A series of high resolution, 3D, resistive MHD numerical simulations of the reversed-field pinch are performed to obtain scaling laws for poloidal beta and energy confinement at Lundquist numbers approaching ${10}^6$. Optimum plasma conditions are attained by taking the transport coefficients to be classical, and ignoring radiation losses and resistive wall effects. We find that poloidal beta scales as ${\beta }_{\theta }\propto I^{-0.40\mathrm{}}$ and that the energy confinement time scales as ${\tau }_E\propto I^{0.34}$ for fixed $I/N$, with aspect ratio $R/a=1.25\mathrm{}$.

• Received 17 May 1999

DOI:https://doi.org/10.1103/PhysRevLett.85.322