Ion Cyclotron Harmonics Research Articles

Stability analysis of plasma waves driven by runaway electrons in tokamak hot plasmas

The local stability analysis of plasma waves driven by runaway electrons (REs) has been performed considering hot plasma Maxwellian background, with electron and ion temperatures of the order of 1 keV. It is shown that hot plasma waves, namely electron plasma waves (EPWs) and ion Bernstein waves (IBWs) can be driven unstable by RE at their coalescence frequency via Cherenkov resonance by RE with energy distribution peaked at about 8 MeV. A skew-normal distribution is used as a model of the RE energy distribution. The EPW and IBW couples of waves occur between any successive ion-cyclotron harmonics frequencies nf ci, above the lower hybrid resonance. At their confluence, the perpendicular group velocity vanishes and significant RF emissions are expected. The frequency gap between two successive confluences is ∼f ci. Groups of RF line emissions, separated by almost constant frequency gap ∼f ci/2 are detected during various quiescent runaway plasma discharges in the FTU tokamak. The analysis of a specific discharge suggests that the frequencies of the line emissions observed and the frequencies occurring at the EPW-IBW confluences are in reasonable agreement. A possible explanation of the line emissions with ∼f ci/2 gap in terms of nonlinear mode coupling is proposed.

Ion cyclotron emission in Maxwellian plasmas

Destabilization of ion cyclotron waves—waves with frequencies close to ion cyclotron harmonics—in inhomogeneous plasmas with Maxwell velocity distribution is considered. A new mechanism of destabilization of these waves is found, whereas the known interaction between cyclotron waves and drift waves is shown to be hardly able to lead to instabilities in realistic tokamak plasmas. Our finding is that the resonance wave–particle interaction in the presence of temperature gradient can change the diamagnetic drift frequency in such a way that the destabilizing influence of the diamagnetic drift exceeds Landau damping. This occurs when the energy of resonance particles is sufficiently high, which is always the case due to the infinite tail of the Maxwell distribution. Particles with higher energies provide a larger ratio of drive to damping, but the number of resonance particles and, thus, instability growth rates are exponentially small when particle energy is very high. Therefore, only moderately suprathermal particles can lead to observable instabilities. A condition for instabilities driven by these particles is obtained. Destabilization of electrostatic cyclotron waves and ordinary cyclotron waves is studied.

Evaluation of Particle Scattering by Oxygen Ion Cyclotron Harmonic Waves in the Inner Magnetosphere

AbstractThe scattering of charged particles by oxygen ion cyclotron harmonic (OCH) waves in the inner magnetosphere is investigated by evaluating the relevant quasi‐linear diffusion coefficients. Recent studies demonstrated that OCH waves are oxygen ion Bernstein modes and their complex kinetic dispersion relation has made it challenging to assess their role in scattering charged particles. The present study calculates the quasi‐linear diffusion coefficients for the scattering of electrons and ions by OCH waves using their kinetic dispersion relation. The results show that OCH waves can effectively scatter electrons between ∼100 eV and 100s keV via Landau resonance. They are also capable of heating cold helium and oxygen ions through cyclotron resonances. Specially, it is found that the 4th harmonic of OCH waves can lead to effective heating of helium ions, while oxygen ions would interact more efficiently with lower harmonics of OCH waves.

The ion cyclotron parametric instabilities and the anomalous heating of ions in the scrape-off layer of tokamak plasma in the high harmonic fast wave heating regime

The electrostatic parametric instabilities of a plasma, driven by the high harmonic fast wave (HHFW) with frequency at ion cyclotron (IC) harmonics of order 30–50 are investigated numerically. The derived numerical results are consistent with parametric decay of HHFW into the high harmonic IC (Bernstein) wave and an unobserved IC quasimode under conditions of the negligible small electron Landau damping. The detected instability develops in the finite interval of the HHFW wavelength along the toroidal magnetic field. The development of this ion kinetic quasimode decay instability is accompanied by the anomalous anisotropic heating of ions, resulted from the interaction of ions with IC parametric turbulence. It was found that the anomalous heating rate of ions across the magnetic field is much larger than the heating rate of ions along the magnetic field. The anisotropic heating of the scrape-off layer ions was observed on the National Spherical Torus Experiment experiments with HHFW heating and current drive at IC harmonics of order 10 [G. Taylor et al. Phys. Plasmas 17, 056114 (2010), and J. Hosea et al. Phys. Plasmas 15, 056104 (2008)]. The derived results predict that these experimental results will be reproduced qualitatively in the experiments with HHFW heating and current drive using HHFW at IC harmonics of order 30–50.

Bicoherence Analysis of Oxygen Ion Cyclotron Harmonic Waves Observed by Van Allen Probes

AbstractBicoherence analysis is statistically performed for the oxygen ion cyclotron harmonic (OCH) waves observed by Van Allen Probes. While OCH waves and so‐called electromagnetic ion cyclotron harmonics have indistinguishable spectral characteristics in observation, they are believed to be excited by different mechanisms with the latter being suggested to arise from nonlinear wave‐wave coupling. Our result reveals that most of the OCH wave events have small bicoherence indices, so they are unlikely excited by wave‐wave coupling. The result is not much affected by the parameter choice in the bicoherence analysis, although increasing the subinterval length and/or reducing the subinterval overlap increases the chance of getting large bicoherence index values. Furthermore, the examination of two special events with large bicoherence indices shows that the observed phase relationship among different wave components does not align with the expectation from wave‐wave coupling. The events cannot be convincingly confirmed to be generated through wave‐wave coupling.

ICE modes with high wave numbers

This work deals with high-k modes of the ion cyclotron emission (ICE)—the modes with frequencies close to ion cyclotron harmonics and wave numbers well exceeding those of fast magnetoacoustic modes (FMM). These modes exist due to finite Larmor radius of the ions. They are responsible for the ICE recently observed in the DIII-D tokamak [N. A. Crocker et al., Nucl. Fusion 62, 026023 (2022)]. The work is aimed at knowing the radial structure of high-k eigenmodes. Its analysis is relied on a comprehensive study carried out by employing a general dispersion equation for traveling waves, which allowed to group modes and determine conditions of their existence. Differential equations for various eigenmodes (standing waves) were obtained and analyzed. In particular, electrostatic modes and electromagnetic modes with various ratios of the longitudinal phase velocity to the electron thermal velocity were considered. A numerical code solving these equations was developed. It is found that high-k modes with sufficiently large poloidal mode numbers are located at the plasma periphery, and their amplitudes in the plasma core are very small. It is concluded that high-k modes are not an exceptional case, although presumably FMMs can explain most ICE experiments. They exist in plasmas with various magnitudes of β, representing different wave branches associated with finite Larmor radius of the ions. The mentioned experiment on DIII-D is discussed.

Interpretation of ion cyclotron emission from sub-Alfvénic beam-injected ions heated plasmas soon after L-H mode transition in EAST

Ion cyclotron emission (ICE) at deuterium ion cyclotron harmonics, driven by sub-Alfvénic beam-injected deuterium ions, has been observed by the high-frequency B-dot probe in the EAST tokamak. The origin of ICE shifts from the plasma core to the plasma edge soon after an L-H mode transition, where the beam-injected deuterium ions have a relatively peak bump-on tail structure in the energy direction and a very intense pitch angle anisotropy. Based on the fast ion distribution function obtained from the TRANSP/NUBEAM code, together with a linear analysis theory of magnetoacoustic cyclotron instability (MCI), the growth rates of MCI could be calculated. It is shown that MCI, resulting in the generation of obliquely propagating fast Alfvén waves at deuterium ion cyclotron harmonics, can occur under such conditions. And the temporal evolution of the MCI growth rate closely follows that of the observed ICE amplitude in the EAST.

First results from third harmonic ion cyclotron acceleration of deuterium beams in EAST ion heating studies experiments

Recent Experimental Advanced Superconductivity Tokamak experiments have been dedicated to the studies of increasing ion temperature using Neutral Beam Injection (NBI) in synergy with radio-frequency waves in the Ion Cyclotron Range of Frequencies (ICRFs) in third harmonic. They showed that this scenario effectively accelerates fast deuterium ions and produces a larger tail of fast neutrons with E > 3.0 MeV, as measured by Neutron Energy Spectrum. Comparing to the scenario with 2.2 MW NBI alone, adding an addition of 0.3 MW ICRF power leads to an enhancement of fusion yield by 67% (from to ) and an increase of core ion temperature by . Besides, the simulation results of TRANSP show that the neutron yield produced by 0.2 MW ICRF in third harmonic with NBI synergy is roughly consistent with the experimental results. Meanwhile, the 80 keV fast ion tail generated by NBI can be heated up to 400 keV and 600 keV by the 0.2 MW and 1.0 MW ICRF with the synergistic effect, respectively. In addition, it is observed for the first time that this ICRF-NBI synergy leads to the excitation of fishbone instabilities with characteristic frequencies of (10–20) kHz. Furthermore, parameter scans of ICRF/NBI power and plasma density were performed for third harmonic ICRF and NBI synergetic heating schemes. It is found that the neutron yield increases nonlinearly as the ICRF power or plasma density increases.

Bump-on-tail distributions caused by Alfvénic redistribution of energetic ions

A series of experiments was performed in the JET tokamak aiming to study the characteristics and eventual effects of beam injected ion populations further accelerated through 2nd harmonic ion cyclotron heating. It was found that the injection of these ions could affect sawtooth stability and that these populations excite toroidicity induced Alfvén eigenmodes (TAEs) in the core of the plasma. More interestingly, measurements of DD beam-plasma neutrons from the TOFOR spectrometer show that these modes caused local bump-on-tail distributions in energy. Numerical simulations performed with the CASTOR-K code found a strong interaction between the core-localized TAEs and ions with energies at which local minima in the energy distribution were measured.

Simultaneous occurrence of four magnetospheric wave modes and the resultant combined scattering effect on radiation belt electrons

We report a representative concurrent event of four wave modes at <italic>L</italic> ≈ 5.0, including electrostatic electron cyclotron harmonic (ECH) waves, exohiss, magnetosonic (MS) waves, and electromagnetic ion cyclotron (EMIC) waves, based on the observations from Van Allen Probe A on October 15, 2015. The diffusion coefficients induced by these waves are calculated by using both the Full Diffusion Code and test particle simulations. Moreover, the scattering effects of these waves on energetic electrons are simulated by using a two-dimensional Fokker–Planck diffusion model. The results show that ECH waves mainly scatter low-pitch-angle (&lt; 20°) electrons at 0.1–10 keV; exohiss can significantly scatter hundreds of kiloelectron volt electrons to form a reversed energy spectrum; MS waves mainly affect high-pitch-angle electrons (&gt; 60°); and EMIC waves scatter only &gt; 5 MeV electrons. The combined scattering effects of exohiss and MS waves are stronger than those of exohiss alone. The top-hat pitch angle distributions produced by exohiss are relaxed after adding the effect of MS waves. Because the energies of electrons scattered by ECH waves and EMIC waves are much lower and higher than those scattered by exohiss and MS waves, respectively, the combined scattering effects with the addition of ECH and EMIC waves show little difference from the results for the combination of MS waves and exohiss. These results suggest that distinct wave modes can occur simultaneously and scatter electrons in combination or individually, which requires careful consideration in future global simulations of the complex dynamics of radiation belt energetic electrons.

Iterative addition of finite Larmor radius effects to finite element models using wavelet decomposition

Modeling the propagation and damping of electromagnetic waves in a hot magnetized plasma is difficult due to spatial dispersion. In such media, the dielectric response becomes non-local and the wave equation an integro-differential equation. In the application of RF heating and current drive in tokamak plasmas, the finite Larmor radius (FLR) causes spatial dispersion, which gives rise to physical phenomena such as higher harmonic ion cyclotron damping and mode conversion to electrostatic waves. In this paper, a new numerical method based on an iterative wavelet finite element scheme is presented, which is suitable for adding non-local effects to the wave equation by iterations. To verify the method, we apply it to a case of one-dimensional fast wave heating at the second harmonic ion cyclotron resonance, and study mode conversion to ion Bernstein waves (IBW) in a toroidal plasma. Comparison with a local (truncated FLR) model showed good agreement in general. The observed difference is in the damping of the IBW, where the proposed method predicts stronger damping on the IBW.

Double Plasma Resonance at Ion Cyclotron Harmonics in the Jovian Magnetosphere

AbstractThe ion cyclotron waves instability near the frequencies of ionic cyclotron harmonics is studied under conditions typical for the Jovian kilometer radio emission source. This instability is caused by the presence of the ions with a nonequilibrium loss cone‐type distribution function in the source. Expressions for the growth rate of the ion cyclotron wave's instability are obtained, and it is shown that the amplification of these waves significantly increases when the frequency of the lower‐hybrid resonance coincides with one of the ion cyclotron harmonics. Possible mechanisms for conversion of the ion cyclotron waves excited in the Jovian kilometer radio emission source into electromagnetic radiation are discussed. It is shown that the conversion of ion cyclotron waves, due to their coalescence with high‐frequency plasma waves, is possible only into ordinary electromagnetic waves, while the process capable of providing conversion of ion cyclotron waves into fast extraordinary electromagnetic waves is scattering by suprathermal electron fluxes. In the latter, despite the thermal spread of electron velocities, the radiation that leaves the source region is concentrated in a narrow frequency range Δω ≪ ω near the local gyrofrequency ω≃ωBe, and the polarization of this radiation corresponds to the extraordinary wave. The estimates of the electron energy, which is necessary for such conversion, have shown the possibility of the process realizing under conditions characteristic for the Jovian kilometer radio emission source.

MMS Observations of Harmonic Electromagnetic Ion Cyclotron Waves

AbstractHarmonically related electromagnetic ion cyclotron waves with the fundamental frequency near the double oxygen cyclotron frequency were observed by the MMS spacecraft on 18–20 May 2016. The wave activity lasted for three days, detected by the spacecraft on their consecutive inbound passages through the Earth's plasma sheet boundary layer. The waves were seen in both magnetic and electric fields, formed by over 10 higher order harmonics. Simultaneous ion flux measurements show the presence of ion ring distributions suggesting the energy source for the observed waves. The ion cyclotron harmonics were observed together with broadband waves extending from ~Hz to ~kHz frequency range, ion and electron phase space holes, and chorus waves. During some intervals, there is a clear modulation of chorus wave packets at the ion cyclotron fundamental harmonic frequency. These observations are particularly interesting since they suggest cross‐frequency and cross‐species coupling between processes happening on ion and electron scales.

Observations of core ion cyclotron emission on ASDEX Upgrade tokamak.

The B-dot probe diagnostic suite on the ASDEX Upgrade tokamak has recently been upgraded with a new 125 MHz, 14 bit resolution digitizer to study ion cyclotron emission (ICE). While classic edge emission from the low field side plasma is often observed, we also measure waves originating from the core with fast fusion protons or beam injected deuterons being a possible emission driver. Comparing the measured frequency values with ion cyclotron harmonics present in the plasma places the origin of this emission on the magnetic axis, with the fundamental hydrogen/second deuterium cyclotron harmonic matching the observed values. The actual values range from ∼27 MHz at the on-axis toroidal field BT = -1.79 T to ∼40 MHz at BT = -2.62 T. When the magnetic axis position evolves during this emission, the measured frequency values track the changes in the estimated on-axis cyclotron frequency values. Core ICE is usually a transient event lasting ∼100 ms during the neutral beam startup phase. However, in some cases, core emission occurs in steady-state plasmas and lasts for longer than 1 s. These observations suggest an attractive possibility of using a non-perturbing ICE-based diagnostic to passively monitor fusion alpha particles at the location of their birth in the plasma core, in deuterium-tritium burning devices such as ITER and DEMO.

AORSA full wave calculations of helicon waves in DIII-D and ITER

Helicon waves have been recently proposed as an off-axis current drive actuator for DIII-D, FNSF, and DEMO tokamaks. Previous ray tracing modeling using GENRAY predicts strong single pass absorption and current drive in the mid-radius region on DIII-D in high beta tokamak discharges. The full wave code AORSA, which is valid to all order of Larmor radius and can resolve arbitrary ion cyclotron harmonics, has been used to validate the ray tracing technique. If the scrape-off-layer (SOL) is ignored in the modeling, AORSA agrees with GENRAY in both the amplitude and location of driven current for DIII-D and ITER cases. These models also show that helicon current drive can possibly be an efficient current drive actuator for ITER. Previous GENRAY analysis did not include the SOL. AORSA has also been used to extend the simulations to include the SOL and to estimate possible power losses of helicon waves in the SOL. AORSA calculations show that another mode can propagate in the SOL and lead to significant (~10%–20%) SOL losses at high SOL densities. Optimizing the SOL density profile can reduce these SOL losses to a few percent.

Evidence of 9Be + p nuclear reactions during 2ωCH and hydrogen minority ICRH in JET-ILW hydrogen and deuterium plasmas

The intensity of 9Be + p nuclear fusion reactions was experimentally studied during second harmonic (2ωCH) ion-cyclotron resonance heating (ICRH) and further analyzed during fundamental hydrogen minority ICRH of JET-ILW hydrogen and deuterium plasmas. In relatively low-density plasmas with a high ICRH power, a population of fast H+ ions was created and measured by neutral particle analyzers. Primary and secondary nuclear reaction products, due to 9Be + p interaction, were observed with fast ion loss detectors, γ-ray spectrometers and neutron flux monitors and spectrometers. The possibility of using 9Be(p, d)2α and 9Be(p, α)6Li nuclear reactions to create a population of fast alpha particles and study their behaviour in non-active stage of ITER operation is discussed in the paper.

Design and RF test of a prototype traveling wave antenna for helicon current drive in KSTAR

Non-inductive current drive by fast wave at very high ion cyclotron harmonics, known as ‘helicons’ has the potential for high off-axis current drive efficiency compared with the other known non-inductive current drive techniques. However, non-inductive current drive by helicon wave has not been validated experimentally. To validate its anticipated performance experimentally, an antenna design is one of the most important issues. A Traveling wave antenna has particularly valuable features for launching the fast wave such as load resiliency, narrow n|| spectrum, and simple RF circuits without additional-external matching systems. Low power level helicon wave coupling experiments has been conducted successfully using a mock-up TWA in KSTAR. In the next step, in order to investigate a high power performance, a new prototype TWA based on the mock-up TWA has been designed, fabricated and measured for a medium power (100–300kW) RF system. The prototype TWA having a Faraday shield was made of copper and consists of 10 current straps with 5inch coaxial feeding lines as input and output ports. The detailed design parameters and electromagnetic characteristics of prototype TWA are discussed.

Phase-space resolved measurement of 2nd harmonic ion cyclotron heating using FIDA tomography at the ASDEX Upgrade tokamak

Recent upgrades to the FIDA (fast-ion D-alpha) diagnostic at ASDEX Upgrade allow to reconstruct the fast-ion phase space at several radial positions with decent energy and pitch resolution. These new diagnostic capabilities are applied to study the physics of 2nd harmonic ion cyclotron heating, which is a foreseen heating scenario for ITER. In particular, the acceleration of deuterium beam ions above the injection energy by absorption of ion cyclotron waves at the 2nd harmonic is investigated and compared to theoretical predictions by the TORIC-SSFPQL and TORIC-NUBEAM code packages. Furthermore, comparisons to other fast-ion diagnostics (neutron yield and neutral particle analyzers) are discussed.

Gyrokinetic electron and fully kinetic ion simulations of fast magnetosonic waves in the magnetosphere

Two-dimensional simulations using a gyrokinetic electron and fully kinetic ion (GeFi) scheme are preformed to study the excitation of fast magnetosonic waves in the terrestrial magnetosphere, which arise from the ion Bernstein instability driven by proton velocity distributions with a positive slope with respect to the perpendicular velocity. Since both ion and electron kinetics are relevant, particle-in-cell (PIC) simulations have often been employed to study the wave excitation. However, the full particle-in-cell scheme is computationally expensive for simulating waves in the ion scale because the electron scale must be fully resolved. Therefore, such simulations are limited to reduced proton-to-electron mass ratio (mp/me) and light-to-Alfvén speed ratio (c/vA). The present study exploits the GeFi scheme that can break through these limitations to some extent, so larger mp/me and c/vA can be used. In the simulations presented, the ion Bernstein instability is driven by a proton velocity distribution composed of 10% energetic protons with a shell distribution and 90% relatively cool, background protons with a Maxwellian distribution. The capability of the GeFi code in simulating the ion Bernstein instability is first demonstrated by comparing a GeFi simulation using reduced mass ratio (mp/me=100) and speed ratio (c/vA=15) to a corresponding PIC simulation as well as linear dispersion analysis. A realistic speed ratio (c/vA=400) and a larger mass ratio (mp/me=400) are then adopted in the GeFi code to explore how the results vary. It is shown that, as the increased mp/me and c/vA lead to a larger lower hybrid frequency, ion Bernstein waves are excited at more ion cyclotron harmonics, consistent with the general prediction of linear dispersion theory. On the other hand, the GeFi simulations also revealed some interesting features after the instability saturation, which are likely related to nonlinear wave-wave interactions.

MeV-range velocity-space tomography from gamma-ray and neutron emission spectrometry measurements at JET

We demonstrate the measurement of a 2D MeV-range ion velocity distribution function by velocity-space tomography at JET. Deuterium ions were accelerated into the MeV-range by third harmonic ion cyclotron resonance heating. We made measurements with three neutron emission spectrometers and a high-resolution γ-ray spectrometer detecting the γ-rays released in two reactions. The tomographic inversion based on these five spectra is in excellent agreement with numerical simulations with the ASCOT–RFOF and the SPOT–RFOF codes. The length of the measured fast-ion tail corroborates the prediction that very few particles are accelerated above 2 MeV due to the weak wave-particle interaction at higher energies.