Thermal transport induced by stochastic magnetic fields and turbulence during the thermal quench in tokamak plasmas

Abstract The timescale of thermal quench (TQ) remains a long-lasting issue in tokamak plasmas, which has not been fully understood yet. In this work, based on our previous thermal diffusion model and further considering the scattering caused by the electrostatic turbulence into account, a more generalized evolution equation of the electron temperature is derived from the electron drift-kinetic equation. This equation is applicable to all collisional regimes and a wide range of the stochastic magnetic fields (SMF) amplitude <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:mrow> <mml:msub> <mml:mrow> <mml:mover> <mml:mi>b</mml:mi> <mml:mo stretchy="true">~</mml:mo> </mml:mover> </mml:mrow> <mml:mi>r</mml:mi> </mml:msub> </mml:mrow> </mml:mrow> </mml:math> . On the one hand, the heat flux induced by the <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:mrow> <mml:mover> <mml:mrow> <mml:mi mathvariant="bold">E</mml:mi> </mml:mrow> <mml:mo stretchy="true">~</mml:mo> </mml:mover> </mml:mrow> <mml:mo>×</mml:mo> <mml:mrow> <mml:mrow> <mml:mi mathvariant="bold">B</mml:mi> </mml:mrow> </mml:mrow> </mml:mrow> </mml:math> drift is comparable to that induced by the SMF under DIII-D parameters, but becomes negligible under International Tokamak Experimental Reactor (ITER)-like parameters. However, the overall impact of electrostatic turbulence appears to be insignificant in both scenarios. This is because the direct transport caused by <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:mrow> <mml:mover> <mml:mrow> <mml:mi mathvariant="bold">E</mml:mi> </mml:mrow> <mml:mo stretchy="true">~</mml:mo> </mml:mover> </mml:mrow> <mml:mo>×</mml:mo> <mml:mrow> <mml:mrow> <mml:mi mathvariant="bold">B</mml:mi> </mml:mrow> </mml:mrow> </mml:mrow> </mml:math> drift is basically counterbalanced by the reduction of the transport induced by the SMF due to the modification effect of electrostatic turbulence. On the other hand, numerical results indicate the timescale of the TQ is strongly dependent on the SMF amplitude and can reach the order of 100 <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:mrow> <mml:mtext>us</mml:mtext> </mml:mrow> </mml:mrow> </mml:math> when <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:mrow> <mml:msub> <mml:mrow> <mml:mover> <mml:mi>b</mml:mi> <mml:mo stretchy="true">~</mml:mo> </mml:mover> </mml:mrow> <mml:mi>r</mml:mi> </mml:msub> </mml:mrow> <mml:mo>∼</mml:mo> <mml:mrow> <mml:msup> <mml:mn>10</mml:mn> <mml:mrow> <mml:mo>−</mml:mo> <mml:mn>2</mml:mn> </mml:mrow> </mml:msup> </mml:mrow> </mml:mrow> </mml:math> . The scaling of TQ timescale being approximately proportional to device size remains invariant under varying SMF amplitudes, and the extrapolations from DIII-D to ITER-like case based on this scaling demonstrate alignment with numerical results. It is also shown that the collisionality-dependent and SMF amplitude-dependent of thermal diffusivity should be carefully considered to predict the TQ timescale. Moreover, it is also discussed that SMF amplitude exceeding 4 × 10 −3 would lead to unacceptable thermal loading on divertor target during TQ in ITER.