High Harmonic Fast Wave Research Articles

Experiments on helicons in DIII-D—investigation of the physics of a reactor-relevant non-inductive current drive technology**Paper based on contribution EX/P3-22 presented at IAEA FEC, Kyoto, October 2016.

Experiments have begun in DIII-D to evaluate a toroidally-directed spectrum of helicon waves (also known as ‘very high harmonic fast waves’, ‘fast waves in the lower hybrid range of frequencies’, or ‘whistlers’) that can generate efficient non-inductive current drive by Landau absorption in a reactor plasma. Modeling has shown (Prater et al 2014 Nucl. Fusion 54 083024) that non-inductive current drive at mid-radius (ρ ~ 0.5) should be achievable in DIII-D with fast waves at 0.5 GHz in high-beta conditions with an efficiency twice that of other non-inductive current drive tools currently available on DIII-D (neutral beams and electron cyclotron current drive). An innovative traveling wave antenna (TWA) of the ‘comb-line’ type with 12 radiating modules has been constructed, installed in DIII-D, and has been tested at very low power (<0.4 kW) to evaluate the antenna coupling in the linear regime, and to test technological aspects of such structures in the tokamak environment. Results show favorably strong antenna/plasma coupling in several plasma regimes, most significantly in the high-beta ELMing H-mode case with calculated full first-pass absorption of the helicon waves in the desired mid-radius region. No evidence of significant excitation of the undesirable slow wave was found when the total magnetic field adjacent to the structure was approximately aligned with the tilted Faraday screen of the antenna. The implications of these results for a high-power experiment currently under construction are discussed.

Regarding the optimization of O1-mode ECRH and the feasibility of EBW startup on NSTX-U

Recently published scenarios for fully non-inductive startup and operation on the National Spherical Torus eXperiment Upgrade (NSTX-U) (Menard et al 2012 Nucl. Fusion 52 083015) show Electron Cyclotron Resonance Heating (ECRH) as an important component in preparing a target plasma for efficient High Harmonic Fast Wave and Neutral Beam heating. The modeling of the propagation and absorption of EC waves in the evolving plasma is required to define the most effective window of operation, and to optimize the launcher geometry for maximal heating and current drive during this window. Here, we extend a previous optimization of O1-mode ECRH on NSTX-U to account for the full time-dependent performance of the ECRH using simulations performed with TRANSP. We find that the evolution of the density profile has a prominent role in the optimization by defining the time window of operation, which in certain cases may be a more important metric to compare launcher performance than the average power absorption. This feature cannot be captured by analysis on static profiles, and should be accounted for when optimizing ECRH on any device that operates near the cutoff density. Additionally, the utility of the electron Bernstein wave (EBW) in driving current and generating closed flux surfaces in the early startup phase has been demonstrated on a number of devices. Using standalone GENRAY simulations, we find that efficient EBW current drive is possible on NSTX-U if the injection angle is shifted below the midplane and aimed towards the top half of the vacuum vessel. However, collisional damping of the EBW is projected to be significant, in some cases accounting for up to 97% of the absorbed EBW power.

Edge loss of high-harmonic fast-wave heating power in NSTX: a cylindrical model

Efficient high-harmonic fast-wave (HHFW) heating in the National Spherical Torus Experiment Upgrade (NSTX-U) would facilitate experiments in turbulence, transport, fast-ion studies, and more. However, previous HHFW operation in NSTX exhibited a large loss of fast-wave power to the divertor along the scrape-off layer field lines for edge densities above the fast-wave cutoff. It was postulated that the wave amplitude is enhanced in the scrape-off layer due to cavity-like modes, and that these enhanced fields drive sheath losses through RF rectification. As part of ongoing work to confirm this hypothesis, we have developed a cylindrical cold-plasma model to identify and understand scenarios where a substantial fraction of wave power is confined to the plasma periphery. We previously identified a peculiar class of modes, named annulus resonances, that conduct approximately half of their wave power in the periphery and can also account for a significant fraction of the total wave power. Here, we study the influence of annulus resonances on wave field reconstructions and find instances where annulus-resonant modes dominate the spectrum and trap over half of the total wave power at the edge. The work is part of an ongoing effort to determine the mechanism underlying these scrape-off layer losses in NSTX, identify optimal conditions for operation in NSTX-U, and predict whether similar losses occur for the ion-cyclotron minority heating scheme for both current experiments and future devices such as ITER.

The role of rectified currents in far-field RF sheaths and in SOL losses of HHFW power on NSTX

Radio-frequency (RF) rectification is an important sheath phenomenon for wave heating of plasma in fusion devices and is proposed to be the mechanism responsible for converting high-harmonic fast-wave (HHFW) power in the National Spherical Torus eXperiment (NSTX) into a heat flux to the divertor. RF rectification has two aspects: current rectification and voltage rectification, and, while the latter is emphasized in many application, we demonstrate the importance of current rectification in analysis of the NSTX divertor during HHFW heating. When rectified currents are accounted for in first-principle models for the heat flux to the tiles, we predict a sizeable enhancement for the heat flux in the presence of an RF field: for one case studied, the predicted heat flux increases from 0.103 MW/m2 to 0.209 MW/m2. We also demonstrate how this rectification scales with injected HHFW power by tracking probe characteristics during a HHFW power ramp; the rectified current may be clamped at a certain level. This work is important for minimizing SOL losses of HHFW power in NSTX-U but may also have implications for near-field studies of ICRF antennae: ignoring rectified current may lead to underestimated heat fluxes and overestimated rectified voltages.

Full-wave simulations of ICRF heating regimes in toroidal plasma with non-Maxwellian distribution functions

At the power levels required for significant heating and current drive in magnetically-confined toroidal plasma, modification of the particle distribution function from a Maxwellian shape is likely (Stix 1975 Nucl. Fusion 15 737), with consequent changes in wave propagation and in the location and amount of absorption. In order to study these effects computationally, both the finite-Larmor-radius and the high-harmonic fast wave (HHFW), versions of the full-wave, hot-plasma toroidal simulation code TORIC (Brambilla 1999 Plasma Phys. Control. Fusion 41 1 and Brambilla 2002 Plasma Phys. Control. Fusion 44 2423), have been extended to allow the prescription of arbitrary velocity distributions of the form . For hydrogen (H) minority heating of a deuterium (D) plasma with anisotropic Maxwellian H distributions, the fractional H absorption varies significantly with changes in parallel temperature but is essentially independent of perpendicular temperature. On the other hand, for HHFW regime with anisotropic Maxwellian fast ion distribution, the fractional beam ion absorption varies mainly with changes in the perpendicular temperature. The evaluation of the wave-field and power absorption, through the full wave solver, with the ion distribution function provided by either a Monte-Carlo particle and Fokker–Planck codes is also examined for Alcator C-Mod and NSTX plasmas. Non-Maxwellian effects generally tend to increase the absorption with respect to the equivalent Maxwellian distribution.

Self-consistent calculation of the effects of RF injection in the HHFW heating regimes on the evolution of fast ions in toroidal plasmas

A critical question for the use of ion cyclotron range of frequency (ICRF) heating in the ITER device and beyond is interaction of fast waves with energetic ion populations from neutral beam injection (NBI), fusion reactions, and minority ions accelerated by the RF waves themselves. Several experiments have demonstrated that the interaction between fast waves and fast ions can indeed be strong enough to significantly modify the NB ion population. To model the RF/fast ion interaction and the resulting fast ion distribution, a recent extension of the full wave solver TORIC v.5 that includes non-Maxwellian effects has been combined with the Monte Carlo NUBEAM code through an RF “kick” operator. In this work, we present an initial verification of the NUBEAM RF “kick” operator for high harmonic fast wave (HHFW) heating regime in NSTX plasma.

A Finite-Orbit-Width Fokker-Planck solver for modeling of energetic particle interactions with waves, with application to Helicons in ITER

The bounce-average (BA) finite-difference Fokker-Planck (FP) code CQL3D [1,2] now includes the essential physics to describe the RF heating of Finite-Orbit-Width (FOW) ions in tokamaks. The FP equation is reformulated in terms of Constants-Of-Motion coordinates, which we select to be particle speed, pitch angle, and major radius on the equatorial plane thus obtaining the distribution function directly at this location. Full-orbit, low collisionality neoclassical radial transport emerges from averaging the local friction and diffusion coefficients along guiding center orbits. Similarly, the BA of local quasilinear RF diffusion terms gives rise to additional radial transport. The local RF electric field components needed for the BA operator are usually obtained by a ray-tracing code, such as GENRAY, or in conjunction with full-wave codes. As a new, practical application, the CQL3D-FOW version is used for simulation of alpha-particle heating by high-harmonic waves in ITER. Coupling of high harmonic or helicon fast waves power to electrons is a promising current drive (CD) scenario for high beta plasmas. However, the efficiency of current drive can be diminished by parasitic channeling of RF power into fast ions, such as alphas, through finite Larmor-radius effects. We investigate possibilities to reduce the fast ion heating in CD scenarios.

2D full-wave simulation of waves in space and tokamak plasmas

Simulation results using a 2D full-wave code (FW2D) for space and NSTX fusion plasmas are presented. The FW2D code solves the cold plasma wave equations using the finite element method. The wave code has been successfully applied to describe low frequency waves in planetary magnetospheres (i.e., dipole geometry) and the results include generation and propagation of externally driven ultra-low frequency waves via mode conversion at Mercury and mode coupling, refraction and reflection of internally driven field-aligned propagating left-handed electromagnetic ion cyclotron (EMIC) waves at Earth. In this paper, global structure of linearly polarized EMIC waves is examined and the result shows such resonant wave modes can be localized near the equatorial plane. We also adopt the FW2D code to tokamak geometry and examine radio frequency (RF) waves in the scape-off layer (SOL) of tokamaks. By adopting the rectangular and limiter boundary, we compare the results with existing AORSA simulations. The FW2D code results for the high harmonic fast wave heating case on NSTX with a rectangular vessel boundary shows excellent agreement with the AORSA code.

Development of slow and fast wave coupling and heating from the C-Stellarator to NSTX

A historical perspective on key discoveries which contributed to understanding the properties of coupling both slow and fast waves and the effects on plasma heating and current drive will be presented. Important steps made include the demonstration that the Alfven resonance was in fact a mode conversion on the C-stellarator, that toroidal m = -1 eigenmodes were excited in toroidal geometry and impurity influx caused the Z mode on the ST tokamak, that the H minority regime provided strong heating and that 3 He minority could be used as well on PLT, that the 2nd harmonic majority tritium regime was viable on TFTR, and that high harmonic fast wave heating was efficient when the SOL losses were avoided on NSTX.

Current drive with combined electron cyclotron wave and high harmonic fast wave in tokamak plasmas

The current driven by combined electron cyclotron wave (ECW) and high harmonic fast wave is investigated using the GENRAY/CQL3D package. It is shown that no significant synergetic current is found in a range of cases with a combined ECW and fast wave (FW). This result is consistent with a previous study [Harvey et al., in Proceedings of IAEA TCM on Fast Wave Current Drive in Reactor Scale Tokamaks (Synergy and Complimentarily with LHCD and ECRH), Arles, France, IAEA, Vienna, 1991]. However, a positive synergy effect does appear with the FW in the lower hybrid range of frequencies. This positive synergy effect can be explained using a picture of the electron distribution function induced by the ECW and a very high harmonic fast wave (helicon). The dependence of the synergy effect on the radial position of the power deposition, the wave power, the wave frequency, and the parallel refractive index is also analyzed, both numerically and physically.

A generalized plasma dispersion function for electron damping in tokamak plasmas

Radio frequency wave propagation in finite temperature, magnetized plasmas exhibits a wide range of physics phenomena. The plasma response is nonlocal in space and time, and numerous modes are possible with the potential for mode conversions and transformations. In addition, diffraction effects are important due to finite wavelength and finite-size wave launchers. Multidimensional simulations are required to describe these phenomena, but even with this complexity, the fundamental plasma response is assumed to be the uniform plasma response with the assumption that the local plasma current for a Fourier mode can be described by the “Stix” conductivity. However, for plasmas with non-uniform magnetic fields, the wave vector itself is nonlocal. When resolved into components perpendicular (k⊥) and parallel (k||) to the magnetic field, locality of the parallel component can easily be violated when the wavelength is large. The impact of this inconsistency is that estimates of the wave damping can be incorrect (typically low) due to unresolved resonances. For the case of ion cyclotron damping, this issue has already been addressed by including the effect of parallel magnetic field gradients. In this case, a modified plasma response (Z function) allows resonance broadening even when k|| = 0, and this improves the convergence and accuracy of wave simulations. In this paper, we extend this formalism to include electron damping and find improved convergence and accuracy for parameters where electron damping is dominant, such as high harmonic fast wave heating in the NSTX-U tokamak, and helicon wave launch for off-axis current drive in the DIII-D tokamak.

Full wave simulations of fast wave efficiency and power losses in the scrape-off layer of tokamak plasmas in mid/high harmonic and minority heating regimes**This article is dedicated to the memory of Cynthia K. Phillips

Several experiments on different machines and in different fast wave (FW) heating regimes, such as hydrogen minority heating and high harmonic fast waves (HHFW), have found strong interaction between radio-frequency (RF) waves and the scrape-off layer (SOL) region. This paper examines the propagation and the power loss in the SOL by using the full wave code AORSA, in which the edge plasma beyond the last closed flux surface (LCFS) is included in the solution domain and a collisional damping parameter is used as a proxy to represent the real, and most likely nonlinear, damping processes. 2D and 3D AORSA results for the National Spherical Torus eXperiment (NSTX) have shown a strong transition to higher SOL power losses (driven by the RF field) when the FW cut-off is removed from in front of the antenna by increasing the edge density. Here, full wave simulations have been extended for ‘conventional’ tokamaks with higher aspect ratios, such as the DIII-D, Alcator C-Mod, and EAST devices. DIII-D results in HHFW regime show similar behavior found in NSTX and NSTX-U, consistent with previous DIII-D experimental observations. In contrast, a different behavior has been found for C-Mod and EAST, which operate in the minority heating regime.

Simulations towards the achievement of non-inductive current ramp-up and sustainment in the National Spherical Torus Experiment Upgrade

One of the goals of the National Spherical Torus Experiment Upgrade (NSTX-U) (Menard et al 2012 Nucl. Fusion 52 083015) is the demonstration of fully non-inductive start-up, current ramp-up and sustainment. This work discusses predictive simulations where the available heating and current drive systems are combined to maximize the non-inductive current and minimize the solenoidal contribution. Radio-frequency waves at harmonics higher than the ion cyclotron resonance (high-harmonic fast waves (HHFW)) and neutral beam injection are used to ramp the plasma current non-inductively starting from an initial Ohmic plasma. An interesting synergy is observed in the simulations between the HHFW and electron cyclotron (EC) wave heating. Time-dependent simulations indicate that, depending on the phasing of the HHFW antenna, EC wave heating can significantly increase the effectiveness of the radio-frequency power, by heating the electrons and increasing the current drive efficiency, thus relaxing the requirements on the level of HHFW power that needs to be absorbed in the core plasma to drive the same amount of fast-wave current.

Modeling of high harmonic fast wave current drive on EAST tokamak

High harmonic fast waves (HHFW) are among the candidates for non-inductive current drive (CD), which is essential for long-pulse or steady-state operation of tokamaks. Current driven with HHFW in EAST tokamak plasmas is numerically studied. The HHFW CD efficiency is found to increase non-monotonically with the wave frequency, and this phenomenon is attributed to the multi-pass absorption of HHFW. The sensitivity of CD efficiency to the value of the parallel refraction index of the launched wave is confirmed. The quasilinear effects, assessed as significant in HHFW current drive with the GENRAY/CQL3D package, cause a significant increase in CD efficiency as RF power is increased, which is very different from helicon current drive. Simulations for a range of toroidal dc electric fields, in combination with a range of fast wave powers, are also presented and indicate that the presence of the DC field can also enhance the CD efficiency.

Integrated modeling applications for tokamak experiments with OMFIT

One modeling framework for integrated tasks (OMFIT) is a comprehensive integrated modeling framework which has been developed to enable physics codes to interact in complicated workflows, and support scientists at all stages of the modeling cycle. The OMFIT development follows a unique bottom-up approach, where the framework design and capabilities organically evolve to support progressive integration of the components that are required to accomplish physics goals of increasing complexity. OMFIT provides a workflow for easily generating full kinetic equilibrium reconstructions that are constrained by magnetic and motional Stark effect measurements, and kinetic profile information that includes fast-ion pressure modeled by a transport code. It was found that magnetic measurements can be used to quantify the amount of anomalous fast-ion diffusion that is present in DIII-D discharges, and provide an estimate that is consistent with what would be needed for transport simulations to match the measured neutron rates. OMFIT was used to streamline edge-stability analyses, and evaluate the effect of resonant magnetic perturbation (RMP) on the pedestal stability, which have been found to be consistent with the experimental observations. The development of a five-dimensional numerical fluid model for estimating the effects of the interaction between magnetohydrodynamic (MHD) and microturbulence, and its systematic verification against analytic models was also supported by the framework. OMFIT was used for optimizing an innovative high-harmonic fast wave system proposed for DIII-D. For a parallel refractive index , the conditions for strong electron-Landau damping were found to be independent of launched and poloidal angle. OMFIT has been the platform of choice for developing a neural-network based approach to efficiently perform a non-linear multivariate regression of local transport fluxes as a function of local dimensionless parameters. Transport predictions for thousands of DIII-D discharges showed excellent agreement with the power balance calculations across the whole plasma radius and over a broad range of operating regimes. Concerning predictive transport simulations, the framework made possible the design and automation of a workflow that enables self-consistent predictions of kinetic profiles and the plasma equilibrium. It is found that the feedback between the transport fluxes and plasma equilibrium can significantly affect the kinetic profiles predictions. Such a rich set of results provide tangible evidence of how bottom-up approaches can potentially provide a fast track to integrated modeling solutions that are functional, cost-effective, and in sync with the research effort of the community.

The contribution of radio-frequency rectification to field-aligned losses of high-harmonic fast wave power to the divertor in the National Spherical Torus eXperiment

The National Spherical Torus eXperiment (NSTX) can exhibit a major loss of high-harmonic fast wave (HHFW) power along scrape-off layer (SOL) field lines passing in front of the antenna, resulting in bright and hot spirals on both the upper and lower divertor regions. One possible mechanism for this loss is RF sheaths forming at the divertors. Here, we demonstrate that swept-voltage Langmuir probe characteristics for probes under the spiral are shifted relative to those not under the spiral in a manner consistent with RF rectification. We estimate both the magnitude of the RF voltage across the sheath and the sheath heat flux transmission coefficient in the presence of the RF field. Although precise comparison between the computed heat flux and infrared (IR) thermography cannot yet be made, the computed heat deposition compares favorably with the projections from IR camera measurements. The RF sheath losses are significant and contribute substantially to the total SOL losses of HHFW power to the divertor for the cases studied. This work will guide future experimentation on NSTX-U, where a wide-angle IR camera and a dedicated set of coaxial Langmuir probes for measuring the RF sheath voltage directly will quantify the contribution of RF sheath rectification to the heat deposition from the SOL to the divertor.

Suppression of energetic particle driven instabilities with HHFW heating

In plasmas in the National Spherical Torus Experiment (NSTX) (Ono et al 2000 Nucl. Fusion 40 557) heated with neutral beams, the beam ions typically excite energetic particle modes (or fishbones), and toroidal, global or compressional Alfvén eigenmodes. These modes can redistribute the energetic beam ions, altering the beam driven current profile and the plasma heating profile, or they may affect electron thermal transport or cause losses of the beam ions. In this paper we present experimental results where these instabilities, driven by the super-thermal beam ions, are suppressed with the application of high harmonic fast wave heating.

Application of very high harmonic fast waves for off-axis current drive in the DIII-D and FNSF-AT tokamaks

Fast waves at frequencies far above the ion cyclotron frequency and approaching the lower hybrid frequency (also called 'helicons' or ‘whistlers’) have application to off-axis current drive in tokamaks with high electron beta. The high frequency causes the whistler-like behaviour of the wave power nearly following field lines, but with a small radial component, so the waves spiral slowly towards the plasma centre. The high frequency also contributes to strong damping. Modelling predicts robust off-axis current drive with good efficiency compared to alternatives in high performance discharges in DIII-D and Fusion Nuclear Science Facility (FNSF) when the electron beta is above about 1.8%. Detailed analysis of ray behaviour shows that ray trajectories and damping are deterministic (that is, not strongly affected by plasma profiles or initial ray conditions), unlike the chaotic ray behaviour in lower frequency fast wave experiments. Current drive was found to not be sensitive to the launched value of the parallel index of refraction n‖, so wave accessibility issues can be reduced. Use of a travelling wave antenna provides a very narrow n‖spectrum, which also helps avoid accessibility problems.

Mode conversion and absorption of fast waves at high ion cyclotron harmonics in inhomogeneous magnetic fields

The propagation and absorption of high harmonic fast waves is of interest for non-inductive current drives in fusion experiments. The fast wave can be coupled with the ion Bernstein wave that propagates in the high magnetic field side of an ion cyclotron harmonic resonance layer. This coupling and the absorption are analyzed using the hot plasma dispersion relation and a wave equation that was converted from an approximate dispersion relation for the case where λi=k⊥2ρi2/2≳1 (where k⊥ is the perpendicular wave number and ρi is the ion Larmor radius). It is found that both reflection and conversion may occur near the harmonic resonance layer but that they decrease rapidly, giving rise to a sharp increase in the absorption as the parallel wave number increases.

Observation of EHO in NSTX and theoretical study of its active control using HHFW antenna

Two important topics for tokamak edge-localized modes (ELM) control, based on non-axisymmetric (3D) magnetic perturbations, are studied in NSTX and combined envisioning ELM control in the future NSTX-U operation: experimental observations of the edge harmonic oscillation (EHO) in NSTX (with lower frequency than EHOs in DIII-D and elsewhere), and theoretical study of its external drive using the high-harmonic fast wave (HHFW) antenna as a 3D field coil. EHOs were observed particularly clearly in NSTX ELM-free operation with very low n core modes. A number of diagnostics have confirmed n = 4–6 edge-localized and coherent oscillations in the 2–8 kHz frequency range. These oscillations seem to have a favoured operational window in rotational shear, similar to EHOs in DIII-D quiescent H modes. However, in NSTX, they are not observed to provide significant particle or impurity transport, possibly due to their weak amplitudes, of a few mm displacements, as measured by reflectometry. The external drive of these modes has been proposed in NSTX, by utilizing audio-frequency currents in the HHFW antenna straps. Analysis shows that the HHFW straps can be optimized to maximize n = 4–6 while minimizing n = 1–3. Also, ideal perturbed equilibrium code calculations show that the optimized configuration with only 1 kAt current can produce comparable or larger displacements than the observed internal modes. Thus it may be possible to use externally driven EHOs to relax the edge pressure gradient and control ELMs in NSTX-U and future devices. Fine and external control over the edge pressure gradient would be a very valuable tool for tokamak control.