On How Avalanches Penetrate the SOL and Broaden Heat Loads

TL;DR

The paper addresses how heat avalanches can penetrate the SOL and broaden the SOL width by deriving a shock-based threshold within a damped Burgers framework for the SOL temperature perturbation. A critical condition $|\partial_r\delta T|_{rms,sep}>1/(\alpha\tau_\parallel)$ (equivalently $|\partial_\xi\hat{\delta T}|>1/\hat{v}_{NL}$) governs penetration, where parallel damping competes with nonlinear steepening; penetration leads to SOL broadening beyond the heuristic drift limit. Numerical experiments with isolated pulses and dynamic boundary forcing show that deeper penetration correlates positively with the nonlinear drive parameter $v_{NL}$ and can be enhanced by shocks and front propagation. The work connects observed $D_\alpha$-related heat-load signatures to nonlocal avalanche dynamics, providing a criterion for penetration and guidance for interpreting experiments and improving simulations (e.g., BOUT++) of SOL transport.

Abstract

Recent experiments reported a correlation between power law core temperature spectra and $D_α$ emission, suggesting that heat avalanches penetrate the SOL. This paper derives a threshold criterion for avalanche penetration using a reduced model. Avalanches with $(\nabla\tilde T)_{rms}>\nabla\tilde T_{crit}$ at the separatrix are predicted to penetrate, and so broaden the SOL and heat load distribution. $\nabla\tilde T_{crit}$ is $\sim 1/τ_\parallel$, where $τ_\parallel$ is the parallel heat flow time through the SOL. Penetration occurs when avalanches are strong enough to steepen sufficiently to shock at the separatrix. A positive correlation is found between the nonlinear drive for steepening and the penetration depth. In particular, penetration depth exceeds that of the heuristic drift limit when shocks form. Implications for numerical and physical experiments are also discussed.

Figures (16)

• Figure 1: A schematic picture of non-local drive of turbulence in the SOL. Avalanches and turbulence can propagate from the main plasma to reach the LCFS and to penetrate and broaden the SOL.
• Figure 2: A schematic picture of the dependence of the heat flux SOL width on the root-mean square value of the temperature perturbation at the LCFS. When the temperature perturbation at the LCFS exceeds a critical value, the width can exceed that of the heuristic drift model.
• Figure 3: Demonstration of Burgers equation having solutions with joint reflection symmetry
• Figure 4: Avalanches in the SOL suffer additional damping from the parallel loss.
• Figure 5: Characteristics for damped Burgers equation. The yellow curve intersects the blue curve, at which point discontinuity forms and shock formation is expected. For the green curve, this is not the case. The condition for intersection, or shock formation, is set by the gradient of initial data (Eq.(\ref{['Eq:ShockCondition']})).