Dependence of ion-cyclotron range of frequencies instabilities on species mix and fast-ion distribution: I. Stability

Abstract Ion cyclotron emission (ICE) driven by fast ions has the potential to be a reactor relevant diagnostic of confined and escaping fast ions; moreover, controlled experiments in magnetic fusion devices can shed light on similar magnetospheric instabilities below and above the ion cyclotron frequency <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:msub> <mml:mi>f</mml:mi> <mml:mrow> <mml:mi>ci</mml:mi> </mml:mrow> </mml:msub> </mml:mrow> </mml:math> . Dedicated DIII-D experiments studied instabilities below <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:msub> <mml:mi>f</mml:mi> <mml:mrow> <mml:mi>ci</mml:mi> </mml:mrow> </mml:msub> </mml:mrow> </mml:math> and at cyclotron harmonics <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:mi>l</mml:mi> <mml:msub> <mml:mi>f</mml:mi> <mml:mrow> <mml:mi>ci</mml:mi> </mml:mrow> </mml:msub> </mml:mrow> </mml:math> by injecting thirteen different neutral beam populations into plasmas with different thermal compositions of H, D, and 3 He at five different values of toroidal field. High-frequency magnetic loops diagnose mode properties. Each beam type is individually injected for an approximate slowing-down time ( <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:mrow> <mml:mo>∼</mml:mo> </mml:mrow> <mml:mn>100</mml:mn> </mml:mrow> </mml:math> ms), resulting in a database of 2529 conditions that are analyzed in frequency bands corresponding to ICE harmonics and <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:mo>&lt;</mml:mo> <mml:mstyle scriptlevel="0"/> <mml:mstyle scriptlevel="0"/> <mml:msub> <mml:mi>f</mml:mi> <mml:mrow> <mml:mi>ci</mml:mi> </mml:mrow> </mml:msub> </mml:mrow> </mml:math> global Alfvén eigenmodes. The sub-cyclotron modes are more unstable at low field and in plasmas with large H concentration. For D injection, first harmonic ICE at <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:msub> <mml:mi>f</mml:mi> <mml:mrow> <mml:mi>cD</mml:mi> </mml:mrow> </mml:msub> </mml:mrow> </mml:math> is more unstable in hydrogen plasmas but, for H injection, the converse is true (ICE at <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:msub> <mml:mi>f</mml:mi> <mml:mrow> <mml:mi>cH</mml:mi> </mml:mrow> </mml:msub> </mml:mrow> </mml:math> is more unstable in D), suggesting that thermal same-species ions damp fundamental ICE. ICE stability also depends upon the pitch-angle anisotropy gradient and upon the ‘bump-on-tail’ gradient <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:mi>∂</mml:mi> <mml:mi>f</mml:mi> <mml:mrow> <mml:mo>/</mml:mo> </mml:mrow> <mml:mi>∂</mml:mi> <mml:mi>v</mml:mi> </mml:mrow> </mml:math> . Although the frequency of unstable ICE in these plasmas always occurs near the central cyclotron frequency, the precise value also depends on the Alfvén speed and beam direction, consistent with the idea that instability occurs for modes that simultaneously satisfy <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:mi>ω</mml:mi> <mml:mo>≃</mml:mo> <mml:mn>2</mml:mn> <mml:mi>π</mml:mi> <mml:mi>l</mml:mi> <mml:msub> <mml:mi>f</mml:mi> <mml:mrow> <mml:mi>ci</mml:mi> </mml:mrow> </mml:msub> </mml:mrow> </mml:math> , the magnetosonic dispersion relation, and the Doppler-shifted resonance condition.