Density profile consistency, particle pinch, and cold pulse propagation in DIII-D

It has been recently proposed that, for highly turbulent discharges, there exists a consistent density profile for the trapped electrons in a high aspect ratio circular cross-section tokamak, which has a radial variation proportional to $\text{1/q(r),}$ where $q$ is the usual safety factor. It is shown here that this result can be extended to include passing electrons and noncircular cross-section moderate aspect ratio tokamaks. This new prediction for the density profile is compared to the time evolution of the measured electron density profile in low confinement mode (L-mode) shots in the tokamak known as DIII-D [L. Luxon et al., Plasma Physics and Controlled Nuclear Fusion Research, 1986 (International Atomic Energy Agency, Vienna, 1987), Vol. I. p. 159], where the $q$ profile is changed in time during the discharge. Once an expression for the consistent density profile is known, it is trivial to obtain an expression for $V_p\mathrm{/D,}$ where $V_p$ is the particle pinch velocity and $D$ is the particle diffusion coefficient. This expression is compared with the value of $V_p\mathrm{/D,}$ which is obtained from an analysis, utilizing the ONETWO transport code [R. Dominguez and R. Waltz, Nucl. Fusion 27, 65 (1987)], of certain high confinement mode (H-mode) DIII-D discharges, which are free from edge localized modes. The dependence of density on $q$ can be extended to a dependence of temperature on $q$ through the adiabatic relation. The dependence of temperature on $q$ can then predict one type of cold pulse propagation phenomena. By way of introduction, a simple analogy with a dynamic incompressible fluid system is made.