High Harmonic Fast Wave Research Articles

Real-time capable modeling of ICRF heating on NSTX and WEST via machine learning approaches

A real-time capable core Ion Cyclotron Range of Frequencies (ICRF) heating model on NSTX and WEST is developed. The model is based on two nonlinear regression algorithms, the random forest ensemble of decision trees and the multilayer perceptron neural network. The algorithms are trained on TORIC ICRF spectrum solver simulations of the expected flat-top operation scenarios in NSTX and WEST assuming Maxwellian plasmas. The surrogate models are shown to successfully capture the multi-species core ICRF power absorption predicted by the original model for the high harmonic fast wave and the ion cyclotron minority heating schemes while reducing the computational time by six orders of magnitude. Although these models can be expanded, the achieved regression scoring, computational efficiency and increased model robustness suggest these strategies can be implemented into integrated modeling frameworks for real-time control applications.

The combined current drive of the lower hybrid wave and the high harmonic fast wave under the influence of the radial transport of fast electrons

The combined current drive of the lower hybrid wave and the high harmonic fast wave under the influence of the radial transport of fast electrons

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.

RF dispersion relations in FRC geometries and HHFW regime

Field reversed configurations (FRC) are characterized by a magnetic field topology, which exhibits the inversion of the external magnetic field through plasma sustained current and the subsequent presence of a null field surface. A monotonical radial decrease in the longitudinal magnetic field leads to the potential presence of harmonics of the ion cyclotron frequency of any order in the region included between the outer wall and the null field surface. What is the effective hot-plasma dispersion relation obtained through the convolution of a large ensemble of high harmonics fast waves (HHFW) confined in a finite radial region represents an open question that we attempt to address here. In particular, we discuss a combination of analytical modeling and numerical treatment, which allows us to retrieve the resulting high harmonic fast wave complex wavevector for any radial location of any FRC radial profile. Moreover, we show how the obtained hot-plasma HHFW wavevector relates to the cold-plasma solution, and how it depends on the plasma parameters.

Physics basis for the Wisconsin HTS Axisymmetric Mirror (WHAM)

The Wisconsin high-temperature superconductor axisymmetric mirror experiment (WHAM) will be a high-field platform for prototyping technologies, validating interchange stabilization techniques and benchmarking numerical code performance, enabling the next step up to reactor parameters. A detailed overview of the experimental apparatus and its various subsystems is presented. WHAM will use electron cyclotron heating to ionize and build a dense target plasma for neutral beam injection of fast ions, stabilized by edge-biased sheared flow. At 25 keV injection energies, charge exchange dominates over impact ionization and limits the effectiveness of neutral beam injection fuelling. This paper outlines an iterative technique for self-consistently predicting the neutral beam driven anisotropic ion distribution and its role in the finite beta equilibrium. Beginning with recent work by Egedalet al.(Nucl. Fusion, vol. 62, no. 12, 2022, p. 126053) on the WHAM geometry, we detail how the FIDASIM code is used to model the charge exchange sources and sinks in the distribution function, and both are combined with an anisotropic magnetohydrodynamic equilibrium solver method to self-consistently reach an equilibrium. We compare this with recent results using the CQL3D code adapted for the mirror geometry, which includes the high-harmonic fast wave heating of fast ions.

Radio-frequency sheath excitation at the extremities of scrape-off layer plasma filaments, mediated by resonant high harmonic fast wave scattering

Resonant filament-assisted mode conversion (FAMC) scattering of high harmonic fast waves (HHFW) by cylindrical field-aligned density inhomogeneities can efficiently redirect a fraction of the launched HHFW power flux into the parallel direction. Within a simplified analytic approach, this contribution compares the parallel propagation, reflection and dissipation of nearly resonant FAMC modes for three magnetic field line geometries in the scrape-off layer, in the presence of radio-frequency (RF) sheaths at field line extremities and phenomenological wave damping in the plasma volume. When a FAMC mode, excited at the HHFW antenna parallel location and guided along the open magnetic field lines, impinges onto a boundary at normal incidence, we show that it can excite sheath RF oscillations, even toroidally far away from the HHFW launcher. The RF sheaths then dissipate part of the power flux carried by the incident mode, while another part reflects into the FAMC mode with the opposite wave vector parallel to the magnetic field. The reflected FAMC mode in turn propagates and can possibly interact with the sheath at the opposite field line boundary. The two counter-propagating modes then form in the bounded magnetic flux tube a lossy cavity excited by the HHFW scattering. We investigate how the presence of field line boundaries affects the total HHFW power redirected into the filament, and its splitting between sheath and volume losses, as a function of relevant parameters in the model.

On the origin of high harmonic fast wave edge losses in NSTX

Many mechanisms have been proposed to explain the high harmonic fast wave edge losses in the National Spherical Torus Experiment (NSTX) (Perkins et al 2012 Phys. Rev. Lett. 109 045001). Here, we discuss a newly discovered edge loss mechanism (Tierens et al 2021 Plasma Phys. Control. Fusion 64 035001) which involves the resonant excitation of surface waves on filaments. We show that this edge loss mechanism can explain the main parameter dependencies observed in NSTX experiments.

New synergy effects of the lower hybrid wave and the high harmonic fast wave current drive

The combined drive current of the lower hybrid wave (LHW) and the high harmonic fast wave (HHFW) was studied theoretically for the first time, based on the use of low and higher β e operational parameters in EAST. Broad and significant synergistic effects are found in the simulation, the current drive (CD) efficiency is greatly improved, and the current profile is modified as a result of the synergy between the two types of waves. The LHW interacted with the resonant electrons in low parallel velocity region and pushes them into the adjacent resonance region of the high phase velocity wave (HHFW), thus the number of fast electrons resonant with the HHFW is increased dramatically, and the driven current is enhanced. Therefore the synergy effect strongly depends on the positional relation between the velocity resonance regions of the two waves. Moreover, the effects of the parallel refractive index, the wave frequency and the wave power on the synergy effect are examined. Some problems well known in the single LHW CD or the HHFW CD may be overcome by the combined CD.

NSTX-U theory, modeling and analysis results

The mission of the low aspect ratio spherical tokamak NSTX-U is to advance the physics basis and technical solutions required for optimizing the configuration of next-step steady-state tokamak fusion devices. NSTX-U will ultimately operate at up to 2 MA of plasma current and 1 T toroidal field on axis for 5 s, and has available up to 15 MW of neutral beam injection power at different tangency radii and 6 MW of high harmonic fast wave heating. With these capabilities NSTX-U will develop the physics understanding and control tools to ramp-up and sustain high performance fully non-inductive plasmas with large bootstrap fraction and enhanced confinement enabled via the low aspect ratio, high beta configuration. With its unique capabilities, NSTX-U research also supports ITER and other critical fusion development needs. Super-Alfvénic ions in beam-heated NSTX-U plasmas access energetic particle (EP) parameter space that is relevant for both α-heated conventional and low aspect ratio burning plasmas. NSTX-U can also generate very large target heat fluxes to test conventional and innovative plasma exhaust and plasma facing component solutions. This paper summarizes recent analysis, theory and modelling progress to advance the tokamak physics basis in the areas of macrostability and 3D fields, EP stability and fast ion transport, thermal transport and pedestal structure, boundary and plasma material interaction, RF heating, scenario optimization and real-time control.

NSTX-U theory, modeling and analysis results

Abstract The mission of the low aspect ratio spherical tokamak NSTX-U is to advance the physics basis and technical solutions required for optimizing the configuration of next-step steady-state tokamak fusion devices. NSTX-U will ultimately operate at up to 2 MA of plasma current and 1 T toroidal field on axis for 5 seconds, and has available up to 15 MW of Neutral Beam Injection (NBI) power at different tangency radii and 6 MW of High Harmonic Fast Wave (HHFW) heating. With these capabilities NSTX-U will develop the physics understanding and control tools to ramp-up and sustain high performance fully non-inductive plasmas with large bootstrap fraction and enhanced confinement enabled via the low aspect ratio, high beta configuration. With its unique capabilities, NSTX-U research also supports ITER and other critical fusion development needs. Super-Alfvénic ions in beam-heated NSTX-U plasmas access energetic particle parameter space that is relevant for both -heated conventional and low aspect ratio burning plasmas. NSTX-U can also generate very large target heat fluxes to test conventional and innovative plasma exhaust and plasma facing component (PFC) solutions. This paper summarizes recent analysis, theory and modelling progress to advance the tokamak physics basis in the areas of macrostability and 3D fields, energetic particle stability and fast ion transport, thermal transport and pedestal structure, boundary and plasma material interaction, RF heating, scenario optimization and real-time control.

Resonant wave–filament interactions as a loss mechanism for HHFW heating and current drive

Perkins et al (2012 Phys. Rev. Lett. 109 045001) reported unexpected power losses during high harmonic fast wave (HHFW) heating and current drive in the National Spherical Torus Experiment (NSTX). Recently, Tierens et al (2020 Phys. Plasmas 27 010702) proposed that these losses may be attributable to surface waves on field-aligned plasma filaments, which carry power along the filaments, to be lost at the endpoints where the filaments intersect the limiters. In this work, we show that there is indeed a resonant loss mechanism associated with the excitation of these surface waves, and derive an analytic expression for the power lost to surface wave modes at each filament.

Scoping study of detecting high harmonic fast waves in NSTX-U hot core plasma directly using beam emission spectroscopy.

In this paper, we used radio frequency (RF) full wave simulation to explore the feasibility of generating a density beat oscillation formed by high harmonic fast waves (HHFWs) in the National Spherical Tokamak Experiment-Upgrade (NSTX-U) and of measuring it numerically with 2D beam emission spectroscopy (BES). This oscillation is of interest as it can be used to determine the injected RF fields. We began by computing HHFW fields in NSTX-U under a variety of experimental conditions and antenna configurations with Petra-M, a 3D RF wavefield solver. These fields were then used to evaluate the amplitude of δne,beat/ne0 in the volume of measurement, which we predict to be between 5 × 10-10 and 10-9, although it is highly dependent on plasma parameters. Trends in magnetic field, core temperature, core density, and antenna phasing are presented, and the parameters most suitable to this measurement are identified. Finally, we developed a synthetic BES diagnostic to compare the experimental BES signal against.

Study of the Design and Assembly of a High Harmonic Fast Wave Antenna for an LAPD

The simulation survey of TAE Technologies has demonstrated that high harmonic fast wave (HHFW) heating is a promising method for core electron heating of FRC plasma. This study mainly describes the HHFW antenna mechanical design and assembly on the basis of the results of electromagnetic simulations performed by Oak Ridge National Laboratory (ORNL), the available port dimensions, and antenna installation position of the LAPD. Compared to the original scheme, this antenna is also optimized in the design. It is found that the E field distribution of optimized antenna becomes even, and the maximum electric field decreases by approximately 14%. The current on the antenna box and FS is reduced after optimization, whereas the maximum J density decreases from 53.3 kA to 14.5 kA. The reflection performance of the port at 30 MHz is also improved after the structural optimization; The k// spectrum distribution is sharper at the monopole phase (0, 0, 0, 0) and dipole phase (0, π, 0, π) and (0, 90, 270,180) than other phases. The optimized antenna can obtain a maximum |k//| spectrum, which peaks about |k//| = 30 m−1 at the dipole phase (0, π, 0, π). The analysis results and assembly strategy can provide useful reference and guidance for the study of HHFW antenna design and fabrication in LAPD or other magnetic confined fusion devices.

Integrated modeling of CFETR hybrid scenario plasmas

Demonstration of DEMO relevant fusion power (P fus) level and tritium self-sufficiency are two important goals of the China fusion engineering testing reactor (CFETR). In this work the integrated modeling including self-consistent core–pedestal coupling are used to design the hybrid scenario plasmas at flat-top phase for these goals. Such plasmas have been taken as the reference plasma for studying the compatibility of the hybrid scenario with CFETR engineering design in the past two years. The physics justification for the selection of plasma density, Z eff, safety factor profile, and in particular the choice of auxiliary heating and current drive is presented. According to a scan of plasma density and Z eff, the target of P fus ≈ 1 GW and finite ohmic flux consumption ∆Φohm (4 h) ⩽ 250 Vs can be met with Z eff = 1.9–2.2 and the density at the pedestal top set at 90% of the Greenwald limit. Turbulent transport analysis using the gyro-Landau-fluid model TGLF shows that the electromagnetic effects can enhance the energy confinement but reduce the particle confinement and thus P fus. A baseline hybrid scenario case matching the target in the concept design is built using a combination of neutral beams (NB) and electron cyclotron (EC) waves to flatten the safety factor profile in the deep core region (with the normalized plasma radius ρ ⩽ 0.4). Such profile can yield better particle and energy confinement than that with either higher magnetic shear in the deep core region or higher q value in outer core region (e.g., due to the addition of lower hybrid current drive). Switching a part of auxiliary heating from electron to ions, e.g., replacing a part of EC waves by waves in the ion cyclotron range of frequencies, reduces the particle confinement and thus P fus. Since high harmonic fast waves (HHFW) can drive current at the same location as ECCD with higher current drive efficiency than ECCD and yield more electron heating than NB, the case using HHFW to replace a part of EC waves and NB can yield higher P fus and lower ∆Φohm than the baseline case. A discussion is given on future simulations to explore the improvement in plasma performance and the broadening of the feasible design space.

Numerical simulation of very high harmonic fast waves for an off-axis current drive in a China fusion engineering test reactor by the GENRAY code

Recent studies have shown that helicon waves may be an attractive option for driving an efficient off-axis current drive in order to supplement bootstrap current for steady state operation in fusion reactors. Based on the China fusion engineering test reactor parameters, the helicon wave trajectories, profiles of driven current and current driven efficiency are calculated with the ray-tracing code GENRAY. Both the peak position and the peak value of driven current profiles are dependent on the wave frequency. In the frequency range of 1.6 GHz–2.0 GHz, the peak value increases with the increase of frequency, and the peak position has a slight change (concentrate around ρ= 0.75). High electron temperature and low electron density seem to be favorable for the helicon wave absorption. A driving current of I/P > 70 kA MW−1 at the off-axis position of ρ < 0.7 can be obtained with the electron temperature at the plasma center, T e(0) < 25.4 keV and the electron density at the plasma center, n e(0) ∼ 0.7 × 7.8 × 1019m−3–0.8 × 7.8 × 1019m−3. The current drive efficiency decreases with the increase of the electron density. Peak positon of the driven current profile is insensitive to the parallel refractive index n ∥. It is found that the poloidal launch angle has some effect on the peak positon and its value.

Off-Axis Current Drive with Helicon Waves for CFETR

Off-axis current drive is necessary for Tokamak to maintain and regulate the current profile. Helicon wave is the high order harmonic fast wave and helicon wave current drive (HCD) is one of the key issues in the China Fusion Engineering Test Reactor (CFETR). The theory of HCD is briefly introduced and the simulation results are listed. Helicon waves can realize off-axis current drive under CFETR plasma parameters when the frequency is greater than 1 GHz and drive current is insensitive to the launched value of the parallel index of refraction n||, so wave accessibility issues can be reduced. Travelling Wave Antenna was analyzed by the commercial software package-CST. Near the resonant frequency of the antenna, the Voltage Standing Wave Ratio < 1.2 is obtained for the antenna in the bandwidth of 50 MHz, which means that the antenna does not require a matching system.

Modeling of high harmonic fast wave scenarios for NSTX Upgrade**This article is dedicated to the memory of Joel C. Hosea.

NSTX-Upgrade will operate with toroidal magnetic fields () up to 1 T, nearly twice the value used in the experiments on NSTX, and the available neutral beam injection (NBI) power will be doubled. The doubling of while retaining the 30 MHz RF source frequency has moved the heating regime from the high harmonic fast wave (HHFW) regime used in NSTX to the mid harmonic fast wave regime. By making use of the full wave code AORSA (assuming a Maxwellian plasma), this work explores different HHFW scenarios for two possible antenna frequencies (30 and 60 MHz) and with and without NBI. Both frequencies have large electron absorption for large wave toroidal number particularly without NBI. With the presence of NBI, the fast ions absorption can be dominant in some scenarios. Therefore, a competition between electron and fast ion absorption is clearly apparent partially explaining why in previous NSTX HHFW experiments, a less efficient electron heating was observed. Moreover at the toroidal field of 1 T, a direct thermal ion damping might be possible under the condition when the ion temperature is larger than electron temperature. In general, the electron and ion absorption are found very sensitive to the ratio of electron and ion temperature. The impact of the hydrogen species is also studied showing that, for hydrogen concentration below , the hydrogen absorption is not significant. However, a larger hydrogen concentration could open up new HHFW heating scenarios in NSTX-U. Launching at high toroidal wave number appears to be one way to significantly reduce the ion damping and in turn to obtain large electron damping in the core which can play an important role in the transport studies for NSTX-U. Finally, an higher magnetic field could also playing a role in increasing the electron temperature and consequently the electron absorption. Indeed a magnetic field scan is also shown and discussed.

Investigation of high harmonic fast wave for current drive on CFETR

High harmonic fast wave (HHFW) current drive at frequency near the lower hybrid wave is calculated under CFETR conditions. Modelling results show that the HHFW has excellent off-axis current drive capacity with high efficiency in a wide range of n// (1.5–2.9) and wave frequency (0.6–2.4 GHz), the peak driven current is about 35 kA/MW and the current drive efficiency η = neICDR/P ∼ 2.7×1019 AW−1 m−2. Under the same parameters, smaller n// leads to more peaked driven current and higher wave frequency corresponding to more outside current peak position. The comparisons of driven current properties with LHCD indicate that the current drive efficiency of HHFW is comparable to LHCD and the driven current profile is also more flexible. Scanning results of density and temperature show that low density and/or high temperature help to obtain more driven current, and the current drive efficiency can be improved at high temperatures and/or high densities.

Effect of wall boundary on the scrape-off layer losses of high harmonic fast wave in NSTX and NSTX-U

We perform numerical simulations of high harmonic fast waves (HHFWs) in the scrape-off-layer (SOL) of National Spherical Torus Experiment (NSTX)/NSTX-U using a recently developed 2D full wave code. We particularly show that a realistic NSTX SOL boundary can significantly affect HHFW propagation and power losses in the SOL. In NSTX SOL boundaries, HHFW is easily localized near the antenna and propagates less to the SOL, and thus, less power is lost to the SOL. We also show that the lower SOL power losses occur when the SOL volume is smaller and the distance between the last closed flux surface and the antenna is shorter. We investigate the effect of electron density in front of the antenna and the ambient magnetic field strengths on the SOL power losses as well. Showing consistency with the experiments, SOL losses are minimized when the SOL density is near the critical density where the fast wave cutoff is open, and the plasma is strongly magnetized.

A high-power helicon antenna for the DIII-D tokamak and its electromagnetic aspects

A comb-line antenna to demonstrate efficient off-axis non-inductive current drive from the absorption of toroidally directed very high harmonic fast waves is being designed and built for DIII-D. The antenna consists of a toroidal array of 30 modules, spanning 1.7 m on the outer vessel wall just above the tokamak midplane. This antenna will be fed with 1 MW of RF power at 476 MHz through a stripline (SL) feed on both sides inside the vacuum vessel. COMSOL Multiphysics, a commercial finite element analysis software, was used to perform the RF analysis and the induced force analysis due to plasma disruption events on the whole antenna system. Results on the RF performance of the SL and the RF coupling into and between the modules, and the SL and modules’ RF losses will be presented. In addition, the disruption induced current and forces are shown, and a method to mitigate them is presented.