\documentclass{article}

\begin{document}

%\begin{center}
%{\bf Poloidal Flows in Tokamaks and MHD Pedestal Formation.}
%{\it L.~Guazzotto and R.~Betti}
%\end{center}

\title{Extension of Physics of the MHD Pedestal Formation} % with Poloidal Viscosity.}
\author{L.~Guazzotto$^1$ and R.~Betti$^2$
\date{$^1$ Auburn University\\ $^2$University of Rochester} % and Princeton Plasma Physics Laboratory}
}

\maketitle


Finite toroidal and poloidal flows are routinely observed in the edge plasma region of tokamak experiments.
MHD theory predicts that when the poloidal velocity is transonic with respect to the poloidal sound speed ($c_{sp} \equiv  c_s B_p/B$, where $B_p$ is the poloidal field) a transient will develop.
After the end of the transient, a steady-state MHD pedestal in plasma density and pressure is left, with the height of the pedestal depending on the poloidal location.
The formation of the MHD pedestal was demonstrated with time-dependent simulations with the resistive-MHD  code SIM2D.
In the present work, we explore the effect of additional physics on the properties of the transonic discontinuity, focusing in particular on poloidal viscosity. % and the
Analytic expressions are used for the poloidal viscosity and applied to fast rotating plasmas of increasing complexity, from one-dimensional equilibrium models to numerical solutions of the transonic equilibrium problems to snapshots of the time-dependent evolution of plasmas with poloidal momentum sources.
Results are used to compare the power dissipated by viscosity with the input power and to obtain an estimate of the accuracy of the MHD model for the problem under investigation.
%The advanced model implemented in M3DC1 is used to validate and extend SIM2D calculations.
%Since M3DC1, contrary to SIM2D, was not developed to study transonic transients, this also gives a strong independent verification of the correctness of the MHD pedestal model.
%Special focus is given to . %, which is already implemented in M3DC1 and is being implemented in SIM2D.
%Analytic calculations complement and support numerical results.
Work supported by US Department of Energy Contract No.~DE-FG02-93ER54215.

%6.15
%
%In the present work, we explore the effect of poloidal viscosity on the formation of the MHD pedestal and investigate whether the presence of poloidal viscosity will inhibit the formation of a steady-state pedestal.
%Two approaches are used.
%First, the SIM2D code is modified to include the implementation of analytic expression for the poloidal viscosity obtained from the literature.
%%analytic expressions are implemented in SIM2D.
%Second, the M3DC1 code is used to perform simulations of transonic poloidal flows.
%In addition to giving us the chance to obtain an independent confirmation of the SIM2D results, the use of the M3DC1 code will also provide us with a tool in which poloidal viscosity expressions are already implemented.
%Therefore, M3DC1 will also give us an independent approach for evaluating the effect of poloidal viscosity on the formation of the MHD pedestal.
%Work supported by US Department of Energy Contract No.~DE-FG02-93ER54215.



\end{document}