Toroidal Alfvén eigenmodes observed in low power JET deuterium–tritium plasmas
James Oliver, S. E. Sharapov, Ž. Štancar, Michael L. Fitzgerald, E. Tholerus, B. N. Breǐzman, M. Dreval, J. Ferreira, A. Figueiredo, J. García, N. Hawkes, D. Keeling, P. Puglia, P. Rodrigues, R. A. Tinguely, JET Contributors
Abstract
Abstract The Joint European Torus recently carried out an experimental campaign using a plasma consisting of both deuterium (D) and tritium (T). We observed a high-frequency mode using a reflectometer and an interferometer in a D-T plasma heated with low power neutral beam injection, <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msub> <mml:mi>P</mml:mi> <mml:mrow> <mml:mi mathvariant="normal">N</mml:mi> <mml:mi mathvariant="normal">B</mml:mi> <mml:mi mathvariant="normal">I</mml:mi> </mml:mrow> </mml:msub> <mml:mo>=</mml:mo> <mml:mn>11.6</mml:mn> <mml:mrow> <mml:mtext>MW</mml:mtext> </mml:mrow> </mml:math> . This mode was observed at a frequency <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mi>f</mml:mi> <mml:mo>=</mml:mo> <mml:mn>156</mml:mn> <mml:mrow> <mml:mtext>kHz</mml:mtext> </mml:mrow> </mml:math> and was located at major radii <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:mn>3.1</mml:mn> <mml:mo>⩽</mml:mo> <mml:mi>R</mml:mi> <mml:mo stretchy="false">(</mml:mo> <mml:mtext>m</mml:mtext> <mml:mo stretchy="false">)</mml:mo> <mml:mo>⩽</mml:mo> <mml:mn>3.3</mml:mn> </mml:mrow> </mml:math> . The observed mode was identified as a toroidal Alfvén eigenmode (TAE) using the linear MHD code, MISHKA. Beam ions and fusion-born alpha particles were modelled using the full orbit particle tracking code LOCUST, which produces smooth distribution functions suitable for stability calculations without analytical fits or the use of moments. We calculated the stability of the 21 candidate modes using the HALO code. These calculations revealed that beam ions can drive TAEs with toroidal mode numbers <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mi>n</mml:mi> <mml:mo>⩾</mml:mo> <mml:mn>8</mml:mn> </mml:math> with linear growth rates <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msub> <mml:mi>γ</mml:mi> <mml:mi>b</mml:mi> </mml:msub> <mml:mrow> <mml:mo>/</mml:mo> </mml:mrow> <mml:mi>ω</mml:mi> <mml:mo>∼</mml:mo> <mml:mn>1</mml:mn> <mml:mi mathvariant="normal">%</mml:mi> </mml:math> , while TAEs with n < 8 are damped by the beam ion population. Alpha particles drive modes with significantly smaller linear growth rates, <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:msub> <mml:mi>γ</mml:mi> <mml:mi>α</mml:mi> </mml:msub> <mml:mo>/</mml:mo> <mml:mi>ω</mml:mi> <mml:mo>≲</mml:mo> <mml:mn>0.1</mml:mn> <mml:mi>%</mml:mi> </mml:mrow> </mml:math> due to the low alpha power generated almost exclusively by beam-thermal fusion reactions. Non-ideal effects were calculated using complex resistivity in the CASTOR code, leading to an assessment of radiative, collisional, and continuum damping for all 21 candidate modes. Ion Landau damping was modelled using Maxwellian distribution functions for bulk D and T ions in HALO. Radiative damping, the dominant bulk damping mechanism, suppresses modes with high toroidal mode numbers. Comparing the drive from energetic particles with damping from thermal particles, we find all but one of the candidate modes are damped. The single net-driven n = 9 TAE with a net growth rate <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msub> <mml:mi>γ</mml:mi> <mml:mrow> <mml:mi mathvariant="normal">n</mml:mi> <mml:mi mathvariant="normal">e</mml:mi> <mml:mi mathvariant="normal">t</mml:mi> </mml:mrow> </mml:msub> <mml:mrow> <mml:mo>/</mml:mo> </mml:mrow> <mml:mi>ω</mml:mi> <mml:mo>=</mml:mo> <mml:mn>0.02</mml:mn> <mml:mi mathvariant="normal">%</mml:mi> </mml:math> matches experimental observations with a lab frequency <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mi>f</mml:mi> <mml:mo>=</mml:mo> <mml:mn>163</mml:mn> <mml:mrow> <mml:mtext>kHz</mml:mtext> </mml:mrow> </mml:math> and location <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mi>R</mml:mi> <mml:mo>=</mml:mo> <mml:mn>3.3</mml:mn> <mml:mrow> <mml:mtext>m</mml:mtext> </mml:mrow> </mml:math> . The TAE was driven by co-passing particles through the <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msub> <mml:mi>v</mml:mi> <mml:mo>∥</mml:mo> </mml:msub> <mml:mo>=</mml:mo> <mml:msub> <mml:mi>v</mml:mi> <mml:mi>A</mml:mi> </mml:msub> <mml:mrow> <mml:mo>/</mml:mo> </mml:mrow> <mml:mn>5</mml:mn> </mml:math> resonance. Both co- and counter-passing alpha particles drive the TAE through the <mml:math xmlns:mml="http://www.