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We demonstrate a polarization-independent mode-evolution-based coupler for the silicon-on-insulator platform. The measured coupler has negligible insertion loss over a bandwidth of about 100 nm, i.e., from 1500 to 1600 nm. The measured maximum power imbalances for the polarization-independent coupler are 1.2 and 0.2 dB for the fundamental transverse electric (TE $_\text{00}$ ) mode and the fundamental transverse magnetic (TM $_\text{00}$ ) mode, respectively. Our coupler also has a compact design footprint with mode-evolution region not more than ${75}{-\mu {\rm m}}$ long.

DIII-D experiments at low density (${n}_{e}\ensuremath{\sim}{10}^{19}\text{ }\text{ }{\mathrm{m}}^{\ensuremath{-}3}$) have directly measured whistler waves in the 100--200 MHz range excited by multi-MeV runaway electrons. Whistler activity is correlated with runaway intensity (hard x-ray emission level), occurs in novel discrete frequency bands, and exhibits nonlinear limit-cycle-like behavior. The measured frequencies scale with the magnetic field strength and electron density as expected from the whistler dispersion relation. The modes are stabilized with increasing magnetic field, which is consistent with wave-particle resonance mechanisms. The mode amplitudes show intermittent time variations correlated with changes in the electron cyclotron emission that follow predator-prey cycles. These can be interpreted as wave-induced pitch angle scattering of moderate energy runaways. The tokamak runaway-whistler mechanisms have parallels to whistler phenomena in ionospheric plasmas. The observations also open new directions for the modeling and active control of runaway electrons in tokamaks.

Major developments on the Mega Amp Spherical Tokamak (MAST) have enabled important advances in support of ITER and the physics basis of a spherical tokamak (ST) based component test facility (CTF), as well as providing new insight into underlying tokamak physics. For example, L–H transition studies benefit from high spatial and temporal resolution measurements of pedestal profile evolution (temperature, density and radial electric field) and in support of pedestal stability studies the edge current density profile has been inferred from motional Stark effect measurements. The influence of the q-profile and E × B flow shear on transport has been studied in MAST and equilibrium flow shear has been included in gyro-kinetic codes, improving comparisons with the experimental data. H-modes exhibit a weaker q and stronger collisionality dependence of heat diffusivity than implied by IPB98(y,2) scaling, which may have important implications for the design of an ST-based CTF. ELM mitigation, an important issue for ITER, has been demonstrated by applying resonant magnetic perturbations (RMPs) using both internal and external coils, but full stabilization of type-I ELMs has not been observed. Modelling shows the importance of including the plasma response to the RMP fields. MAST plasmas with q > 1 and weak central magnetic shear regularly exhibit a long-lived saturated ideal internal mode. Measured plasma braking in the presence of this mode compares well with neo-classical toroidal viscosity theory. In support of basic physics understanding, high resolution Thomson scattering measurements are providing new insight into sawtooth crash dynamics and neo-classical tearing mode critical island widths. Retarding field analyser measurements show elevated ion temperatures in the scrape-off layer of L-mode plasmas and, in the presence of type-I ELMs, ions with energy greater than 500 eV are detected 20 cm outside the separatrix. Disruption mitigation by massive gas injection has reduced divertor heat loads by up to 70%.

Energetic minority protons with ~100 keV effective temperature are routinely created in Alcator C-Mod plasmas with the application of ion-cyclotron-range-of-frequency (ICRF) heating. A multichannel compact neutral particle analyzer (CNPA) is used to make measurements of these distributions in Alcator C-Mod's unique and reactor-relevant operating space via active and passive charge-exchange techniques. A radially injected 50 keV diagnostic hydrogen neutral beam is used for active analysis. Using a detailed model that accounts for beam, halo and impurity electron donors, core proton temperatures of ~30–120 keV are directly measured for the first time in lower density (ne0 ~ (0.8–1.5) × 1020 m−3) Alcator C-Mod plasmas with up to only ~0.5 MW of ICRF power. The model found that the minority proton temperatures are peaked spatially away from r/a = 0, even for an on-axis resonance. Additionally, noticeable phase-space anisotropy is seen as expected for ICRF heating. The measured effective temperatures also scale approximately with the Stix parameter. The CNPA temperature measurements are compared with several leading simulation packages such as the TORIC/FPPRF and AORSA/CQL3D full-wave/Fokker–Planck (FW/FP) solvers. Preliminary comparisons with the AORSA/CQL3D code which include results from a new synthetic diagnostic show good agreement and demonstrate that accurate tracking of the minority distribution during iterations of the FW and FP solvers is required to simulate Alcator C-Mod's energetic minority populations with accuracy. Physically, poor wave focusing and preferential heating of trapped energetic protons are found to move the fast proton temperature profiles off-axis. These FW/FP analyses represent the first comparison between predictions of these detailed codes and core minority tail experimental measurements on Alcator C-Mod.

Mode conversion of fast waves in the ion cyclotron range of frequencies (ICRF) is known to result in current drive and flow drive under optimised conditions, which may be utilized to control plasma profiles and improve fusion plasma performance. To describe these processes accurately in a realistic toroidal geometry, numerical simulations are essential. Quantitative comparison of these simulations and the actual experimental measurements is important to validate their predictions and to evaluate their limitations. The phase contrast imaging (PCI) diagnostic has been used to directly detect the ICRF waves in the Alcator C-Mod tokamak. The measurements have been compared with full-wave simulations through a synthetic diagnostic technique. Recently, the frequency response of the PCI detector array on Alcator C-Mod was recalibrated, which greatly improved the comparison between the measurements and the simulations. In this study, mode converted waves for D-{superscript 3]He and D-H plasmas with various ion species compositions were re-analyzed with the new calibration. For the minority heating cases, self-consistent electric fields and a minority ion distribution function were simulated by iterating a full-wave code and a Fokker-Planck code. The simulated mode converted wave intensity was in quite reasonable agreement with the measurements close to the antenna, but discrepancies remain for comparison at larger distances., United States. Department of Energy (Grant DE-FG02- 94ER54235)

Recent efforts have shown that helicon waves (fast waves at > 20ωci) may be an attractive option for driving efficient off-axis current drive during non-inductive tokamak operation for DIII-D, ITER and DEMO. For DIII-D scenarios, the ray tracing code, GENRAY, has been extensively used to study helicon current drive efficiency and location as a function of many plasma parameters. The full wave code, AORSA, which is applicable to arbitrary Larmor radius and can resolve arbitrary ion cyclotron harmonic order, has been recently used to validate the ray tracing technique at these high cyclotron harmonics. If the SOL is ignored, it will be shown that the GENRAY and AORSA calculated current drive profiles are comparable for the envisioned high beta advanced scenarios for DIII-D, where there is high single pass absorption due to electron Landau damping and minimal ion damping. AORSA is also been used to estimate possible SOL effects on helicon current drive coupling and SOL absorption due to collisional and slow wave effects.

Waves in the ion cyclotron range of frequencies (ICRF) are one of the major tools to heat fusion plasmas. Full-wave simulations are essential to predict the wave propagation and absorption quantitatively, and it is important that these codes be validated against actual experimental measurements. In this work, the absolute intensity of the ICRF waves previously measured with a phase contrast imaging diagnostic was recalibrated and compared once more with full-wave predictions. In the earlier work, significant discrepancies were found between the measured and the simulated mode converted wave intensity [N. Tsujii et al., Phys. Plasmas 19, 082508]. With the new calibration of the detector array, the measured mode converted wave intensity is now in much better agreement with the full-wave predictions. The agreement is especially good for comparisons performed close to the antenna.

The National Spherical Torus Experiment (NSTX) is currently being upgraded to operate at twice the toroidal field and plasma current (up to 1 T and 2 MA), with a second, more tangentially aimed neutral beam (NB) for current and rotation control, allowing for pulse lengths up to 5 s. Recent NSTX physics analyses have addressed topics that will allow NSTX-Upgrade to achieve the research goals critical to a Fusion Nuclear Science Facility. These include producing stable, 100% non-inductive operation in high-performance plasmas, assessing plasma–material interface (PMI) solutions to handle the high heat loads expected in the next-step devices and exploring the unique spherical torus (ST) parameter regimes to advance predictive capability. Non-inductive operation and current profile control in NSTX-U will be facilitated by co-axial helicity injection (CHI) as well as radio frequency (RF) and NB heating. CHI studies using NIMROD indicate that the reconnection process is consistent with the 2D Sweet–Parker theory. Full-wave AORSA simulations show that RF power losses in the scrape-off layer (SOL) increase significantly for both NSTX and NSTX-U when the launched waves propagate in the SOL. Toroidal Alfven eigenmode avalanches and higher frequency Alfven eigenmodes can affect NB-driven current through energy loss and redistribution of fast ions. The inclusion of rotation and kinetic resonances, which depend on collisionality, is necessary for predicting experimental stability thresholds of fast growing ideal wall and resistive wall modes. Neutral beams and neoclassical toroidal viscosity generated from applied 3D fields can be used as actuators to produce rotation profiles optimized for global stability. DEGAS-2 has been used to study the dependence of gas penetration on SOL temperatures and densities for the MGI system being implemented on the Upgrade for disruption mitigation. PMI studies have focused on the effect of ELMs and 3D fields on plasma detachment and heat flux handling. Simulations indicate that snowflake and impurity seeded radiative divertors are candidates for heat flux mitigation in NSTX-U. Studies of lithium evaporation on graphite surfaces indicate that lithium increases oxygen surface concentrations on graphite, and deuterium–oxygen affinity, which increases deuterium pumping and reduces recycling. In situ and test-stand experiments of lithiated graphite and molybdenum indicate temperature-enhanced sputtering, although that test-stand studies also show the potential for heat flux reduction through lithium vapour shielding. Non-linear gyro kinetic simulations have indicated that ion transport can be enhanced by a shear-flow instability, and that non-local effects are necessary to explain the observed rapid changes in plasma turbulence. Predictive simulations have shown agreement between a microtearing-based reduced transport model and the measured electron temperatures in a microtearing unstable regime. Two Alfven eigenmode-driven fast ion transport models have been developed and successfully benchmarked against NSTX data. Upgrade construction is moving on schedule with initial physics research operation of NSTX-U planned for mid-2015.

The AORSA global-wave solver is combined with the CQL3D bounce-averaged Fokker-Planck code to simulate the quasilinear evolution of non-thermal distributions in ion cyclotron resonance heating of tokamak plasmas. A novel re-formulation of the quasilinear operator enables calculation of the velocity space diffusion coefficients directly from the global wave fields. To obtain self-consistency between the wave fields and particle distribution function, AORSA and CQL3D have been iteratively coupled using Python. The combined selfconsistent model is applied to minority ion heating in the Alcator C-Mod tokamak. Results show the formation of a 70 keV ion tail near the minority ion cyclotron resonance layer in approximate agreement with measurements from charge exchange neutral particle analyzers.

Nonlinear interactions of ion cyclotron range of frequency (ICRF) waves with fusion plasmas are reviewed. Although the linear theory of ICRF waves, including fast waves (FWs), high-harmonic fast waves and ion Bernstein waves (IBWs), is widely applicable, nonlinear effects can still be important, especially in the edge plasma or for novel core applications. Here the topics of flow drive, ponderomotive forces, radiofrequency (rf) sheaths, parametric decay and related interactions with the edge plasma are considered. Primary emphasis is placed on the basic underlying physics and tokamak applications. For FW antennas, the parallel electric field near launching structures is known to drive rf sheaths which can give rise to convective cells, interaction with plasma 'blobs', impurity production and edge power dissipation. In addition to sheaths, IBW waves in the edge plasma are subject to strong ponderomotive effects and parametric decay. In the core plasma, slow waves can sometimes induce nonlinear effects. Mechanisms by which these waves can influence the radial electric field and its shear are summarized and related to the general (reactive-ponderomotive and dissipative) force on a plasma from rf waves. Standard ICRF codes have begun to incorporate the nonlinear topics described here. Further progress in integrated simulation should allow new predictive modelling capabilities.

Global wave solutions with self-consistent velocity distributions are calculated for ion cyclotron heating in non-Maxwellian plasmas. The all-orders spectral algorithm (AORSA) global wave solver is generalized to treat non-thermal velocity distributions arising from fusion reactions, neutral beam injection and wave driven diffusion in velocity space. Quasi-linear diffusion coefficients are derived directly from the wave electric field and used to calculate ion velocity distribution functions with the CQL3D Fokker–Planck code. Alternatively, the quasi-linear coefficients can be calculated numerically by integrating the Lorentz force equations along particle orbits. Self-consistency between the wave electric field and resonant ion distribution function is achieved by iterating between the global-wave and Fokker–Planck solutions.

Fast waves (FW) are a primary technique for heating and current drive (CD) on the proposed burning plasma device, International Tokamak Experimental Reactor (ITER) and lower hybrid (LH) waves are a candidate for edge current profile control. The models used to simulate these two waves rely on assumptions of Maxwellian populations that allow efficient analytic implementations of the plasma response, and in the case of the LH wave, the ray tracing models used are able to follow the very small wavelengths in a continuum manner without requiring a fine computational grid. Recent advances in algorithms and parallel computational methods have allowed these assumptions to be tested, permitting more accurate estimates of heating deposition and CD efficiencies in a burning plasma. Absorption by energetic particles for both waves can be significant, reducing electron heating and associated CD. Wave propagation and absorption are dependent on the velocity space distribution of particles in the plasma and geometric effects of focusing and diffraction. Fusion-born alpha particles and neutral beam ions may interact with these waves in a manner that cannot be accurately modelled by Maxwellian distributions. The AORSA2D code has been modified to use a generalized non-Maxwellian conductivity and applied to ITER reference scenarios. The effects of diffraction on LH waves in toroidal geometry are not well understood because computational limits have prohibited full-wave simulations at those small wavelengths. Simulations of LH waves have been restricted to WKB ray tracing techniques and one-dimensional full-wave in the past, but the availability of massively parallel architectures has made full-wave calculations using an electromagnetic field solver tractable. The TORIC code has been adapted to run on parallel architectures making it possible to resolve the slow electrostatic LH wave. We present full-wave simulations of LH slow and FW in toroidal geometry using a Maxwellian distribution with non-relativistic electron damping in Alcator C-Mod at values of (ωpe/ωce)2 comparable to those expected in the ITER device.

The major objective of the National Spherical Torus Experiment (NSTX) is to understand basic toroidal confinement physics at low aspect ratio and high βT in order to advance the spherical torus (ST) concept. In order to do this, NSTX utilizes up to 7.5 MW of neutral beam injection, up to 6 MW of high harmonic fast waves (HHFWs), and it operates with plasma currents up to 1.5 MA and elongations of up to 2.6 at a toroidal field up to 0.45 T. New facility, and diagnostic and modelling capabilities developed over the past two years have enabled the NSTX research team to make significant progress towards establishing this physics basis for future ST devices. Improvements in plasma control have led to more routine operation at high elongation and high βT (up to ~40%) lasting for many energy confinement times. βT can be limited by either internal or external modes. The installation of an active error field (EF) correction coil pair has expanded the operating regime at low density and has allowed for initial resonant EF amplification experiments. The determination of the confinement and transport properties of NSTX plasmas has benefitted greatly from the implementation of higher spatial resolution kinetic diagnostics. The parametric variation of confinement is similar to that at conventional aspect ratio but with values enhanced relative to those determined from conventional aspect ratio scalings and with a BT dependence. The transport is highly dependent on details of both the flow and magnetic shear. Core turbulence was measured for the first time in an ST through correlation reflectometry. Non-inductive start-up has been explored using PF-only and transient co-axial helicity injection techniques, resulting in up to 140 kA of toroidal current generated by the latter technique. Calculated bootstrap and beam-driven currents have sustained up to 60% of the flat-top plasma current in NBI discharges. Studies of HHFW absorption have indicated parametric decay of the wave and associated edge thermal ion heating. Energetic particle modes, most notably toroidal Alfven eigenmodes and fishbone-like modes result in fast particle losses, and these instabilities may affect fast ion confinement on devices such as ITER. Finally, a variety of techniques has been developed for fuelling and power and particle control.

Ion absorption of the high harmonic fast wave in a spherical torus [Y.-K. M. Peng et al., Nucl. Fusion 26, 769 (1986)] is of critical importance to assessing the viability of the wave as a means of heating and driving current. Analysis of recent National Spherical Torus Experiment [M. Ono et al., Nucl. Fusion 40, 557 (2000)] shots has revealed that under some conditions when neutral beam and rf power are injected into the plasma simultaneously, a fast ion population with energy above the beam injection energy is sustained by the wave. In agreement with modeling, these experiments find the rf-induced fast ion tail strength and neutron rate at lower B-fields to be less enhanced, likely due to a larger β profile, which promotes greater off-axis absorption where the fast ion population is small. Ion loss codes find the increased loss fraction with decreased B insufficient to account for the changes in tail strength, providing further evidence that this is a rf interaction effect. Though greater ion absorption...

The ability to obtain high plasma densities with high fractional ionization using readily available, low-cost components makes the helicon a candidate plasma source for many applications, including plasma rocket propulsion, fusion component testing, and materials processing. However, operation of a helicon can be a sensitive function of the magnetic field strength and geometry as well as the driving frequency, especially when using light feedstock gases such as hydrogen or helium. In this paper, we compare results from a coupled radio frequency (RF) and transport model with experiments in the axially inhomogeneous Mini-Radio Frequency Test Facility (Mini-RFTF). Experimental observations of the radial shape of the density profile can be quantitatively reproduced by iteratively converging a high-resolution RF calculation including the RF parallel electric field with a transport model using reasonable choices for the transport parameters. The experimentally observed transition into the high density helicon mode is observed in the model, appearing as a nonlinear synergism between radial diffusion, the RF coupling to parallel electric fields that damp near the plasma edge, and propagation of helicon waves that collisionally damp near the axis of the device. Power deposition from various electric field components indicates that inductive coupling and absorption in the edge region can reduce the efficiency for high-density operation. These findings can be used to optimize helicon discharges for use in Variable Specific Impulse Magnetoplasma Rocket (VASIMR) designs, and estimates for the helicon power required to perform ion cyclotron heating experiments in the Mini-RFTF are given.

ICRF (ion cyclotron range of frequencies) heating experiments were performed in D-H plasmas at various H concentrations on ASDEX Upgrade. The rf power was modulated to measure the electron power deposition profile from electron temperature modulation. To minimize the contribution from indirect collisional heating and the effect of radial transport, the rf power was modulated at 50 Hz. However, peaking of electron temperature modulation was still observed around the hydrogen cyclotron resonance indicating collisional heating contribution. Time dependent simulation of the hydrogen distribution function was performed for the discharges, using the full-wave code AORSA (E.F. Jaeger, et al., Phys. Plasmas, Vol. 8, page 1573 (2001)) coupled to the Fokker-Planck code CO1.31) (R.W. Harvey, et al., Proc. IAEA (1992)). In the present experimental conditions, it was found that modulation of the collisional heating was comparable to that of direct wave damping. Impact of radial transport was also analyzed and found to appreciably smear out the modulation profile and reduce the phase delay.

NSTX-Upgrade will operate with toroidal magnetic fields (BT) up to 1 T, nearly twice the value used in the experiments on NSTX, and the available NBI power will be doubled. The doubling of BT 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 (MHFW) regime. By making use of the full wave code AORSA, this work shows that direct ion damping (mainly by thermal ions localized at the 5th harmonic resonance) might be significant in NSTX-Upgrade under TRANSP predicted full performance conditions and the electron and ion absorption is sensitive to the ratio of electron and ion temperature. Launching at high toroidal wave number appears to be one way to significantly reduce the ion damping. By using the extended AORSA code, which includes a detailed description of the scrape-off layer in the field solutions, we found a large electric field amplitude outside of the last closed flux surface as previousl...

Spectral calculations of radio-frequency (rf) heating in tokamak plasmas are extended to two dimensions (2-D) by taking advantage of new computational tools for distributed memory, parallel computers. The integral form of the wave equation is solved in 2-D without any assumption regarding the smallness of the ion Larmor radius (ρ) relative to the perpendicular wavelength (λ⊥). Results are therefore applicable to all orders in k⊥ρ, where k⊥=2π/λ⊥. Previous calculations of rf wave propagation and heating in 2-D magnetized plasmas have relied on finite Larmor radius expansions (k⊥ρ≪1) and are thus limited to relatively long wavelengths. In this paper, no such assumption is made, and we consider short wavelength processes such as the excitation and absorption of ion Bernstein waves in 2-D with k⊥ρ>1. Results show that this phenomenon is far more complex than simple one-dimensional plasma models would suggest. Other applications include fully self-consistent 2-D solutions for high-harmonic fast-wave heating in...

A full-wave, one-dimensional spectral model is developed to study sheared poloidal flow driven by high-harmonic ion Bernstein waves (IBWs) in tokamak plasmas. The local plasma conductivity is corrected to lowest order in ρ/L where ρ is the ion Larmor radius and L is the equilibrium scale length. This correction takes into account gradients in equilibrium quantities and is necessary for conservation of energy. It is equivalent to the “odd-order derivative” terms in finite difference models. No assumption is made regarding the smallness of the ion Larmor radius relative to wavelength, and results are applicable to all orders in k⊥ρ where k⊥ is the perpendicular wave number. Previous numerical results for flow drive have relied on expansions in k⊥ρ, and are thus limited to cyclotron harmonics of two and below. In this article, we consider higher-harmonic cases corresponding to recent IBW flow drive experiments on the Tokamak Fusion Test Reactor [B. P. LeBlanc, R. E. Bell, S. Bernabei et al., Phys. Rev. Lett....

Different plasma responses to neutral beam injection in the directions co and counter to the plasma current have long been accepted as well understood in neutral beam heating of tokamak plasmas. Differences can also occur in fast wave heating and current drive in the ion cyclotron range of frequencies (ICRF) when antenna arrays are phased to drive current co and counter to the plasma current. The source of this asymmetry can be easily seen in the cold plasma wave equation with an applied magnetic field in the z direction and the parallel ICRF electric field set to zero (small electron mass limit). In the absence of absorption, the wave equation displays perfect up-down symmetry. However, when absorption is introduced, the up-down symmetry is destroyed by Hall terms, which depend on density and magnetic field gradients. This is confirmed by simple numerical solutions of the cold plasma wave equation with and without collisions. The same up-down asymmetry appears in three dimensional (3-D) antenna coupling calculations with outgoing boundary conditions. These show a natural poloidal shift in the antenna's radiated power spectrum even when no poloidal magnetic field is present. When a poloidal magnetic field is introduced, the up-down asymmetry acquires a toroidal component. This leads to differences in electron heating and current drive depending on the direction that fast waves are launched relative to the plasma current. Such differences are clearly seen in full wave modelling calculations of heating and current drive in NSTX, where poloidal and toroidal magnetic fields are comparable in magnitude near the antenna. When density gradients are forced to zero, both up-down and co-counter asymmetries disappear.

An ion cyclotron range of frequencies (ICRF) heating experiment was performed on the Compact Helical System (CHS) device in order to identify the problems in establishing this as a reliable heating method. Radiofrequency heating was applied to plasmas with two ion species produced by ECH. Stored energy increased upto 2.2 kJ with the application of a 590 kW ICRF heating pulse, giving a heating efficiency comparable to that of NBI heating. More importantly, the `flat-top' of the stored energy was maintained during the pulse. Good heating was realized with 30% proton and 70% deuteron plasmas at high density (4*1019 m-3). It was found that the best discharges are dominated by electron ICRF heating, which seems to be the reason for the successful results. On the contrary, a flat-top in stored energy has never been obtained in discharges where ion heating dominates. The loss of high energy ions with large pitch angles produced by ion heating appears to degrade the performance and limit the duration of the heating. A similar degradation was encountered in previous ICRF heating experiments in helical systems. A newly designed detector was used to study the loss of the helically trapped particles

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 (t...

The Alfven resonances may occur on the low- and high-field sides for a low-frequency fast wave current drive scenario proposed for the International Thermonuclear Experimental Reactor (ITER) [Nucl. Fusion 31, 1135 (1991)]. At the resonance on the low-field side, the fast wave may be mode converted into a short-wavelength slow wave, which can be absorbed by electrons at the plasma edge, before the fast wave propagates into the core area of the plasma. Such absorption may cause a significant parasitic power loss.

The first experiments utilizing high‐power radio waves in the ion cyclotron range of frequencies to heat deuterium–tritium (D–T) plasmas have been completed on the Tokamak Fusion Test Reactor [Fusion Technol. 21, 13 (1992)]. Results from the initial series of experiments have demonstrated efficient core second harmonic tritium (2ΩT) heating in parameter regimes approaching those anticipated for the International Thermonuclear Experimental Reactor [D. E. Post, Plasma Physics and Controlled Nuclear Fusion Research, Proceedings of the 13th International Conference, Washington, DC, 1990 (International Atomic Energy Agency, Vienna, 1991), Vol. 3, p. 239]. Observations are consistent with modeling predictions for these plasmas. Efficient electron heating via mode conversion of fast waves to ion Bernstein waves has been observed in D–T, deuterium‐deuterium (D–D), and deuterium–helium‐4 (D–4He) plasmas with high concentrations of minority helium‐3 (3He) (n3He/ne≳10%). Mode conversion current drive in D–T plasmas ...

A new mechanism is identified for radio frequency (RF) wave induced force and current drive caused by a kinetic flux carried by coherent oscillations of plasma particles. The induced force along a magnetic field line by RF heating of plasmas is calculated with a one‐dimensional slab model, and found to be contributed by the plasma power absorption and spatial inhomogeneity. The inhomogeneity term consists of a kinetic flux and a flux related to RF wave helicity injection rate. The effect from the kinetic flux exists only in a warm plasma, whereas, in contrast, the effect from the helicity related flux exists even in a cold plasma. The forces are calculated for both electrons and ions in the ion cyclotron range of frequencies (ICRF), and the effects from the ion cyclotron and the second harmonic resonance are included.

A two-dimensional (r, z) fluid model is used to study plasma transport in inductively coupled plasmas (ICPS). Electron heating from external RF coil driven at 2 MHz is calculated self-consistently by solving for the time-averaged RF electric field. Radial plasma uniformity has been studied in both high (R/L=2.5) and low (R/L=1) aspect ratio ICP reactors driven with external planar or cylindrical coils. The effect of neutral gas pressure on plasma uniformity is presented for Ar discharges at 5 and 20 mTorr. The location of external coils and corresponding power deposition profile is predicted to have little effect on uniformity except at higher pressure (>or approximately= 20 mTorr) and for large aspect ratios. Planar coils appear superior to cylindrical coils for achieving relatively consistent uniformity over a wide range of pressures and reactor aspect ratios.

Benchmarking full-wave solvers for ion-cyclotron range of frequency (ICRF) simulations is performed using plasma profiles and equilibria obtained from integrated self-consistent modelling predictions of four ITER plasmas. One is for a high-performance baseline (5.3 T, 15 MA) DT H-mode. The others are for half-field, half-current plasmas of interest for the pre-activation phase with bulk plasma ion species being either hydrogen or He4. The predicted profiles are used by six full-wave solver groups to simulate the ICRF electromagnetic fields and heating, and by three of these groups to simulate the current drive. Approximate agreement is achieved by four of the solvers for the heating power partitions for the DT and He4 cases. Factor of two or more disagreements are found for the heating power partitions for the cases with second harmonic He3 heating in bulk H cases. Approximate agreement is achieved simulating the ICRF current-drive 1D profiles.

Fast wave poloidal flow generation at the plasma edge of a tokamak is studied with a one‐dimensional slab model. In the absence of mode conversion, the poloidal flow can be generated by a spatial change of plasma velocity and current density profiles due to strong minority ion power absorption at the minority ion cyclotron resonance. The electromagnetic force plays a more important role in the flow generation than does the plasma Reynolds stress. In the presence of mode conversion, the flow is mainly generated by interference between the long‐wavelength transmitted fast wave and the short‐wavelength ion Bernstein wave (IBW) from mode conversion. Flow shear generated in the presence of mode conversion varies spatially with a scale length similar to the IBW wavelength. With mode conversion, the plasma Reynolds stress becomes more important in the flow shear generation than the electromagnetic force. For both cases, the plasma Reynolds stress and the electromagnetic force are out of phase, so that the result...

An account is given of the high performance plasmas established by development of the H-mode regime in JET in the experimental campaigns up to 1992. High performance in this case is measured in terms of the confinement enhancement achieved over the L-mode scaling as measured using the plasma diamagnetism. Three JET H-mode regimes have achieved enhancement factors (H G DIA ) over Goldston L-mode scaling of 2.5 < H G DIA < 4.0. These are the Pellet Enhanced Performance (PEP) H-MODE, the high bootstrap fraction (high β POL ) H-mode and the Hot Ion (HI) H-mode. The phenomenology of these three regimes is reviewed and contrasts and common threads are elucidated

Observations of improved radio frequency (rf) heating efficiency in ITER relevant high-confinement ($H$-)mode plasmas on the National Spherical Tokamak Experiment are investigated by whole-device linear simulation. The steady-state rf electric field is calculated for various antenna spectra and the results examined for characteristics that correlate with observations of improved or reduced rf heating efficiency. We find that launching toroidal wave numbers that give fast-wave propagation in the scrape-off plasma excites large amplitude ($\ensuremath{\sim}\mathrm{kV}\text{ }{\mathrm{m}}^{\ensuremath{-}1}$) coaxial standing modes between the confined plasma density pedestal and conducting vessel wall. Qualitative comparison with measurements of the stored plasma energy suggests that these modes are a probable cause of degraded heating efficiency.

Theoretical considerations and high spatial resolution numerical simulations of radio frequency (rf) wave heating in tokamaks and in spherical toruses (ST) indicate that fast waves launched into tokamaks in the ion cyclotron range of frequencies (ICRF) or into spherical toruses in the high harmonic fast wave (HHFW) regime may excite a short wavelength slow mode inside of the plasma discharge due to the presence of hot electrons that satisfy the condition ω

The validity of ICRF quasilinear (QL) diffusion theory is examined in the context of the C‐Mod ICRF experiment by comparison with coefficients calculated from Lorentz orbits in AORSA full‐wave fields, using the DC (Diffusion Coefficient) code. The “exact” Lorentz orbit results largely agree with QL theory, although there are differences in detail. Overall conclusions are that approximation of the excited RF by a single toroidal mode leads, in the Lorentz calculation, to strong correlation pitch angle modification of the RF diffusion; this thereby modifies self‐consistent radial power absorption calculated with the CQL3D Fokker‐Planck code. However, inclusion of a full toroidal mode spectrum results in most, but not all, correlations ceasing to exist. Hence, modeling of ICRF power absorption using a correlation‐less QL theory is reasonably accurate, even with a suitably chosen single toroidal mode. Multi‐mode correlations remain, particularly for neighboring resonances such as when the trapped particles pa...

We present a qualitative comparison of NSTX HHFW heating efficiency observations[1, 2] with results from the AORSA[3] whole‐device, linear simulation. The simulation retains a realistic geometry and core plasma kinetic physics such that scrape‐off plasma linear RF fields can be calculated. By examining L‐mode and neutral beam heated H‐mode scenarios we quantify the conditions that result in a fast‐wave coaxial mode in the scrape‐off plasma. These large amplitude coaxial modes are expected to damp on collisions or couple to non‐linear damping mechanisms and be correlated to an observed drop in core heating efficiency.

30 MHz high‐harmonic fast wave (HHFW) heating and current drive are being developed to assist fully non‐inductive plasma current (Ip) ramp‐up in NSTX. The initial approach to achieving this goal has been to heat Ip = 300 kA inductive plasmas with current drive antenna phasing in order to generate an HHFW H‐mode with significant bootstrap and RF‐driven current. Recent experiments, using only 1.4 MW of RF power (PRF), achieved a non‐inductive current fraction, fNI∼0.65. Improved antenna conditioning resulted in the generation of Ip = 650 kA HHFW H‐mode plasmas, with fNI∼0.35, when PRF≥2.5 MW. These plasmas have little or no edge localized mode (ELM) activity during HHFW heating, a substantial increase in stored energy and a sustained central electron temperature of 5–6 keV. Another focus of NSTX HHFW research is to heat an H‐mode generated by 90 keV neutral beam injection (NBI). Improved HHFW coupling to NBI‐generated H‐modes has resulted in a broad increase in electron temperature profile when HHFW heating...

In recent moderate to high harmonic fast wave heating and current drive experiments in DIII‐D, a synergy effect was observed when the 6th harmonic 90 MHz fast wave power is applied to the plasma preheated by neutral beams and the 4th harmonic 60 MHz fast wave. In this paper, we investigate how the synergy can occur using ORBIT‐RF coupled with AORSA. Preliminary simulations suggest that damping of 4th harmonic FW on beam ions accelerates them above the injection energy, which may allow significant damping of 6th harmonic FW on beam ion tails to produce synergy.

Waves in the ion cyclotron range of frequencies (ICRF) are widely used to heat toka‐mak plasmas. In a multi‐ion‐species plasma, the FW converts to ion cyclotron waves (ICW) and ion Bernstein waves (IBW) around the ion‐ion hybrid resonance (mode conversion). The mode converted wave is of interest as an actuator to optimise plasma performance through flow drive and current drive. Numerical simulations are essential to describe these processes accurately, and it is important that these simulation codes be validated. On Alcator C‐Mod, direct measurements of the mode converted waves have been performed using Phase Contrast Imaging (PCI), which measures the line‐integrated electron density fluctuations. The results were compared to full‐wave simulations AORSA and TORIC. AORSA is coupled to a Fokker‐Planck code CQL3D for self‐consistent simulation of the wave electric field and the minority distribution function. The simulation results are compared to PCI measurements using synthetic diagnostic. The experiments ...

ELMs reduce the stored energy achieved with HHFW heating compared with the ELM free case as also occurs for NBI heating alone. This reduction can be attributed both to direct ELM ejection of stored energy and to an increase in edge density with ELMs that exceeds the onset density for perpendicular wave propagation near the antenna [1,2], and leads to significantly more edge RF power deposition. This latter effect causes a more intense RF “hot” zone in the lower divertor scrape off region due to an increase in edge RF power propagating to the divertor from the antenna region along the magnetic field lines. Fast IR measurements of the direct ELM heat deposition at the lower divertor shows it to be peaked in the vicinity of the outer strike radius and to fall off strongly as the “hot” zone is approached, indicating little direct ELM effect on the “hot” zone heating. Physics studies of the “hot” zone have begun with sweeping the RF “hot” zone spiral over Rogowski instrumented divertor region tiles to show tha...

Analysis of fast‐ion distributions >100 Te is important for both ITER and a fusion reactor, as both will have a significant population of fusion‐born alpha particles. Furthermore, energetic ions may display transport properties that differ from the bulk plasma. It is imperative to benchmark current simulation codes with measurements of highly energetic fast‐ions on current devices. Experimental measurements of ICRF heated H‐minority plasmas on Alcator C‐Mod are performed with an upgraded Compact Neutral Particle Analyzer (CNPA). The CNPA consists of vertically‐viewing photodiode detectors with viewing chords from r/a = ∼0.18 to 0.6 and energies from 150 keV to 1.5 MeV. The CNPA measurements are compared to the output of a synthetic diagnostic that has been added to the Fokker‐Planck solver CQL3D. CQL3D is coupled with the full‐wave solver AORSA to evolve a self‐consistent fast‐ion distribution. Good agreement is obtained between simulation and experiment for fast ion distributions that are in steady‐state...

Improved core high-harmonic fast wave (HHFW) heating at longer wavelengths and during start-up and plasma current ramp-up has now been obtained by lowering the edge density with lithium wall conditioning, thereby moving the critical density for perpendicular fast-wave propagation away from the vessel wall. Lithium conditioning allowed significant HHFW core electron heating of deuterium neutral beam injection (NBI) fuelled H-mode plasmas to be observed for the first time. Large edge localized modes were observed immediately after the termination of rf power. Visible and infrared camera images show that fast wave interactions can deposit considerable rf energy on the outboard divertor. HHFW-generated parametric decay instabilities were observed to heat ions in the plasma edge and may be the cause for a measured drag on edge toroidal rotation during HHFW heating. A significant enhancement in neutron rate and fast-ion profile was measured in NBI-fuelled plasmas when HHFW heating was applied. © 2010 American Institute of Physics.

Fast wave heating experiments in the ion cyclotron range of frequencies (ICRF) were performed on target plasmas produced by 350 kW of electron cyclotron heating at 53 GHz and also by neutral beam injection in the Advanced Toroidal Facility (ATF). Various heating regimes were investigated in the frequency range between 9.2 MHz and 28.8 MHz with magnetic fields of 0.95 T and 1.9 T on axis. The nominal pulse lengths of up to 200 kW RF power were in the range between 100 and 400 ms. Data from spectroscopy, loading measurements, and edge RF and Langmuir probes were used to characterize the RF induced effects on the ATF plasma. In the hydrogen minority regime at low plasma density, large suprathermal ion tails were observed with a neutral particle analyser. At high density (ne ≥ 5.0 × 1013 cm-3) substantial increases in antenna loading were observed, but ICRF power was insufficient to produce definitive heating results. A two-dimensional RF heating code, ORION, and a Fokker-Planck code, RFTRANS, were used to simulate these experiments. A simulation of future high power, higher density experiments in ATF indicates improved bulk heating results due to the improved loading and more efficient thermalization of the minority tail

The heating of the electrons in a plasma by radio frequency (rf) fields results in an electron distribution function that can be highly non‐Maxwellian. The response of these heated electrons can lead to a substantially larger total potential drop than that obtained by arbitrarily choosing a single‐temperature parameter to describe the electron distribution in a traditional Boltzmann approximation. Electromotively driven rf fields can have scale lengths along a static magnetic field line that are much larger than a Debye length and produce electron–sheath interactions that are best described as collisions. Estimates of the floating potential of a plasma that is excited by electromotively driven rf plasma currents parallel to a strong static magnetic field have been made using a Fermi acceleration heating model and linear estimates for the rf fields with plasma. When this non‐Maxwellian distribution function is used for estimates of the static potential, the results show that the total potential drop is proportional to the rf oscillation energy and the square root of the ion to electron mass ratio. Numerical solutions to Poisson’s equation are presented for non‐Boltzmann electrons. Analytic estimates of parasitic rf power absorption and edge profile modification using a Bohm diffusion model are presented. Estimates for a purely electrostatic heating operator with rf fields that are assumed to scale as the Debye length along static magnetic field lines are also made for comparison with the electromagnetic result.

Recent improvements in high-harmonic fast wave (HHFW) core heating in NSTX are attributed to using lithium conditioning, and other wall conditioning techniques, to move the onset density for perpendicular fast wave propagation further from the antenna. This has resulted in the first observation of HHFW core electron heating in deuterium plasma at a launched toroidal wavenumber, kφ = -3 m-1, NSTX record core electron temperatures of 5 keV in helium and deuterium discharges and, for the first time, significant HHFW core electron heating of deuterium neutral-beam-fuelled H-mode plasmas. Also, kφ = -8 m-1 heating of the plasma startup and plasma current ramp-up has resulted in significant core electron heating, even at central electron densities as low as ~ 4x1018 m-3.

The goal of the high harmonic fast wave (HHFW) research on NSTX is to maximize the coupling of RF power to the core of the plasma by minimizing the coupling of RF power to edge loss processes. HHFW core plasma heating efficiency in helium and deuterium L-mode discharges is found to improve markedly on NSTX when the density 2 cm in front of the antenna is reduced below that for the onset of perpendicular wave propagation (nonset ∝ B*k|| 2/ω). In NSTX, the observed RF power losses in the plasma edge are driven in the vicinity of the antenna as opposed to resulting from multi-pass edge damping. PDI surface losses through ion-electron collisions are estimated to be significant. Recent spectroscopic measurements suggest that additional PDI losses could be caused by the loss of energetic edge ions on direct loss orbits and perhaps result in the observed clamping of the edge rotation. Initial deuterium H-mode heating studies reveal that core heating is degraded at lower kφ (- 8 m-1 relative to 13 m-1) as for the Lmode case at elevated edge density. Fast visible camera images clearly indicate that a major edge loss process is occurring from the plasma scrape off layer (SOL) in the vicinity of the antenna and along the magnetic field lines to the lower outer divertor plate. Large type I ELMs, which are observed at both kφ values, appear after antenna arcs caused by precursor blobs, low level ELMs, or dust. For large ELMs without arcs, the source reflection coefficients rise on a 0.1 ms time scale, which indicates that the time derivative of the reflection coefficient can be used to discriminate between arcs and ELMs.

The rf‐SciDAC collaboration is developing computer simulations to predict the damping of radio frequency (rf) waves in fusion plasmas. Here we extend self‐consistent quasi‐linear calculations of ion cyclotron resonant heating to include the finite drift of ions from magnetic flux surfaces and rf induced spatial transport. The all‐orders spectral wave solver AORSA is iteratively coupled with a particle based update of the plasma distribution function using a quasi‐linear diffusion tensor representative of the k spectrum. Initial results are presented for a high power minority heating scenario on the Alcator C‐Mod tokamak and a high harmonic beam heating scenario on DIII‐D. Finite orbit effects are shown to give a less peaked perpendicular energy profile and rf induced transport.

To fully account for finite drift orbit effect of fast ions on wave‐particle interaction in ion‐cyclotron radio frequency (ICRF) heating experiments in tokamaks, the 5‐D finite orbit Monte‐Carlo plasma distribution solver ORBIT‐RF is coupled with the 2‐D full wave code AORSA in a self‐consistent way. Comparison results of ORBIT‐RF/AORSA simulation against fast‐ion Dα (FIDA) measurement of fast‐ion distribution as well as CQL3D/ray‐tracing simulation with zero‐orbit approximation in the DIII‐D ICRF wave beam‐ion acceleration experiment are presented. Preliminary ORBIT‐RF/AORSA results suggest that finite orbit width effects may explain the outward radial shift of the spatial profile measured by FIDA.

The current collected by a finite‐length cylindrical probe is calculated numerically from a self‐consistent solution to the Poisson–Vlasov system of equations. A Boltzmann distribution is assumed for the electrons, and results are compared to the standard ‘‘orbital‐motion‐limited’’ theory. When the probe is very long compared to the sheath thickness and the ratio of probe radius to electron Debye length, Rp/λDe ≲ 1, the collected current agrees with the orbital‐motion theory for cylindrical probes; when the probe is very short compared to the sheath thickness and Rp/λDe ≲ 1, the collected current agrees with the orbital‐motion theory for spherical probes. When the probe length is comparable to the sheath thickness, there is a critical potential above which the probe behaves as a sphere and below which it behaves as a cylinder. Ion charge density, space potential, and ion particle orbits are displayed graphically in the sheath plasma surrounding the probe tip.

Theoretical models are presented to explain the edge plasma-antenna interaction that occurs during ICRF heating. The periodic structure of the Faraday shield is found to result in strong ponderomotive force in the vicinity of the antenna. A fluid model, which incorporates the ponderomotive force, predicts an increase in particle transport to the Faraday shield. Kinetic modelling shows that the strong antenna near-fields act to increase the energy of deuterons that strike the shield, thereby increasing the sputtering of shield material. In addition, kinetic modelling shows that E1 induced between adjacent shield elements acts to heat edge electrons that transit close to the antenna. The predictions of the models are shown to be consistent with measurements of enhanced transport on PLT.

An analytic model has been developed to describe the increased plasma potential and acceleration of ions in the vicinity of an ICRF Faraday shield. This model gives an estimate for the electron distribution function using a heating model for electromotive fields with decorrelation caused by reflection of the electrons from the static sheath at the point where a magnetic field line intersects a grounded wall. The loss rate of the electrons from the system can be calculated from this distribution function. The expected static potential is then estimated by equating electron and ion loss rates, assuming either that the ion loss satisfies the Bohm sheath criterion or that ion gyro-orbits strike a nearby wall. The analytic model for the electrons is in good agreement with a Monte Carlo model using realistic values of the RF electric fields. These RF near-field values have been calculated, including the linear near-field plasma response and the Faraday shield. Results include the findings that a linear model for the RF plasma response is valid for typical experimental parameters and that plasma currents must be included in the RF near-field calculation. It is also found that the static potential is sufficiently increased by electron heating so that it could easily cause impurities to be generated from the antenna structure. Results of the expected static potential are given for various ion species.