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\begin{document}

\title{Stream-Aligned Magnetohydrodynamics for Solar Wind Simulations}



\author[1,1]{Igor Sokolov}%
\author[2,2]{Lulu Zhao}%
\author[2,2]{Tamas I Gombosi}%
\affil[1]{University if Michigan}%
\affil[2]{University of Michigan}%


\vspace{-1em}



  
  \date{May 27, 2024}


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\begin{abstract}
We present a reduced magnetohydrodynamic (MHD) mathematical model
describing the dynamical behavior of highly conducting plasmas with
frozen-in magnetic fields, constrained by the assumption that, there
exists a frame of reference, where the magnetic field vector, B, is
aligned with the plasma velocity vector, u, at each point. We call this
solution ``stream-aligned MHD'' (SA-MHD). Within the framework of this
model, the electric field, E = -u x B [?] 0, in the induction equation
vanishes identically and so does the electromagnetic energy flux
(Poynting flux), E x B [?] 0, in the energy equation. At the same time,
the force effect from the magnetic field on the plasma motion (the
Ampere force) is fully taken into account in the momentum equation. Any
steady-state solution of the proposed model is a legitimate solution of
the full MHD system of equations. However, the converse statement is not
true: in an arbitrary steady-state magnetic field the electric field
does not have to vanish identically (its curl has to, though).
Specifically, realistic tree-dimensional solutions for the steady-state
(ambient) solar atmosphere in the form of so-called Parker (1958)
spirals, can be efficiently generated within the stream-aligned MHD
(SA-MHD) with no loss in generality.%
\end{abstract}%



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