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The effect of the plasma shaping (triangularity and elongation) on the continuous spectrum, frequency gaps, and number of eigenmodes is studied. The plasma shaping affects the coupling between Alfvén and slow magnetosonic waves via the geodesic magnetic curvature and the plasma pressure. The Alfvén-slow coupling creates a large number of new gaps in the continuous spectrum below the Alfvén frequency where discrete modes can reside. In ideal magnetohydrodynamic simulations a large number (a few hundred or more) of potential eigenmodes are found. The number of eigenmodes is correlated with the maximum geodesic curvature and a minimum number of possible discrete eigenmodes is found at a negative triangularity of −0.3. It is hypothesized that these possible eigenmodes form a low amplitude and dense discrete spectrum, which can be studied experimentally.

Using the SPIRAL Monte Carlo, full particle-orbit simulation code, we investigate the effects of neoclassical tearing modes (NTMs) and toroidal field (TF) ripple on alpha power losses during steady-state operation of the SPARC primary reference discharge. Model perturbations for TF ripple and the m / n = 2 / 1 and 3 / 2 NTMs with exaggerated widths selected based on an H-mode plasma approaching thermal quench are added to a simulated SPARC magnetic equilibrium through which marker particles are tracked. The 3/2 and 2/1 NTMs are located at ρ p o l ∼ 0.76 and ρ p o l ∼ 0.86 respectively, well positioned to increase alpha particle transport into and within an outer lossy region of the plasma beyond ρ p o l ∼ 0.8 where over 95% of lost alpha particles are born. Total alpha power losses are shown to increase modestly from 1.73% lost at a minimum to 2.34% lost at a maximum, and alpha particle surface power densities form localized hotspots on the first-wall near the low-field side midplane due to NTMs and TF ripple. We establish a conservative upper limit for first-wall alpha surface power densities on a toroidally symmetric wall for typical, flattop operation and motivate the consideration of NTMs in the design of three dimensional limiter surfaces for SPARC.

An Electron Cyclotron Emission Imaging (ECEI) data analysis module has been developed for the OMFIT platform to accommodate the needs of users at the DIII-D tokamak for physics applications. The user can easily access the ECEI spatial observation windows in the plasma that are calculated based on the automatically retrieved hardware setup and available DIII-D equilibria, perform spectral analysis, and obtain 2D electron temperature fluctuation images. The module provides a powerful data post-processing package for extracting important physics parameters from the 2D measurements, including the radial structure and poloidal mode number of Alfven eigenmodes, as well as the frequency-vs-wavenumber dispersion relationship of broadband MHD. The module propagates characterized synthetic fluctuations for the user, so one can perform forward modeling tasks with simple analytical fluctuations.

Monolithic, millimeter-wave "system-on-chip" (SoC) technology has been employed in heterodyne receiver integrated circuit radiometers in a newly developed Electron Cyclotron Emission Imaging (ECEI) system on the DIII-D tokamak for 2D electron temperature profile and fluctuation evolution diagnostics. A prototype module operating in the E-band (72 GHz-80 GHz) was first employed in a 2 × 10 element array that demonstrated significant improvements over the previous quasi-optical Schottky diode mixer arrays during the 2018 operational campaign of the DIII-D tokamak. For compatibility with International Thermonuclear Experimental Reactor relevant scenarios on DIII-D, the SoC ECEI system was upgraded with 20 horn-waveguide receiver modules. Each individual module contains a University of California Davis designed W-band (75 GHz-110 GHz) receiver die that integrates a broadband low noise amplifier, a double balanced down-converting mixer, and a ×4 multiplier on the local oscillator (LO) chain. A ×2 multiplier and two IF amplifiers are packaged and selected to further boost the signal strength and downconvert the signal frequency. The upgraded W-band array exhibits >30 dB additional gain and 20× improvement in noise temperature compared with the previous Schottky diode radio frequency mixer input systems; an internal 8 times multiplier chain is used to bring down the LO frequency below 12 GHz, thereby obviating the need for a large aperture for quasi-optical LO coupling and replacing it with coaxial connectors. Horn-waveguide shielding housing avoids out-of-band noise interference on each individual module. The upgraded ECEI system plays an important role for absolute electron temperature evolution and fluctuation measurements for edge and core region transport physics studies.

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.

This paper reports the significant advancement of our ability to model and to understand how RF waves interact with the SOL plasma, by simulating the full torus 3D SOL plasma together with the antenna and core plasma. We introduce and use a recently developed and open source code, Petra-M, which was constructed on the scalable MFEM C++ finite element library, and performed 3D full wave simulations in the HHFW regime for both NSTX-U and LAPD plasmas. A first full wave simulation for a full 3D torus including a realistic antenna geometry and SOL plasma region for NSTX-U is presented. A scan of the antenna phasing shows a strong interaction between FWs and the SOL plasma for lower antenna phasing, which is consistent with previous NSTX HHFW observations. The effect of the 3D wave field on the fast ion population from NBI beams in NSTX-U is also discussed by using the 3D field obtained from the Petra-M simulations in the full-orbit following particle SPIRAL code. On LAPD, 3D full wave simulations of a new HHFW 4-strap antenna recently installed by TAE Technologies on LAPD are performed showing a qualitative agreement with experimental data.

Significant noise suppression for magnetohydrodynamics (MHD) mode characterization in the spatial and spectral domain is achieved by processing two-dimensional (2D) electron cyclotron emission imaging (ECEI) data with a one-dimensional (1D) ECEI technique using a short time window ( 1 ms ). The technique is applied to detect toroidal Alfven eigenmodes (TAEs) in the temporal spectrum and fit their radial envelope using the data from the DIII-D tokamak W-band 2D ECEI system. Using the data length (time window) of only 1 ms , the 1D ECEI can clearly detect the TAEs (∼100 kHz ) on the spectrum, while similar spectrum quality requires ∼10 ms data length with the cross power spectrum between two midplane ECEI channels. The 1D ECEI technique also effectively avoids biased fitting when resolving the fine structure of the TAE’s radial envelope. The radially spatial resolution of 1D ECEI is constrained by the finite ECE radiation volume of the ECEI receiver. With forward radiation modeling, we find the DIII-D ECEI system can sensitively measure the even parity MHD activities, for which the mode width is >15 mm, and tearing modes (odd parity MHD activities), for which the island full width is >30 mm.

Final design studies in preparation for manufacturing have been performed for functional components of the vacuum portion of the ITER Low-Field Side Reflectometer (LFSR). These components consist of an antenna array, electron cyclotron heating (ECH) protection mirrors, phase calibration mirrors, and vacuum windows. Evaluation of these components was conducted at the LFSR test facility and DIII-D. The antenna array consists of six corrugated-waveguide antennas for simultaneous profile, fluctuation, and Doppler measurements. A diffraction grating, incorporated into the plasma-facing miter bend, provides protection of sensitive components from stray ECH at 170 GHz. For in situ phase calibration of the LFSR profile reflectometer, an embossed mirror is incorporated into the adjacent miter bend. Measurements of the radiated beam profile indicate that these components have a small, acceptable effect on mode conversion and beam quality. Baseline transmission characteristics of the dual-disk vacuum window are obtained and are used to guide ongoing developments. Preliminary simulations indicate that a surface-relief structure on the window surfaces can greatly improve transmission. The workability of real-time phase measurements was demonstrated on the DIII-D profile reflectometer. The new automated real-time analysis agrees well with the standard post-processing routine.

The thermal and fast-ion transport properties of DIII-D steady-state hybrid discharges with normalized beta β N ≳ 3 are studied at low injected torque and an increased electron to ion temperature ratio T e/T i. Linear stability analysis performed with the TGLF turbulent code indicates that a high-k mode is usually dominant at smaller radii, whereas a low-k mode is usually dominant at larger radii in these plasmas. A reduction in the net injected torque from 8.6 to 4.3 N-m leads to reduced E × B shear and hence, an enhanced turbulence that was observed on the Doppler backscattering diagnostic and was also computed with TGLF. As T e/T i in the core was increased from 0.57 to 0.66 by adding electron cyclotron current drive (ECCD) to these plasmas, higher levels of transport are observed with increased high-k modes indicated by TGLF. The fast-ion transport level varied over an order of magnitude in these discharges depending on whether Alfvén eigenmodes, fishbones, or no instabilities were observed. Hybrid plasmas with fishbones have decreased fast-ion transport, compared to plasmas with Alfvén eigenmodes, since they are resonant with a smaller portion of phase space and their resonance is farther from the wall. This reduction in fast-ion transport with ECCD mitigates the increase in turbulent transport, resulting in higher performance than expected during strong electron heating. Similarly, the lowest fast-ion transport was observed in the low torque plasma, which also led to better than expected performance at this torque value. The thermal and fast-ion transport changes observed as the torque/rotation and T e/T i are varied indicate possible methods for transferring this scenario to a reactor.

The interaction between neutrals outside tokamak plasmas and fast ions that are generated by neutral beam injection and pass outside the plasma is studied. It is shown that at beam energies (up to ~100~keV) fast-ion losses are significant, up to 20% in the studied case, because of charge exchange reactions between the neutrals and the fast ions. About half of the fast ions that neutralize outside the plasma get lost to the wall while the other half re-enter the plasma and ionize again, often on better confined orbits which is visible as an enhanced beam power deposition in the plasma core (rho ~< 0.7). As a result, the the plasma performance as measured from the beam-thermal neutrons is hardly changed despite the significant fast-ion losses toward the plasma edge.

A new generation of millimeter-wave heterodyne imaging receiver arrays has been developed and demonstrated on the DIII-D electron cyclotron emission imaging (ECEI) system. Improved circuit integration, improved noise performance, and enhanced shielding from out-of-band emission are made possible by using advanced liquid crystal polymer (LCP) substrates and monolithic microwave integrated circuit (MMIC) receiver chips. This array exhibits ∼15 dB additional gain and >30× reduction in noise temperature compared to previous generation ECEI arrays. Each LCP horn-waveguide module houses a 3 × 3 mm GaAs MMIC receiver chip, which consists of a low noise millimeter-wave preamplifier, balanced mixer, and IF amplifier together with a local oscillator multiplier chain driven at ∼12 GHz. A proof-of-principle partial LCP instrument with 5 poloidal channels was installed on DIII-D in 2017, with a full proof-of-principle system (20 poloidal × 8 radial channels) installed and commissioned in early 2018. The enhanced shielding of the LCP modules is seen to greatly reduce the sensitivity of ECEI signals to out-of-band microwave noise which has plagued previous ECEI studies on DIII-D. The LCP ECEI system is expected to be a valuable diagnostic tool for pedestal region measurements, focusing particularly on electron temperature evolution during edge localized mode bursting.

The sawtooth oscillation involves a topological change of the magnetic field lines in the core of a tokamak discharge. We simulate a steady state sawtoothing discharge using the M3D$C^1$-code. During the sawtooth the topological structure of the magnetic field is analyzed by tracking the fixed points of the field line map: the mapping induced by the field lines going once around the tokamak. We numerically locate the fixed points of the field line map (of which the magnetic axis is one) and use them construct a Poincar\'e section that resolves the core region and the (1,1) island. By following the evolution of the magnetic field through the motion and bifurcation of the fixed points of the field line map we get an intuitive picture of the processes that take place during a Kadomtsev style sawtooth crash.

An analytical theory based on the MHD model is presented for understanding the coupling between the shear Alfven wave and the slow magnetosonic wave (or the so called slow mode) in the frequency range below the Toroidal Alfven Eigenmode (TAE) continuum spectrum gap. In tokamak plasmas, coupling of the Alfven m poloidal harmonic and the slow mode m ± 1 harmonics causes the Alfven m harmonic continuous spectrum to be uplifted from the uncoupled Alfven spectrum by an amount related to the plasma pressure and the geodesic magnetic field curvature. However, the frequency of one of the slow mode m ± 1 harmonics is reduced by the same pressure-curvature coupling effect. But the frequency of the other slow mode harmonic is relatively unaffected. As a result, the Alfven-slow (AS) mode continuous spectrum is broken up into two Alfven-Slow (AS) gaps below the TAE continuum gap. Coupling of the Alfven m harmonic with the slow mode m ± 2 harmonics also creates additional AS gaps if their frequencies cross each other. The AS gap widths increase with the plasma pressure. The creation of AS gaps allows the existence of several new types of Alfven-Slow Eigenmodes (ASEs). The radial structure of these new ASEs does not intersect with the continuous spectrum and thus does not suffer from continuum damping. The Beta-induced Alfven-Acoustic Eigenmode (BAAE) is one type of ASEs with frequency in the lowest AS frequency gap. However, the BAAE usually interacts with the Alfven-Slow continuum and suffers from continuum damping. The existence of ASEs is ubiquitous for normal and reserve safety factor profiles, broad range of plasma β values, different plasma shapes, and many different toroidal mode numbers. The newly discovered ASEs provide explanation for the experimentally observed Beta-induced Alfven Eigenmodes destabilized by fast ions with frequencies below the TAE frequency gap.

Radially curved Alfven eigenmode wavefronts as observed on the electron cyclotron emission imaging diagnostic indicate that the modes are associated with a net radial energy flow. This energy flow is due to a radial mismatch in the location of the drive and damping of the mode. Energy transport is created by an enhanced parallel fluctuating magnetic field that is generated by the radial wavefront curvature.

The edge-harmonic oscillation (EHO) mode is one of the characteristic modes that provides an edge transport channel during high-confinement ELM-free phase (the so-called Quiescent High-confinement phase). Recent theoretical work and extensive experimental observations have suggested that the large rotational E × B shear is the key to destabilize an EHO. As the eigenmode grows to large amplitude, it will exert a drag on the rotation, resulting in EHO's saturation (Snyder et al 2007 Nucl. Fusion 47 961). However, detailed mechanisms concerning this process remain vague. We have performed continuous tracking on how the E × B shear affects the EHO mode structure to search for a possible explanation of the saturation mechanism. Two edge density fluctuation diagnostics are employed to observe the eigenmode structure evolution of EHO in the pedestal region in the radial and poloidal directions, respectively. Our results show that the EHO mode's radial wavenumber is strongly correlated with the E × B shear rate, while the poloidal wavenumber is unaffected by the E × B shear rate. During the EHO existence, with the E × B shearing rate ramping down, the radial wavenumber is also observed to be decreasing.

Here, the pulsed application of n = 3 magnetic perturbation fields with amplitudes below that which triggers ELMs results in distinct, transient responses observable on several edge and divertor diagnostics in NSTX. We refer to these responses as Sub-Threshold Edge Perturbations (STEPs). An analysis of edge measurements suggests that STEPs result in increased transport in the plasma edge and scrape-off layer, which leads to augmentation of the intrinsic strike point splitting due to error fields, i.e., an intensification of the helical divertor footprint flux pattern. These effects are much smaller in magnitude than those of triggered ELMs, and are observed for the duration of the field perturbation measured internal to the vacuum vessel. In addition, STEPs are correlated with changes to the MHD activity, along with transient reductions in the neutron production rate. Ideally the STEPs could be used to provide density control and prevent impurity accumulation, in the same manner that on-demand ELM triggering is used on NSTX, without the impulsive divertor fluxes and potential for damage to plasma facing components associated with ELMs.

Joint DIII-D/EAST experiments in the radio-frequency (RF) heated H-mode scheme with comparison to that of neutral beam (NB) heated H-mode scheme were carried out on DIII-D and EAST under similar conditions to examine the effect of heating scheme on scrape-off layer (SOL) width in H-mode plasmas for application to ITER. A dimensionally similar plasma equilibrium was used to match the EAST shape parameters. The divertor heat flux and SOL widths were measured with infra-red camera in DIII-D, while with divertor Langmuir probe array in EAST. It has been demonstrated on both DIII-D and EAST that RF-heated plasma has a broader SOL than NB-heated plasma when the edge electrons are effectively heated in low plasma current and low density regime with low edge collisionality. Detailed edge and pedestal profile analysis on DIII-D suggests that the low edge collisionality and ion orbit loss effect may account for the observed broadening. The joint experiment in DIII-D has also demonstrated the strong inverse dependence of SOL width on the plasma current in electron cyclotron heated (ECH) H-mode plasmas. Keywords: SOL width, Radio-frequency heating, Neutral beam heating, Low collisionality

Modulation of various neutral beam sources probes the interaction of fast ions with tearing modes (TM) in the DIII-D tokamak. As measured by electron cyclotron emission, the tearing modes have an island width of ~8 cm and change phase at the q = 2 surface. (Here, m is the poloidal mode number and n is the toroidal mode number.) Deuterium neutral beam injection by six sources with differing injection geometries produces the fast ions. To study the interaction in different parts of phase space, on successive discharges, one of the six sources is modulated at 20 Hz to populate different fast-ion orbits. The modulation only changes the island width by a few millimeters, implying that any fast-ion effect on mode stability is below detection limits. When compared to the expected signals in the absence of TM-induced transport, both the average and modulated neutron signals deviate, implying that fast-ion transport occurs in much of phase space. Fast-ion D α (FIDA) measurements detect reductions in signal at wavelengths that are sensitive to counter-passing ions. Neutral particle analyzer data imply poor confinement of trapped fast ions. Calculations of the expected fast-ion transport that use measured TM properties successfully reproduce the data.

A general criterion is proposed and found to successfully predict the emergence of chirping oscillations of unstable Alfv\'enic eigenmodes in tokamak plasma experiments. The model includes realistic eigenfunction structure, detailed phase-space dependences of the instability drive, stochastic scattering and the Coulomb drag. The stochastic scattering combines the effects of collisional pitch angle scattering and micro-turbulence spatial diffusion. The latter mechanism is essential to accurately identify the transition between the fixed-frequency mode behavior and rapid chirping in tokamaks and to resolve the disparity with respect to chirping observation in spherical and conventional tokamaks.

Momentum confinement was investigated on DIII-D as a function of applied neutral beam torque at constant normalized beta βN, by varying the mix of co (parallel to the plasma current) and counter neutral beams. Under balanced neutral beam injection (i.e. zero total torque to the plasma), the plasma maintains a significant rotation in the co-direction. This 'intrinsic' rotation can be modeled as being due to an offset in the applied torque (i.e. an 'anomalous torque'). This anomalous torque appears to have a magnitude comparable to one co neutral beam source. The presence of such an anomalous torque source must be taken into account to obtain meaningful quantities describing momentum transport, such as the global momentum confinement time and local diffusivities.Studies of the mechanical angular momentum in ELMing H-mode plasmas with elevated qmin show that the momentum confinement time improves as the torque is reduced. In hybrid plasmas, the opposite effect is observed, namely that momentum confinement improves at high torque/rotation. GLF23 modeling suggests that the role of E × B shearing is quite different between the two plasmas, which may help to explain the different dependence of the momentum confinement on torque.

High-resolution quadrature reflectometer measurements of density fluctuation levels have been obtained on DIII-D for H-mode edge pedestal studies. Initial results are presented from the L–H transition to the first ELM for two cases: (i) a low pedestal beta discharge, in which density turbulence in the pedestal has little change during the ELM-free phase, and (ii) a high pedestal beta discharge in which both density and magnetic turbulence are observed to increase before the first ELM. These high beta data are consistent with the existence of electromagnetic turbulence suggested by some transport models. During Type-I ELM cycles, when little magnetic turbulence can be observed, pedestal turbulence increases just after an ELM crash and then decreases before next ELM strikes, in contrast to a drop after ELM crash and then it re-grows when strong magnetic turbulence shows similar behavior. Clear ELM precursors are observed on ⩽20% of Type-I ELMs observed to date.

An overview of the diagnostics installed on the Alcator C-Mod tokamak is presented. Approximately 25 diagnostic systems are being operated on C-Mod. The compact design of the machine and the cryostat enclosing the vacuum vessel and magnetic field coils make access challenging. Diagnostics are used to study four focus areas: transport, plasma boundary, waves, and macrostability. There is significant overlap between these topics, and they all contribute toward the burning plasma and advanced tokamak thrusts. Several advanced and novel diagnostics contribute to the investigation of C-Mod plasmas, e.g., electron cyclotron emission, phase-contrast imaging, gas puff imaging, probe measurements, and active magnetohydrodynamic antennas.

Recent upgrades to many of the diagnostic systems on DIII-D (Luxon J.L. 2002 Nucl. Fusion 42 614) such as the CO2 interferometer, far-infrared scattering, beam-emission spectroscopy (BES), and quadrature reflectometer have significantly extended their capabilities and made possible the experimental study of Alfven eigenmodes (AEs) through observation of the AE induced density perturbation. Measurements have revealed the presence of several different classes of AEs in DIII-D discharges including the toroidal Alfven eigenmode (TAE), reverse shear AE (RSAE or Alfven cascade) and ellipticity induced Alfven eigenmode. Based on a simple model for the RSAE frequency, a sensitive diagnostic for the evolution of the minimum magnetic safety factor (qmin) is presented and results are compared with motional Stark effect (MSE) measurements. Strong localization of high toroidal mode number RSAEs to regions near the minimum of the magnetic safety factor is exhibited on the CO2 interferometer and BES measurements. Based on this observation, a method for providing constraints on the radial location of qmin is demonstrated and a favourable comparison to MSE measurements is made. Detailed measurements of TAEs using a new all-digital large bandwidth two-colour CO2 interferometer system show a strong asymmetry between vertical and radial viewing interferometer chords confirming previously reported results. Additionally, effects related to line-integrated observations are clearly illustrated by comparison to local BES measurements and potential issues related to this are discussed.

The response of a low-field side X-mode reflectometer system for ITER is simulated with a 2D reflectometer code using a realistic plasma equilibrium. Relativistic corrections to the plasma permitivity due to the high electron temperature were included. It is found that the reflected beam will often miss its launch point by as much as 40 cm and that a vertical array of receiving antennas is essential in order to observe a reflection on the low-field side of ITER. Relativistic absorption effects were studied with a 1D full wave code and found to be insignificant for reflections from the low-field side up to the plasma centre.

Fixed-frequency reflectometers utilizing quadrature phase detection are employed on DIII-D to study both coherent and turbulent density fluctuations. For coherent fluctuations, the reconstructed phase information successfully identifies MHD/coherent mode activity, e.g. tearing modes, compressional Alfven eigenmodes, etc. For an m = 3/n = 2 tearing mode, a basic 1D phase screen model is applied to infer fluctuation levels, and the result is consistent with the beam emission spectroscopy (BES) measurement. For turbulent fluctuation studies, a 2D full-wave code (Valeo E.J., Kramer G.J. and Nazikian R. 2002 Plasma Phys. Control. Fusion 44 L1) is applied to interpret reflectometry data obtained in the H-mode edge pedestal region to deduce density fluctuation levels. The measurement is simulated using realistic geometry, plasma conditions and antenna patterns. Comparison of the fluctuation level deduced from the 2D code with BES measurement shows reasonable agreement.

Based on numerical simulations with the magnetohydrodynamic code NOVA, reversed shear Alfven eigenmodes (RSAE) associated with the ellipticity-induced and non-circular triangularity-induced Alfven eigenmode gaps were found. An analytical model for large aspect ratio plasmas confirms the existence of those modes with a pressure gradient threshold that agrees very well with the NOVA calculations. It is predicted that these higher gap RSAEs might be observed in existing large tokamaks in the early phase of reversed shear discharges when the minimum value of the magnetic safety factor is high (larger than two) and in ITER advanced scenario discharges.

Ideal MHD equations employed in the NOVA code are analysed analytically and numerically in order to investigate the role of the pressure gradient on global reversed shear Alfven eigenmodes (RSAEs) or Alfven cascades. We confirm both numerically and analytically conclusions obtained earlier using the ideal MHD code NOVA [1] and analytically [10] that the plasma pressure gradient plays a key role in the existence condition and in the dispersion relation for the mode. The effect of the plasma pressure gradient is to shift the mode frequency up at the low part of the RSAE frequency chirp and downshift the mode frequency when the frequency approaches the TAE gap. This finding is contrary to predictions in a recent publication [2], where the pressure gradient is found to be always stabilizing by means of downshifting the RSAE frequency and enhancing its interaction with the continuum. We resolve this discrepancy by showing that neglecting the pressure gradient effect on the plasma equilibrium (modification of the Shafranov shift and the averaged curvature) leads to conclusions at variance with the numerical and analytical results presented here. A new variational approximation of the RSAE is introduced which compares remarkably well with NOVA solutions. With this new approximation we clearly demonstrate the diagnostic potential and limitations of the RSAE frequency measurement for MHD spectroscopy.

In preparation for next step burning plasma devices such as ITER, experimental studies of instabilities and confinement of energetic ions were performed on Joint European Torus (JET) and on Mega-Amper Spherical Tokamak (MAST) with innovative diagnostic techniques, in conventional and shear-reversed plasmas, exploring a wide range of effects for energetic ions. A compendium of recent results testing capabilities of the present-day facilities for burning plasma relevant study is presented in this paper. 'Alpha tail' production using 3rd harmonic ion-cyclotron resonance heating (ICRH) of He-4 beam ions has been employed on JET for studying He-4 of the megaelectronvolt energy range in a 'neutron-free' environment. The evolution of ICRH-accelerated ions of He-4 with E >= 1.7 MeV and D with E >= 500 keV was assessed from nuclear gamma-ray emission born by the fast ions colliding with Be and C impurities. A simultaneous measurement of spatial profiles of fast He-4 and fast D ions relevant to ITER was performed for the first time in positive and strongly reversed magnetic shear discharges. Time-resolved gamma-ray diagnostics for ICRH-accelerated He-3 and H minority ions allowed changes in the fast ion distribution function to be assessed in the presence of unstable toroidal Alfven eigenmodes (TAEs) and sawteeth. A significant decrease of gamma-ray intensity from protons with E >= 5 MeV was detected during the 'tornado' modes. This was interpreted as 'tomado'-induced loss of fast ions with the drift orbit width, Delta(f), comparable to the minor radius of tokamak a. Experiments performed in the opposite case, Delta f/a = 500 keV, have shown excitation of numerous Alfven eigenmodes without a significant degradation of the fast ion confinement. The stabilizing effect of fast particles on 'monster' sawteeth was experimentally found to fail in low-density plasmas with high power ion cyclotron resonance frequency (ICRF)-heating. The transition from the 'monster' to short-period 'grassy' sawteeth was investigated with different ICRF phasing, which controls the pinch-effect and radial distribution of ICRF-accelerated ions. Instabilities excited by super-Alfvenic beam ions were investigated on the spherical tokamak MAST. Due to higher values of beta and a higher proportion of fast ions on MAST than on JET, a wider variety of modes and nonlinear regimes for the Alfven instabilities were observed, including the explosive TAE-regimes leading to the formation of hole-clump pairs on the fast ion distribution function. The MAST and START data showed that TAE and chirping modes decrease both in their mode amplitudes and in the number of unstable modes with increasing beta.

Measurements are presented of toroidicity-induced (TAEs) and reverse shear (RSAEs) Alfven eigenmodes made using the standard two-colour CO2 interferometer on DIII-D modified for increased bandwidth. Typical values of the effective line-integrated density perturbation in DIII-D are found to be d(nL)/nL ~ 10−3, and comparisons are made with NOVA calculations as well as magnetic measurements. There is a strong difference in the measured power spectrum between vertical and radial chords through the plasma. On average, vertical views are characterized by a larger line-integrated density perturbation due to TAEs than radial chords. Radial chords, however, can be used much more reliably than vertical chords to identify the presence of RSAEs in the plasma—a result found to be due to the radially localized nature of these modes. In general, the apparent amplitude of the observed modes for both TAE and RSAE is found to be highly dependent on viewing location.

Argon, krypton and xenon were puffed with and without simultaneous hydrogen gas puffing into Ohmically heated plasmas of the JT-60U tokamak with low plasma currents in order to study the capability of disruption mitigation. It was found that krypton gas puffing can provide a plasma termination with smaller amounts of runaway electrons in comparison to argon and xenon gas puffing.

Alfven eignemode experiments have been carried out by using the negative-ion-based neutral beam in JT-60U. For bursting instabilities in the frequency range of Alfvn Eigenmodes, two types of mode activity have been observed. In one type called Abrupt Large-amplitude Event (ALE), enhanced transport of the energetic ions was detected. The enhanced transport showed the clear energy dependence based on measurements performed using a natural diamond detector. In another type of bursting event called the fast Frequency Sweeping (fast FS) mode, frequency up-down chirping is observed on the time-scale of a few ms, much faster than equilibrium changes in the background plasma. This frequency chirping was well reproduced by the non-linear simulation code, MEGA, for magnetohydrodynamics (MHD) with energetic particles. The slow up-frequency sweeping of the Reversed-Shear-induced Alfven Eigenmode (RSAEs), due to the slow evolution of qmin was also observed. These experiments were analyzed by using the NOVA-K code. It is shown that the most unstable modes are localized around the minimum in the magnetic safety factor (qmin) in the analysis.

The inclusion of finite pressure in ideal magnetohydrodynamic theory can explain the reversed magnetic shear Alfven eigenmodes (RSAE) (or Alfven cascades) that have been observed in several large tokamaks without the need to invoke an energetic particle mechanism for the existence of these modes. The chirping of the RSAE is caused by changes in the minimum of the magnetic safety factor, qmin, while finite pressure effects explain the observed non-zero minimum frequency of the RSAE when qmin has a rational value. Finite pressure effects also play a dominant role in the existence of the downward chirping RSAE branch.

The atomistic mechanisms and dynamics of the (1 x 1) --hex surface reconstruction of the clean Pt(100) and its lifting upon CO adsorption have been studied by means of both density functional theory and molecular dynamics simulations based on the modified embedded-atom method. It was found that during the surface reconstruction from the square (1 x 1) to the approximately 20% more dense (quasi)hexagonal phase, the required extra atoms are extracted from the second layer, leaving highly mobile subsurface vacancies, even in the presence of adatom islands or steps. These vacancies will, by surface diffusion, coalesce to form steps. In contrast, during the reverse process--where the hex surface reconstruction is lifted upon adsorption of CO--the roughly 20% excess surface atoms are in a collective manner ejected to form chains of adatoms. In turn, these adatoms coalesce into islands and steps by surface diffusion. A result of the two totally different mechanisms is that the reconstruction process can be concluded not to be the reverse of the deconstruction process.

Recent energetic particle physics research in JT-60U and JFT-2M is reported. Alfven eigenmodes (AEs) are investigated in reversed-shear (RS) plasmas in JT-60U where frequency sweeping (FS) modes are observed to follow the q-profile evolution. The RS-induced AE model can explain the FS of the modes within the context of an evolving q-profile. Enhanced energetic ion transport is also investigated with the appearance of modes in the toroidicity-induced AE range of frequency in JT-60U using a multi-channel neutron profile monitor and in JFT-2M using a lost ion probe. Additionally, the ripple loss in the complex toroidal field ripple due to ferritic steel inserts in JFT-2M is shown and compared with model analysis. The simulation code developed to predict ripple loss in JFT-2M will be of use in estimating the heat flux in the complex ripple field of a future device such as ITER.

Recent progress in the analysis of the low and high frequency beam ion driven instabilities in the National Spherical Tokamak Experiment (NSTX) [S. Kaye et al., Fusion Technol. 36, 16 (1999)] plasma is reported. The low Alfven speed with respect to the beam ion injection velocity in NSTX offers a window in the plasma parameter space to study instabilities driven by super-Alfvenic fusion alphas, which are expected in the International Tokamak Experimental Reactor—ITER [D. J. Campbell, Phys. Plasmas 8, 2041 (2001)]. Low frequency magnetic field activities identified as an instability of toroidicity-induced Alfven eigenmodes (TAEs) have been observed in NSTX and analyzed with the linear hybrid kinetic magnetohydrodynamic stability code NOVA-K [C. Z. Cheng, Phys. Rep. 1, 211 (1992)]. The comparison between the TAE analysis and observations in NSTX and DIII–D [J. L. Luxon, Nucl. Fusion 42, 614 (2002)] similarity experiments confirms that the toroidal mode number of the most unstable TAE modes scales with q−2 a...

Two-dimensional full-wave time-dependent simulations in full plasma geometry are presented, which show that conventional reflectometry (without a lens) can be used to synthetically image density fluctuations in fusion plasmas under conditions where the parallel correlation length greatly exceeds the poloidal correlation length of the turbulence. The advantage of synthetic imaging is that the image can be produced without the need for a large lens of high optical quality, and each frequency that is launched can be independently imaged. A particularly simple arrangement, consisting of a single receiver located at the midpoint of a microwave beam propagating along the plasma midplane is shown to suffice for imaging purposes. However, as the ratio of the parallel to poloidal correlation length decreases, a poloidal array of receivers needs to be used to synthesize the image with high accuracy. Simulations using DIII-D relevant parameters show the similarity of synthetic and optical imaging in present day experiments.

A superheterodyne reflectometer could provide a direct and inexpensive measurement of ion species mixes with different charge-to-mass ratios. Using the cold plasma dispersion relation, the ion–ion hybrid cutoff frequency is uniquely determined by the density ratio and cyclotron frequencies of the two different species. The phase of a 20 MHz wave that travels from the launching point to the cutoff layer to the receiving antenna provides a direct measure of the )

Research on the Alcator C-Mod tokamak [1] is focused on high particle- and power-density plasma regimes to understand particle and energy transport in the core, the dynamics of the H-mode pedestal, and scrape-off layer and divertor physics. The auxiliary heating is provided exclusively by RF waves, and both the physics and technology of RF heating and current drive are studied. The momentum which is manifested in strong toroidal rotation, in the absence of direct momentum input, has been shown to be transported in from the edge of the plasma following the L–H transition, with timescale comparable to that for energy transport. In discharges which develop internal transport barriers, the rotation slows first inside the barrier region, and then subsequently outside of the barrier foot. Heat pulse propagation studies using sawteeth indicate a very narrow region of strongly reduced energy transport, located near r/a = 0.5. Addition of on-axis ICRF heating arrests the buildup of density and impurities, leading to quasi-steady conditions. The quasi-coherent mode associated with enhanced D-Alpha (EDA) H-mode appears to be due to a resistive ballooning instability. As the pedestal pressure gradient and temperature are increased in EDA H-mode, small ELMs appear; detailed modelling indicates that these are due to intermediate n peeling–ballooning modes. Phase contrast imaging has been used to directly detect density fluctuations driven by ICRF waves in the core of the plasma, and mode conversion to an intermediate wavelength ion cyclotron wave has been observed for the first time. The bursty turbulent density fluctuations, observed to drive rapid cross-field particle transport in the edge plasma, appear to play a key role in the dynamics of the density limit. Preparations for quasi-steady-state advanced tokamak studies with lower hybrid current drive are well underway, and time dependent modelling indicates that regimes with high bootstrap fraction can be produced.

Spherical tokamaks have relatively low toroidal field which means that the fast-ion Larmor radius is relatively large (ρfi>0.04 ap) and the fast ion velocity is much greater than the Alfven speed (Vfi>2 VAlfven). This regime of large Larmor radius and low Alfven speed is a regime in which fast ion driven instabilities are potentially virulent. It is therefore an important goal of the present proof-of-principle spherical tokamaks to evaluate the role of fast ion driven instabilities in fast ion confinement. This paper presents the first observations of fast ion losses in a spherical tokamak resulting from energetic particle driven modes. Two classes of instabilities are responsible for the losses. Multiple, simultaneously bursting modes in the toroidal Alfven eigenmode frequency gap cause neutron drops of up to 15%. A bursting, chirping mode identified as precession and/or bounce resonance fishbone also causes significant neutron drops. Both modes are usually present when the losses are observed.

The stability of α-particle driven shear Alfven eigenmodes (AE) for nominal burning plasma (BP) parameters in the proposed international tokamak experimental reactor (ITER), fusion ignition research experiment (FIRE) and IGNITOR tokamaks is studied. JET plasma, where fusion αs were generated in tritium experiments, is also studied to compare the numerical predictions with the existing experiments. An analytic assessment of toroidal AE (TAE) stability is first presented, where the α-particle β due to the fusion reaction rate and electron drag is simply and accurately estimated in plasmas with central temperature in the range of 7–20 keV. In this assessment the hot particle drive is balanced against ion-Landau damping of the background deuterons, and electron collision effects and stability boundaries are determined. Then two numerical studies of AE instability are presented. In one, the HIgh-n STability (HINST) code is used to predict the instabilities of low and moderately high frequency Alfven modes. HINST computes the non-perturbative solutions of the AE including effects of ion finite Larmor radius, orbit width, trapped electrons etc. The stability calculations are repeated using the global code NOVAK. We show that for these plasmas the spectrum of the least stable AE modes is at medium-/high-n numbers. In HINST, TAEs are locally unstable due to the α pressure gradient in all the devices under consideration except IGNITOR. However, NOVAK calculations show that the global mode structure enhances the damping mechanisms and produces stability for the nominal FIRE proposal and near-marginal stability for the nominal ITER proposal. NBI ions produce a strong stabilizing effect for JET. However, in ITER, the beam energies needed to penetrate to the core must be high (~1 MeV) so that a diamagnetic drift frequency comparable to that of α-particles is produced by the beam ions which induces a destabilizing effect. A serious question remains whether the perturbation theory used in NOVAK overestimates the stability predictions, so that it is premature to conclude that the nominal operation of all three BP proposals without neutral beam injection are stable (or marginally stable) to AEs.