On how avalanches penetrate the SOL and broaden heat loads

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 <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:mo stretchy="false">(</mml:mo> <mml:mi mathvariant="normal">∇</mml:mi> <mml:mrow> <mml:mover> <mml:mi>T</mml:mi> <mml:mo stretchy="true">~</mml:mo> </mml:mover> </mml:mrow> <mml:msub> <mml:mo stretchy="false">)</mml:mo> <mml:mrow> <mml:mi>rms</mml:mi> </mml:mrow> </mml:msub> <mml:mo>&gt;</mml:mo> <mml:mi mathvariant="normal">∇</mml:mi> <mml:msub> <mml:mrow> <mml:mover> <mml:mi>T</mml:mi> <mml:mo stretchy="true">~</mml:mo> </mml:mover> </mml:mrow> <mml:mrow> <mml:mi>crit</mml:mi> </mml:mrow> </mml:msub> </mml:mrow> </mml:math> at the separatrix are predicted to penetrate, and so broaden the SOL and heat load distribution. <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:mi mathvariant="normal">∇</mml:mi> <mml:msub> <mml:mrow> <mml:mover> <mml:mi>T</mml:mi> <mml:mo stretchy="true">~</mml:mo> </mml:mover> </mml:mrow> <mml:mrow> <mml:mi>crit</mml:mi> </mml:mrow> </mml:msub> </mml:mrow> </mml:math> is <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:mo>∼</mml:mo> <mml:mn>1</mml:mn> <mml:mrow> <mml:mo>/</mml:mo> </mml:mrow> <mml:msub> <mml:mi>τ</mml:mi> <mml:mo>∥</mml:mo> </mml:msub> </mml:mrow> </mml:math> , where <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:msub> <mml:mi>τ</mml:mi> <mml:mo>∥</mml:mo> </mml:msub> </mml:mrow> </mml:math> 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.