$\beta_{p} $ Scaling of the Heat Flux Width in DIII-D

The scaling of the heat flux width with poloidal beta at the outer midplane, $\beta_{p} $, is a stringent test of the critical gradient model that posits that the heat flux width is set by an edge stability limit dependent on the separatrix pressure gradient. As $\beta_{p} $ was varied by means of a combined density and power scan, the measured pressure gradient was found to scale linearly with $\beta_{p} $ at both low (0.5 MA) and high (1.5 MA) plasma currents, and lie significantly below the infinite-n ideal ballooning limit critical pressure gradient as computed by the BALOO code. At fixed $I_{p} $, this implies that the separatrix pressure gradient scale length is approximately constant, which is consistent with the kinetic profile measurements. The ballooning limit was found to be constant in the $\beta _{p} $ scan and set by the equilibrium with only a minor dependency on the edge pressure and current profiles. Both the pressure gradient and $\beta _{p} $ varied by more than a factor of 2 in the scans.