Transport timescale calculations of sawteeth and helical structures in non-circular tokamak plasmas

We present results of using the implicit 3D MHD code M3D-$C^{1}$ [1,2] to perform 3D nonlinear magnetohydrodynamics calculations of the internal dynamics of a shaped cross-section tokamak plasma that span the timescales associated with ideal and resistive stability as well as parallel and perpendicular transport. We specify the transport coefficients and apply a ``current controller'' that adjusts the boundary loop-voltage to keep the total plasma current fixed. The 3D 2-fluid plasma model advances the magnetic field, velocities, electron and ion temperatures, and plasma density. We find that the plasma either reaches a stationary quasi-helical state in which the central safety factor is approximately unity, or it periodically undergoes either simple or compound sawtooth oscillations [3] with a period that approaches a constant value. By comparing a dee-shaped cross section with an elliptical shaped cross section, it is shown that the plasma shape has a large effect on determining the sawtooth behavior and the associated mode activity. Application to ITER shaped tokamak plasmas predict the magnitude of the 3D boundary deformation as a result of a stationary quasi-helical state forming in the interior. \\[4pt] [1] J. Breslau, N. Ferraro, S.C. Jardin, \textit{Physics of Plasmas} \textbf{16} 092503 (2009) \\[0pt] [2] S. C. Jardin, N. Ferraro, J. Breslau, J. Chen, \textit{Computational Science and Discovery} \textbf{5} 014002 (2012) \\[0pt] [3] X. von Goeler, W. Stodiek, and N. Sauthoff, \textit{Phys. Rev. Lett}. \textbf{33}, 1201 (1974)