How fluctuation intensity flux drives SOL expansion

Abstract

Abstract Predictions of heat load widths <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:msub> <mml:mi>λ</mml:mi> <mml:mi>q</mml:mi> </mml:msub> </mml:mrow> </mml:math> based on particle orbits alone are very pessimistic. This paper shows that pedestal peeling-ballooning (P-B) magnetohydrodynamic (MHD) turbulence broadens the stable scrape-off layer (SOL) by the transport, or spreading, of fluctuation energy from the pedestal. <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:msub> <mml:mi>λ</mml:mi> <mml:mi>q</mml:mi> </mml:msub> </mml:mrow> </mml:math> is seen to increase with <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:msub> <mml:mi mathvariant="normal">Γ</mml:mi> <mml:mi>ε</mml:mi> </mml:msub> </mml:mrow> </mml:math> , the fluctuation energy density flux. We elucidate the fundamental physics of the spreading process. <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:msub> <mml:mi mathvariant="normal">Γ</mml:mi> <mml:mi>ε</mml:mi> </mml:msub> </mml:mrow> </mml:math> increases with pressure fluctuation correlation length. P-B turbulence is seen to be especially effective at spreading, on account of its large effective mixing length. Spreading is shown to be a multiscale process, which is enhanced by the synergy of large and small-scale modes. Pressure fluctuation skewness correlates well with the spreading flux–with the zero crossing of skewness and <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:msub> <mml:mi mathvariant="normal">Γ</mml:mi> <mml:mi>ε</mml:mi> </mml:msub> </mml:mrow> </mml:math> spatially coincident–suggesting the role of coherent fluctuation structures and the presence of intermittency in <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:msub> <mml:mi>λ</mml:mi> <mml:mi>q</mml:mi> </mml:msub> </mml:mrow> </mml:math> broadening. <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:msub> <mml:mi>λ</mml:mi> <mml:mi>q</mml:mi> </mml:msub> </mml:mrow> <mml:mo>∼</mml:mo> <mml:msubsup> <mml:mi>B</mml:mi> <mml:mrow> <mml:mtext>p</mml:mtext> </mml:mrow> <mml:mrow> <mml:mo>−</mml:mo> <mml:mn>1</mml:mn> </mml:mrow> </mml:msubsup> </mml:math> scaling persists for the broadened SOL. We show that the spreading flux increases for increasing pedestal pressure gradient <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mi mathvariant="normal">∇</mml:mi> <mml:mrow> <mml:msub> <mml:mi>P</mml:mi> <mml:mn>0</mml:mn> </mml:msub> </mml:mrow> </mml:math> and for decreasing pedestal collisionality <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msubsup> <mml:mi>υ</mml:mi> <mml:mrow> <mml:mrow> <mml:mtext>ped</mml:mtext> </mml:mrow> </mml:mrow> <mml:mo>∗</mml:mo> </mml:msubsup> </mml:math> . This trend is due to the dominance of peeling modes for large <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mi mathvariant="normal">∇</mml:mi> <mml:mrow> <mml:msub> <mml:mi>P</mml:mi> <mml:mn>0</mml:mn> </mml:msub> </mml:mrow> </mml:math> and low <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msubsup> <mml:mi>υ</mml:mi> <mml:mrow> <mml:mrow> <mml:mtext>ped</mml:mtext> </mml:mrow> </mml:mrow> <mml:mo>∗</mml:mo> </mml:msubsup> </mml:math> . Ultimately, we see that a state of weak MHD turbulence, as for small ELMs, is very attractive for heat load management. Our findings have transformative implications for future fusion reactor designs and call for experimental investigations to validate the observed trends.