Experimental Study of Trapped-Electron-Mode Properties in Tokamaks: Threshold and Stabilization by Collisions

Trapped electron modes are one of the candidates to explain turbulence driven electron heat transport observed in tokamaks. This instability has two characteristics: a threshold in normalized gradient and stabilization by collisions. Experiments using modulated electron cyclotron heating in the ASDEX Upgrade tokamak demonstrate explicitly the existence of the threshold. The stabilization with increasing collisionality is evidenced by a strong decrease of the propagation of heat pulses, explained by a transition to ion temperature gradient driven transport. These results are supported by linear gyrokinetic calculations.

Figure 1

Upper plot: electron heat flux versus $R/L_{T_e}$, experimental data, and simulations with the empirical model. The line indicates the growth rate of the TEM at the maximum of $\gamma /k_{\perp }^2$. Lower plot: ${\chi }_e^{\mathrm{amp}}$ and ${\chi }_e^{\mathrm{phase}}$ versus $R/L_{T_e}$. Experimental data and results from modeling as indicated by the legend.

Figure 2

Left plot: ${\chi }_e^{\mathrm{HP}}$ and ${\chi }_e^{\mathrm{PB}}$ versus $\rho$ for different values of ${\overline{n}}_e$ in ${10}^{19}{\mathrm{m}}^{-3}$ indicated in the plot. The symbols show ${\chi }_e^{\mathrm{HP}}$ and the lines ${\chi }_e^{\mathrm{PB}}$, which decreases with ${\overline{n}}_e$ for the 3 values 2.5, 3.3, and $3.7\times {10}^{19}{\mathrm{m}}^{-3}$. Right plot: Ratio ${\chi }_e^{\mathrm{HP}}/{\chi }_e^{\mathrm{PB}}$ versus normalized ${\nu }_{\mathrm{eff}}$.

Figure 3

Stability diagrams for TEM and ITG showing contours of the mode frequency—positive for ITG, negative for TEM, versus the collisionality used in GS2. In the left plot $T_e/T_i=1.8$, in the right plot $R/L_{T_e}=10$. The range of the experiment is indicated by the dashed polygons.

Figure 4

Upper plots: Electron and ion heat fluxes from the GS2 calculations versus $R/L_{T_e}$ in the TEM-dominated and ITG-dominated cases. Lower plots: ${\chi }_e^{\mathrm{PB}}$ and ${\chi }_e^{\mathrm{PB}}$ derived from the curves given in the upper plots. The experimental value of $R/L_{T_e}$ is at about 10.