Measurements of the polarization of several instabilities in the DIII-D tokamak

Abstract Recently, a method to infer the polarization of modes with frequencies much less than the ion cyclotron frequency was published (Du et al 2024 Phys. Rev. Lett. 132 215101). The method uses measurements of electron temperature and density fluctuations <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:mi>δ</mml:mi> <mml:msub> <mml:mi>T</mml:mi> <mml:mrow> <mml:mi mathvariant="normal">e</mml:mi> </mml:mrow> </mml:msub> </mml:mrow> </mml:math> and <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:mi>δ</mml:mi> <mml:msub> <mml:mi>n</mml:mi> <mml:mrow> <mml:mi mathvariant="normal">e</mml:mi> </mml:mrow> </mml:msub> </mml:mrow> </mml:math> at the same spatial position to infer the local ratio of ‘acoustic polarization,’ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:mo stretchy="false">|</mml:mo> <mml:mi>δ</mml:mi> <mml:msub> <mml:mi>ϕ</mml:mi> <mml:mo>∥</mml:mo> </mml:msub> <mml:mrow> <mml:mo stretchy="false">|</mml:mo> </mml:mrow> <mml:mrow> <mml:mo>/</mml:mo> </mml:mrow> <mml:mo stretchy="false">(</mml:mo> <mml:mrow> <mml:mo stretchy="false">|</mml:mo> </mml:mrow> <mml:mi>δ</mml:mi> <mml:msub> <mml:mi>ϕ</mml:mi> <mml:mo>∥</mml:mo> </mml:msub> <mml:mrow> <mml:mo stretchy="false">|</mml:mo> </mml:mrow> <mml:mo>+</mml:mo> <mml:mrow> <mml:mo stretchy="false">|</mml:mo> </mml:mrow> <mml:mi>δ</mml:mi> <mml:mi>ψ</mml:mi> <mml:mrow> <mml:mo stretchy="false">|</mml:mo> </mml:mrow> <mml:mo stretchy="false">)</mml:mo> </mml:mrow> </mml:math> , where <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:mi>δ</mml:mi> <mml:msub> <mml:mi>ϕ</mml:mi> <mml:mo>∥</mml:mo> </mml:msub> </mml:mrow> </mml:math> is the effective parallel potential and δψ is related to the parallel magnetic vector potential <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:msub> <mml:mi>A</mml:mi> <mml:mo>∥</mml:mo> </mml:msub> </mml:mrow> </mml:math> . This paper summarizes key formulas, with emphasis on their range of validity, and elaborates on the workflow required to infer the acoustic polarization from experimental data. The drift-acoustic polarization of ellipticity-induced, toroidicity-induced, and reversed shear Alfvén eigenmodes (AEs) is nearly zero, as expected for modes with predominately shear-Alfvénic polarization. The polarization of beta-induced AEs contains an acoustic component that increases with poloidal wave number. ‘Low frequency modes,’ (instabilities that appear transiently when the minimum of the safety factor <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:msub> <mml:mi>q</mml:mi> <mml:mrow> <mml:mi>min</mml:mi> </mml:mrow> </mml:msub> </mml:mrow> </mml:math> passes through rational values) have large and highly variable acoustic polarization. In both experiment and simulation, fishbones have non-zero acoustic polarization that increases as the mode chirps down in frequency.