
\documentclass[a4paper,12pt]{article}
    \usepackage{amsmath}
    \usepackage{amssymb}
    \usepackage{breqn}
\usepackage{graphicx}
\usepackage{color}
\usepackage{float}
\usepackage[numbers]{natbib}

\def\apj{ApJ}
\def\apss{Ap{\&}SS}
\def\mnras{MNRAS}
\def\aap{A\&A}
\def\apjl{ApJ}
\def\gafd{Geophys.\ Astrophys.\ Fluid Dyn.}
\def\jfm{JFM}
\def\physrep{PhR}
\def\pre{PRE}
\def\prl{PRL}
\def\apjs{ApJS}
\def\pasa{PASA}
\def\pasj{PASJ}
\def\nat{Natur}
\def\pasp{PASP}
\def\ssr{SSRv}
\def\memsai{Memorie della Societa Astronomica Italiana}
\def\araa{Ann. Rev. of Astron. and Astrophys.}
\newcommand\zhetp{JETP}
\newcommand\jetp{Sov.\ Phys.\ JETP}

	\addtolength{\oddsidemargin}{-.875in}
	\addtolength{\evensidemargin}{-.875in}
	\addtolength{\textwidth}{1.75in}

	\addtolength{\topmargin}{-.875in}
	\addtolength{\textheight}{1.75in}

\input macros.tex

\begin{document}

\section*{Response to previous criticisms}

We are making a new submission of a revised manuscript to be considered for publication in Physical Review Letters. 
The previous submission (LE17401) was reviewed and not accepted for 
publication based on reviews by two referees. We had made an appeal upon which 
Alain Pumir, Divisional Associate Editor reviewed the referee reports and our responses. 
While he agreed that referee B had not appreciated the importance of our results, 
he felt the evidence was not convincing in agreement with Referee A and thus rejected 
our appeal. But he also mentioned the following: ``the authors are very close
to an important result that would clearly deserve to be published
in Physical Review Letters. I would therefore invite the authors to
work further on obtaining better evidence for the exponential growth
of $M_1$."

We have now prepared a new submission, where we address the previous criticisms and present 
the new better evidence. \\

Our work presents a numerical finding which affects the important subject of magnetic field 
generation in astrophysics. We had shown already in the previous version of the manuscript 
that in our direct numerical simulations (DNS), the magnetic field evolution consists of a new regime of fast growth. 
Our DNS consisting of helical turbulence, with and without shear, host turbulent dynamos. 
We showed that, while the kinematic regime is driven by the small-scale dynamo, on its saturation, 
a large-scale dynamo regime is uncovered which leads to what we understood as exponential growth 
of large-scale fields called the quasi-kinematic large-scale dynamo (QKLSD) regime. 
The QKLSD regime is then followed by a resistively driven growth phase. 
The existence of the QKLSD regime was previously unknown and by bringing to the fore, 
our work resolves the long-standing issue of whether the large-scale dynamo manages to grow  
significant large-scale fields despite the more efficient small-scale dynamo growing small-scale fields 
on much faster time scales. \\

The main criticism of the work was that the exponential growth curve in the QKLSD regime 
was not sufficiently convincing. We now present two new points: \\

\noindent 1. We have now additional evidence: we have run a similar DNS with a completely different code called 
Dedalus (https://dedalus-project.org/) with also a different forcing function  
and find that the QKLSD regime appears in the results from that DNS as well!\\

\noindent 2. We have come up with a toy model which is easily understood
as a composite of two exponentially growing dynamos (in two stages) with subsequent saturation
and show that the solutions from the toy model match well with the magnetic field 
evolution curve from the DNS. \\

Now we expand on the above two points to address the previous criticisms. \\

First of all, it should be noted that the nature of the curve in the QKLSD regime 
is not a strict (and clean) exponential (in Figs 1 and 2 from the manuscript). 
Unlike the third stage which is resistively driven and thus involves very slow timescales, 
the QKLSD regime is easily seen as one with fast growth of magnetic fields. 
A fast growth by a turbulent dynamo typically involves an exponential. However, 
since the QKLSD regime is sandwiched between the kinematic regime and the resistive growth regime, 
the corresponding evolution curve is necessarily influenced by the transition to/from the other 
two regimes, which results in the concavity of the curve (as the Divisional Associate Editor had pointed out). 
Thus, the exponential in the QKLSD regime can be considered being modulated by another function 
which includes the influence of going from a regime with much larger growth rate to 
one with a much smaller rate.   \\

1. We show the results from the new DNS using Dedalus in Fig.~2
of the manuscript (note that this simulation is from a recently published paper: Bhat (2021) in MNRAS). 
Here again we find that the QKLSD regime arises with a sharp transition from the kinematic regime. 
And again, note that the QKLSD regime growth is not a strict exponential and is modulated by a certain concavity 
as we previously mentioned is the effect from being sandwiched between the other two regimes. 
Further, it turns out that, despite the DNS being from another code, Dedalus and with a different value of $\urms\sim 1$
and $\kf\sim 8.5$, the efficiency factor obtained from mean-field theory calculation of the growth 
rate, is quite similar to that obtained from runs with {\sc Pencil Code}. 
All of this corroborates our result of the QKLSD regime and demonstrates that it is a robust one. \\

2. The toy model is specified in Eq.~(1) of the manuscript and, as we have explained in the 
text, the model provides two asymptotic exponential growth regimes. The solutions from the 
model have been overlaid on those from the DNS as shown in Figs. 1 and 2. And it can be seen that 
these model solutions match quite well with the simulation evolution and growth rate curves.
This goes to show that understanding of the two stages as back to back exponential curves 
is in principle correct. The only caveat is that the second exponential has an associated modulation.\\ 

With this, we hope that we have made a convincing case for a new submission of our revised manuscript. \\


\bibliographystyle{phcpc}
\bibliography{reftwody}

\end{document}
