\bb}$ is approximately constant in time"
We just wanted to explain why we drop its time derivative.

Regarding helicity fluxes, we now write "demonstration from simulations".
So far, it only works with mean-field models and given fluxes.

Regarding earlier diffusive magnetic helicity flux papers, which ones are
you thinking of? Our joint paper of 2006 is mentioned later. Here the
point is to show that these effects seem to become important only at
very large Rm. It is also important for people to measure 2*eta*<j.b>
in addition to the other two terms.

Before Sec.4.1, the title said "Test-field method and nonlocality in space
and time", but we have now replaced "Test-field method" by "Mean-field
coefficients", which we hope alleviates us from the need to explain
test-field and other methods so early on. It does come a bit later.

Regarding SN explosions, you say they have short correlation times.
I know this argument, but the velocity is not just an artificially
given field (unlike the forcing itself), but the result of a balance
between forcing and dynamical terms (u.gradu). The correlation time
is then 1/urms*kf, so tcor*urms*kf=1.

Regarding test-field method on page 19, you say one should write
arguably. The method has limitations toward large Rm, but other methods
(for example the correlations method) have severe deficiencies even for
small Rm. I know that Bendre *argues* that other methods are right when
the test-field method breaks down, and that the correlation method only
breaks down at small Rm when the test-field method is definitely right.
But should we write "arguably" if we disagree with what sounds like an
arbitrary argument?

On page 20, you said that mean fields can't have sharp structures,
but we just said that you can get this if you neglect nonlocality. One
mustn't do this, and it is only in the last 10 years that we therefore
use an evolution equation for the EMF with a diffusion term.

Below some comments regarding your earlier comments:

> > Regarding your suggestion to remove the Han17 references, is this 
> > because you don't find them useful? (He always emails me, and then I 
> > felt I could quote at least one.
> 
> I find his papers rather shallow and often misleading since they
> contain more or less obvious mistakes. For example, he published papers
> suggesting a very large number of magnetic field reversals in the Milky
> Way based on a clearly faulty data analysis. Referring to him gives more
> credit to those wrong results.

Yes, I understand, and I'm aware of this either from you or from Rainer.

> > Regarding your suggestion to omit the first column of Fig.1, your 
> > argument "never observed" would not really be an argument in favor of 
> > not even trying or explaining how it would look like, we thought.
> 
> But a purely azimuthal field also cannot be maintained by any known
> mechanism. This is a pure fiction -- why showing it then?

I felt this picture with 3 panels is still good to show, because it makes
one aware that one can tell the difference between this and the next one,
because the phase shift is different.

> > Baryshnikova+87 is ok in that respect, but between Eqs. (2) and 
> > (4), the alpha effect is dropped
> 
> No, this is not true -- I've checked again. The alpha-effect is
> there. We adopt the \alpha-\omega approximation but we do NOT neglect
> the alpha-effect!

This is what I meant that the alpha-Omega approximation cannot be made
when looking at nonaxisymmetric modes; this is said more clearly in the
second paragraph of Sec.6.1.1.

> > Stix71 and Roberts+Stix72 had the first nonaxisymmetric models,
> 
> They modelled galactic disc as a oblate spheroid -- the situation
> opposite to the shape of a galactic disc where its thickness increases
> rather than decreases with radius. In this respect, these papers are
> as relevant to galaxies as, e.g., spherical models where m=1 modes were
> discussed from very early times.

You refer perhaps to Stix75, where he really considered a spheroid.
But there, he only used axisymmetric modes. The two references above
are for spheres.

> >> In your book, in 13.6.2, you quote Baryshnikova+87 in connection with 
> > M81, but isn't there the alpha effect neglected in the Bphi equation?
> 
> Only because the \alpha\omega dynamos are considered there -- NOT
> because of any error. The consideration of \alpha\omega dynamos is fully
> appropriate in this context.

My understanding is that nonaxisymmetric modes do require the presence of
alpha in the toroidal equation.

> >> On page 7, you noted that Rm is not decisive for mean-field dynamos.
> > I think I know what you mean, but this is only true if you neglect eta 
> > compared with etat. I don't think that this statement was misleading 
> > or wrong.
> 
> But \eta >> \eta_t in galaxies. So, your statement need to be qualified
> as applicable ONLY to limited numerical simulations rather than reality.

I understand, but here we are on page 7 and just defined eta, and haven't
mentioned etat yet.

> > Where in the
> > Zeldovich+83 book did they talk about non-differentiable?
> 
> I remember well numerous discussions of the non-differentiability for
> \eta = 0 with Zeldovich, Ruzmaikin & Sokoloff -- perhaps it is discussed
> further in their papers with Molchanov.

The Moffatt-Proctor 85 paper showed that the growth rate -> 0 when eta -> 0.
It is very clear and applies to the steady case only. The topic of dynamos
when eta = 0 (and not just -> 0) remains controversial. If you know of some
other clear and maybe recent paper, let me know. Matthias, for example,
thinks that one can have an alpha effect with eta=0. The case eta=0 should
be possible to solve with Euler potentials, but I don't think this works.

> > You commented regarding "higher order contributions to <uxb>; I meant 
> > that etat*J is a higher order contribution relative to alpha*B. Do you 
> > mean one should write higher derivative contributions?
> 
> Yes, these are contributions involving higher-order derivatives rather
> than higher-order contributions.

OK, we now write derivative terms.

> > Regarding the Herzenberg dynamo consisting of stars, yes, there is a 
> > paper on this idea, but I would still regard this as small-scale, 
> > because the scale of the field is that of the eddies (or stars).
> 
> This is exactly why I prefer not to use the terms small-scale and
> large-scale dynamos because what is small in one context can be large
> in another. For example, galaxies have "large-scale" dynamo but their
> size is comparable to the turbulent scale in galaxy clusters to which
> they belong. By your logic and to be consistent, you should say that
> the mean-field galactic dynamos are small-scale. It is by far better
> to talk about the fluctuation and mean-field dynamos -- these are
> exact descriptions of the nature of those processes leaving no room
> for confusion.

Yes, I understand. We do clarify this ambiguity in one place. The term
"fluctuation" becomes questionable for steady flows, and we do have
examples where the mean field fluctuates in z and t, for example.

> > Regarding "cease to exist for large values of Rm", I have now changed 
> > it to "cease to exist in the limit of large Rm" instead of "be efficient".
> > In the *limit*, they really don't exist.
> 
> "Do not exist" is a subjective term. The do exist because all physical
> processes involved still occur but they simply become progressively
> slower, hence inefficient -- but not non-existent. Better to say what
> you mean: e.g., growth rate (i.e., the rate = efficiency) tends to zero.

We are in need of shortening, and since this was going beyond the point,
we omitted the last 2 sentences of this paragraph.

> > Regarding 2-D flows, to me, dimensionality always has to do with 
> > d/dx_i, and not with u_i. Is there an alternative *simple* expression? 
> > Given that the details are given mathematically, there should be no confusion.
> 
> I afraid your understanding of what 2D means is not generally
> accepted. 2D flow is a flow confined to planes -- as an example, consider
> 2D turbulence -- do you want to tell the turbulence people that their
> terminology is wrong?

We've added now non-planar.

> > The Zeldovich 57 ref is not easily accessible, I guess, we not 
> > refer to it in the side margin on page 11.
> 
> Accessible or not but it exists! Google provides the following relevant links:
> https://www.degruyter.com/document/doi/10.1515/9781400862979.93/html?lang=en
> http://www.jetp.ras.ru/cgi-bin/dn/e_051_03_0493.pdf 

Thanks for the links! In the review, we now quote the Almighty chance book,
which is really very good, although no really about pumping. We do refer to
your book in this context instead, where this is well explained.

> > This mean field could be understood as a low Fourier mode filtering.
> > However, then the average of the product of a mean and a fluctuation 
> > vanishes only approximately; see \cite{ZBC18} for the related 
> > discussion on what is known as Reynolds rules for averaging.
> 
> Indeed, the Reynolds rule are not observed for any filtering -- but
> this is NOT a problem.

One question is whether the result becomes inaccurate, or whether even
that is not the case. I suspect that any apparent inaccuracies are
explained by nonlocality, which must not be omitted.
Cheers, Axel