Comparing theory and simulation of ion cyclotron emission from energetic ion populations with spherical shell and ring-beam distributions in velocity-space

Abstract

Observations have recently been made of ion cyclotron emission (ICE) that originates from the core plasma in the DIII-D [1, 2] and ASDEX-Upgrade [3, 4] tokamaks. The ICE spectral peaks correspond to the local cyclotron harmonic frequencies of fusion-born ions close to the magnetic axis, in contrast to the hitherto usual spatial localisation of the ICE source to the outer midplane edge in tokamak and stellarator plasmas. Core ICE is temporally transient, and may sometimes be caused by the rapid onset and increase of local fusion reactivity. This would give rise to a highly non-Maxwellian population of fusion-born ions near their birth energy. In an idealised deuterium-tritium plasma, this distribution would initially be a thin spherical shell in velocity-space. For as long as it persists, as pointed out in Ref.[5], the shell might drive the magnetoacoustic cyclotron instability (MCI), which is the excitation process which underlies ICE. Here we present, under core plasma conditions, direct numerical simulations of ICE generation by a spherical shell distribution of fusion-born ions in velocity-space. These energetic minority ions are found to relax collectively in particle-in-cell (PIC) computations which follow their self-consistent gyro-orbit- resolved dynamics, together with that of the majority thermal ions and electrons, under the Maxwell-Lorentz system of equations. We relate the computational outputs, which extend into the nonlinearly saturated regime of the MCI, to the analytical theory of the linear MCI for shell-type energetic ion distributions, and to fully nonlinear simulations of related ring-beam energetic ion distributions relaxing under the MCI. We find that the MCI is excited in all cases, and that the linear growth phase of the shell simula- tions typically takes almost twice as long to reach saturation than in the ring-beam simulations. It is shown that for both types of velocity distribution, nonlinear wave- wave interactions play a vital role in the excitation of the ICE spectral peaks at lower cyclotron harmonics which are typically detected in experiments. We conclude that in future simulations for ICE interpretation, ring-beam distributions may provide an acceptable proxy for shell distributions, while using significantly fewer computational particles and still maintaining a satisfactory signal-to-noise ratio.