Electron Transport Stiffness and Heat Pulse Propagation on DIII-D

Experiments on \hbox{DIII-D} have measured the stiffness of electron heat transport using a new method that combines heat pulse (HP) propagation and power balance (PB) analysis. Using a single modulated gyrotron, in addition to 5~cw gyrotrons, the radial profiles of $T_e$ oscillations from the fundamental to the 9$^{\rm th}$ harmonic are fit to determine the diffusion (D$_{\rm HP}$), convection (V$_{\rm HP}$) and damping coefficients. The $T_e$ gradient is then systematically scanned by varying the electron cyclotron heating profile on a shot-by-shot basis using the cw gyrotrons. Numerically integrating D$_{\rm HP}$ over this scan gives D$_{\rm PB}$, and the difference between the diffusive heat flux from D$_{\rm PB}$ and the total power-balance heat flux determines V$_{\rm PB}$. The ratio of D$_{\rm HP}$ to D$_{\rm PB}$ measures the transport stiffness, defined as the fractional increase in diffusive heat flux divided by the fractional increase in the $T_e$ gradient. In \hbox{L-mode} plasmas, a sudden increase in electron transport stiffness is seen when the $T_e$ scale length exceeds the theoretically predicted threshold value. Similar electron transport stiffness is observed with and without additional NBI.