Triggers for plasma detachment bifurcation in the edge divertor region of tokamaks

TL;DR

The study investigates the trigger and dynamics of detachment bifurcation in the edge divertor of tokamaks using steady-state and time-dependent UEDGE simulations in forward $B_T$ configurations. A detachment bifurcation is shown to occur when the high-field-side radiation front crosses the LCFS and stabilizes just above the X-point, causing a local $T_e$ cliff (e.g., $T_{e,X}$ dropping from $\sim66$–$68$ eV to $\sim10$ eV) and a reversal of the $E\times B$ flow in the private flux region near the X-point. Time-dependent results reveal a two-phase mechanism: Phase I involves the radiation-front crossing and a rapid, oscillatory reduction of $T_e$ above the X-point, plus a shift in the X-point potential that reverses the PFR $E\times B$ flow within $<0.5$ ms; Phase II sees the reversed flow drive a rapid outer-target $T_e$ collapse ($\sim$1–2 ms) and deep detachment, with transport along the outer leg contributing to the observed timescales. The bifurcation hinges on in–out divertor asymmetry and asymmetric radiation-front evolution, and the work provides insights for detachment control under forward $B_T$ conditions.

Abstract

We report the discovery of the trigger for detachment bifurcation phenomenon in tokamak divertors, revealed through steady-state and time-dependent UEDGE simulations: The observed electron temperature cliff at the outer target in DIII-D H-mode plasmas with ion $B\times \nabla B$ drift driven into the active divertor results from a bifurcation-induced $T_e$ drop above the X-point accompanied by reversal of the $E\times B$ flow pattern in the private flux region. Time-dependent simulations reveal a two-phase transition mechanism: the high-field-side radiation front first extends across the last closed flux surface and stabilizes above the X-point, causing local $T_e$ to drop from $\sim 70\,\mathrm{eV}$ to $\sim 10\,\mathrm{eV}$ and inducing $E\times B$ flow reversal in a thin layer below the X-point, which lasts $< 0.5\,\mathrm{ms}$; Flow reversal below the X-point subsequently triggers the sharp drop in outer target temperature on a timescale of $1-2\,\mathrm{ms}$, establishing deep detachment a few ms thereafter. A bifurcation transition occurs when the high-field-side radiation front crosses the separatrix while the outer divertor remains attached, with the $T_e$ cliff manifesting distinctly when the outer target $T_e \gtrsim 10\,\mathrm{eV}$ prior to the bifurcation. These results demonstrate that the bifurcation is linked to in-out divertor asymmetry and asymmetric radiation front evolution.

Figures (6)

• Figure 1: Peak electron temperature on the outer target from steady-state UEDGE solutions with forward (solid) and backward (dashed) scan of core boundary density with input powers $P=1\,\mathrm{MW}$ (blue) and $P=3\,\mathrm{MW}$ (orange).
• Figure 2: Steady state profiles (zoom-in view of the X-point divertor region) of radiation $P_\mathrm{rad}$ (left column), electron temperature $T_e$ (middle), and potential $\Phi$ (right) with the density $n = 6.2\times 10^{19}\mathrm{m}^{-3}$ slightly lower (top row) and $n = 6.3\times 10^{19}\mathrm{m}^{-3}$ higher (bottom) than the bifurcation transition density, with $P_\mathrm{SOL}=3\,\mathrm{MW}$.
• Figure 3: Steady-state integrated total poloidal ion particle fluxes (solid) and poloidal $E\times B$ ion particle fluxes (dashed) over the PFR mid-surface (marked green in Fig. \ref{['Fig:Xloc']}) as a function core boundary density with input powers $P_\mathrm{SOL}=1\,\mathrm{MW}$ (blue) and $P_\mathrm{SOL}=3\,\mathrm{MW}$ (orange).
• Figure 4: Time-dependent UEDGE solutions of 2D profiles of total radiation $P_\mathrm{rad}$ (top row), electron temperature $T_e$ (middle), and electric potential $\Phi$ (bottom) at time slice of $11.6\,\mathrm{ms}$ (first column), $12.0\,\mathrm{ms}$ (second), $12.5\,\mathrm{ms}$ (third), $13.5\,\mathrm{ms}$ (fourth), $16.0\,\mathrm{ms}$ (fifth). corresponding to the 5 vertical dashed lines in Fig. \ref{['Fig:time1D']}.
• Figure 5: Time-dependent UEDGE results showing averaged total radiation $P_\mathrm{rad}$ above and below the X-point, averaged electron temperature $T_e$ above the X-point and peak outer-target $T_e$, averaged electric potential $\Phi$ above and below the X-point, and poloidal $E\times B$ flux integrated in the PFR below the X-point (solid: mid-surface; dashed: $\sim 4\,\mathrm{cm}$ below the X-point; see Fig. \ref{['Fig:Xloc']}). Averages above (below) the X-point are taken over the four cells marked orange (blue) in Fig. \ref{['Fig:Xloc']}. The right panel shows a zoom of 11.6–12 ms, including the radial position ($\psi_\mathrm{N}$) of the HFS radiation front near the X-point (green, top row).