\newcommand{\beq}{\begin{equation}}
\newcommand{\eeq}{\end{equation}}

\newcommand{\benum}{\begin{enumerate}}
\newcommand{\eenum}{\end{enumerate}}

\def\apj{ApJ}
\def\apjs{ApJS}
\def\aap{A \& Ap}
\def\pasp{PASP}
\def\pasj{PASJ}
\def\ssr{Sp Sci. Rev.}
\def\solphys{Solar Physics}
\def\mA{\mathcal A}
\def\araa{ARAA}
\def\nat{Nature}
\def\mnras{MNRAS}
\def\apj{ApJ}
\def\apjl{ApJL}
\def\aap{A\&A}
\def\apss{Ap\& Spac. Sup.}
\def\jcap{Journal of Cosmology and Astroparticle Physics}
\def\physrep{Physics Reports}
\def\pre{Physical Review E}
\def\physscr{Physica Scripta}
\def\aj{AJ}
\def\aapr{Astron. Astrophys. Rev.}
\def\prd{Phys. Rev. D}
\def\pre{Phys. Rev. E}
\def\prl{Phys. Rev. Lett.}
\def\pnas{Proceedings of the National Academy of Science}
\def\qjras{Quarterly Journal of the Royal Astronomical Society}

\newcommand{\workinghere}{\noindent\makebox[\linewidth]{\rule{\textwidth}{4pt}}}

\newcommand{\titlealpha}{\texorpdfstring{$\bm\alpha$}{p}}

\def\bar{\overline}
\newcommand{\abra}[1]{\left\langle{#1}\right\rangle}

\def\blue{\textcolor{blue}}

%comments
\newcommand{\hz}[1]{{\color{red}[HZ: #1]}}
\newcommand{\ab}[1]{{\color{magenta}[AB: #1]}}
\newcommand{\rs}[1]{{\color{blue}[RS: #1]}}
%\newcommand{\edit}[2]{{\color{orange}\sout{#1}} {\color{olive}{#2}}}
%AB: omit empty space here
\newcommand{\edit}[2]{{\color{orange}\sout{#1}}{\color{olive}{#2}}}

%\bm vectors
\newcommand{\del}{{\bm\nabla}}
\newcommand{\bmA}{{\bm A}}
\newcommand{\bma}{{\bm a}}
\newcommand{\bmB}{{\bm B}}
\newcommand{\bmb}{{\bm b}}
\newcommand{\bmE}{{\bm{E}}}
\newcommand{\bme}{{\bm{e}}}
\newcommand{\bmJ}{{\bm J}}
\newcommand{\bmj}{{\bm j}}
\newcommand{\bmK}{{\bm{K}}}
\newcommand{\bmk}{{\bm{k}}}
\newcommand{\bmU}{{\bm U}}
\def\bmu{\bm{u}}
\newcommand{\bmx}{{\bm{x}}}
\newcommand{\SSSS}{\bm{{\sf S}}}

%dimensional parameters
\newcommand{\nuM}{{\nu_\text{M}}}
\newcommand{\xiM}{\xi_\text{M}}
\newcommand{\EEM}{{\cal E}_\text{M}}
\newcommand{\cs}{c_\text{s}}
\newcommand{\kp}{k_\text{peak}}

%dimensionless parameters
\newcommand{\ReN}{\text{Re}}
\newcommand{\ReM}{{\text{Re}_\text{M}}}
\newcommand{\PrM}{{\text{Pr}_\text{M}}}
\newcommand{\Lu}{\text{Lu}}

%turbulence
\newcommand{\led}{{l_\text{ed}}}
\newcommand{\taued}{{\tau_\text{ed}}}

%dynamo
\newcommand{\emf}{\mathcal{E}}
\newcommand{\bmemf}{{\bm{\emf}}}
\newcommand{\alphaK}{{\alpha^\text{K}}}
\newcommand{\alphaM}{{\alpha^\text{M}}}


\newcommand{\Sp}[1]{\text{Sp}\left({#1}\right)}
\newcommand{\intIH}{\mathcal{I}_H(R)}
\newcommand{\cIH}{I_H}
\newcommand{\tcIH}{\tilde I_H}







