First observation and interpretation of spontaneous collective radiation from fusion-born ions in a stellarator plasma

Abstract

<jats:title>Abstract</jats:title> <jats:p>During bursty MHD events, transient ion cyclotron emission (ICE) is observed from deuterium plasmas in the large helical device (LHD) heliotron-stellarator. Unusually, the frequencies of the successive ICE spectral peaks are not close to integer multiples of the local cyclotron frequency of an energetic ion population in the likely emitting region. We show that this ICE is probably driven by a subset of the fusion-born protons near their birth energy <jats:inline-formula> <jats:tex-math><?CDATA $E_{H} = 3.02$?></jats:tex-math> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msub> <mml:mi>E</mml:mi> <mml:mrow> <mml:mi>H</mml:mi> </mml:mrow> </mml:msub> <mml:mo>=</mml:mo> <mml:mn>3.02</mml:mn> </mml:math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="ppcfac7892ieqn1.gif" xlink:type="simple" /> </jats:inline-formula> MeV. This subset has a kinetic energy component parallel to the magnetic field, <jats:inline-formula> <jats:tex-math><?CDATA $m_{H}v_{\parallel}^2/2$?></jats:tex-math> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msub> <mml:mi>m</mml:mi> <mml:mrow> <mml:mi>H</mml:mi> </mml:mrow> </mml:msub> <mml:msubsup> <mml:mi>v</mml:mi> <mml:mrow> <mml:mo>∥</mml:mo> </mml:mrow> <mml:mn>2</mml:mn> </mml:msubsup> <mml:mrow> <mml:mo>/</mml:mo> </mml:mrow> <mml:mn>2</mml:mn> </mml:math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="ppcfac7892ieqn2.gif" xlink:type="simple" /> </jats:inline-formula>, significantly greater than its perpendicular energy <jats:inline-formula> <jats:tex-math><?CDATA $m_{H}v_{\perp}^2/2$?></jats:tex-math> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msub> <mml:mi>m</mml:mi> <mml:mrow> <mml:mi>H</mml:mi> </mml:mrow> </mml:msub> <mml:msubsup> <mml:mi>v</mml:mi> <mml:mrow> <mml:mo>⊥</mml:mo> </mml:mrow> <mml:mn>2</mml:mn> </mml:msubsup> <mml:mrow> <mml:mo>/</mml:mo> </mml:mrow> <mml:mn>2</mml:mn> </mml:math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="ppcfac7892ieqn3.gif" xlink:type="simple" /> </jats:inline-formula>, for which <jats:inline-formula> <jats:tex-math><?CDATA $v_{\perp} \sim V_{A}$?></jats:tex-math> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msub> <mml:mi>v</mml:mi> <mml:mrow> <mml:mo>⊥</mml:mo> </mml:mrow> </mml:msub> <mml:mo>∼</mml:mo> <mml:msub> <mml:mi>V</mml:mi> <mml:mrow> <mml:mi>A</mml:mi> </mml:mrow> </mml:msub> </mml:math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="ppcfac7892ieqn4.gif" xlink:type="simple" /> </jats:inline-formula>, the Alfvén speed. First principles computations of the collective relaxation of this proton population, within a majority thermal deuterium plasma, are carried out using a particle-in-cell approach. This captures the full gyro-orbit kinetics of all ions which, together with an electron fluid, evolve self-consistently with the electric and magnetic fields under the Maxwell–Lorentz equations. The simulated ICE spectra are derived from the Fourier transform of the fields which are excited. We find substantial frequency shifts in the peaks of the simulated ICE spectra, which correspond closely to the measured ICE spectra following the resonance condition <jats:inline-formula> <jats:tex-math><?CDATA $\omega = k_{\parallel} v_{\parallel} + n \Omega_{H}$?></jats:tex-math> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mi>ω</mml:mi> <mml:mo>=</mml:mo> <mml:msub> <mml:mi>k</mml:mi> <mml:mrow> <mml:mo>∥</mml:mo> </mml:mrow> </mml:msub> <mml:msub> <mml:mi>v</mml:mi> <mml:mrow> <mml:mo>∥</mml:mo> </mml:mrow> </mml:msub> <mml:mo>+</mml:mo> <mml:mi>n</mml:mi> <mml:msub> <mml:mi mathvariant="normal">Ω</mml:mi> <mml:mrow> <mml:mi>H</mml:mi> </mml:mrow> </mml:msub> </mml:math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="ppcfac7892ieqn5.gif" xlink:type="simple" /> </jats:inline-formula> for <jats:italic>n</jats:italic>th proton harmonic. This suggests that the transient ICE in LHD is generated by the identified subset of the fusion-born protons, relaxing under the magnetoacoustic cyclotron instability. So far as is known, this is the first report of a collective radiation signal from fusion-born ions in anon-tokamak magnetically confined plasma. Disambiguation between two or more energetic ion species that could potentially generate complex observed ICE spectra is an increasing challenge, and the results and methodology developed here will assist this. Our approach is also expected to be relevant to ICE driven by ion beams with lower parallel velocities, for example in cylindrical plasma experiments.</jats:p>