Scaling Laws of Confinement Parameters for the Advanced Reversed Field Pinch

A series of resistive magnetohydrodynamic numerical simulations are performed to generate scaling laws for energy confinement time \textit{$\tau $}$_{E}$ and poloidal beta \textit{$\beta $}$_{p}$ for the advanced reversed field-pinch (RFP). Strongly improved scaling with basic initial parameters is obtained as compared to the conventional RFP. Early results indicate an improved scaling of \textit{$\tau $}$_{E}$ with plasma current $I$ and line density $N$ compared to the conventional RFP on the order of \textit{$\tau $}$_{E}$ (\textit{adv.}) / \textit{$\tau $}$_{E}$ (\textit{conv.}) $\propto $ ($I$/$N)^{0.29}I^{0.29}$. The improved behavior of the advanced RFP as compared to the conventional, uncontrolled RFP stems from the introduction of current profile control (CPC). In the present numerical simulations, CPC is performed by implementation of a \textit{parameter free} automatic feedback algorithm, optimized to reduce the fluctuation caused $\left\langle {{\rm {\bf \tilde {v}}}\times {\rm {\bf \tilde {B}}}} \right\rangle $ electric field. The scheme introduces an ad-hoc electric field within the plasma volume, automatically adjusted to dynamically control the plasma into more quiescent behavior by eliminating current driven tearing mode instabilities and reducing resistive interchange modes.