Distinct stages of radio frequency emission at the onset of pedestal collapse in KSTAR H-mode plasmas
Using a high-speed and broadband radio frequency (RF) (0.1–1 GHz) spectrum analyzer developed on the KSTAR tokamak, it is found that several distinct stages of RF emission appear at the pedestal collapse in high confinement discharges. Comparison with 2D electron cyclotron emission (ECE) images has revealed that each stage is related to the instantaneous condition at the outboard mid-plane edge. First, high-harmonic ion cyclotron emissions (ICE) are intensified with the appearance of a non-modal filamentary perturbation in the edge within several tens of microseconds before the collapse. Then, the RF emission becomes broad toward high-frequency range (<500 MHz) at the burst onset of the non-modal filament. During the pedestal collapse initiated by the filament burst, rapid chirping (1–3 μs) appear with additional filament bursts. The strong correlation between the RF spectra and the perturbation structure provides important clues on the stability of edge-localized modes and on the ion dynamics in the plasma boundary.
Comparing theory and simulation of ion cyclotron emission from energetic ion populations with spherical shell and ring-beam distributions in velocity-space
Observations have recently been made of ion cyclotron emission (ICE) that originates from the core plasma in the DIII-D (Thome et al 2018 Rev. Sci. Instrum. 89 10I102, Thome et al 2019 Nucl. Fusion http://iopscience.iop.org/10.1088/1741-4326/ab20e7) and ASDEX-Upgrade (Ochoukov et al 2018 Rev. Sci. Instrum. 89 10J101, Ochoukov et al 2019 Nucl. Fusion 59 014001) 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 (D’Inca 2014 Ion Cyclotron Emission on ASDEX Upgrade PhD Thesis Ludwig-Maximilians-Universitat), 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 simulations 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.
Modeling of chemical reactors—XXIX mixing-cell model for packed bed reactors. Steady state considerations. Problems of multiplicity
Abstract The axial heat and mass transfer in tubular catalytic reactors may be described by mixing-cell model and diffusion model as well. The diffusion description yields for a strong exothermic reaction and adiabatic conditions three steady state profiles, on the other hand the mixing-cell model gives rise to more than three steady states. A simple numerical and graphical analysis for mixing-cell model is presented.