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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.

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...

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.

Alfven waves can induce the ejection of fast ions in different forms in tokamaks. In order to develop predictive capabilities to anticipate the nature of fast ion transport, a methodology is proposed to differentiate the likelihood of energetic-particle-driven instabilities to produce frequency chirping or fixed-frequency oscillations. The proposed method employs numerically calculated eigenstructures and multiple resonance surfaces of a given mode in the presence of energetic ion drag and stochasticity (due to collisions and micro-turbulence). Toroidicity-induced, reversed-shear and beta-induced Alfven-acoustic eigenmodes are used as examples. Waves measured in experiments are characterized, and compatibility is found between the proposed criterion predictions and the experimental observation or lack of observation of chirping behavior of Alfvenic modes in different tokamaks. It is found that the stochastic diffusion due to micro-turbulence can be the dominant energetic particle detuning mechanism near t...

Experiments on the DIII-D tokamak have identified how multiple simultaneous Alfven eigenmodes (AEs) lead to overlapping wave-particle resonances and stochastic fast-ion transport in fusion grade plasmas [C. S. Collins et al., Phys. Rev. Lett. 116, 095001 (2016)]. The behavior results in a sudden increase in fast-ion transport at a threshold that is well above the linear stability threshold for Alfven instability. A novel beam modulation technique [W. W. Heidbrink et al., Nucl. Fusion 56, 112011 (2016)], in conjunction with an array of fast-ion diagnostics, probes the transport by measuring the fast-ion flux in different phase-space volumes. Well above the threshold, simulations that utilize the measured mode amplitudes and structures predict a hollow fast-ion profile that resembles the profile measured by fast-ion Dα spectroscopy; the modelling also successfully reproduces the temporal response of neutral-particle signals to beam modulation. The use of different modulated sources probes the details of phase-space transport by populating different regions in phase space and by altering the amplitude of the AEs. Both effects modulate the phase-space flows.

Microwave reflectometry is now routinely used for probing the structure of magnetohydrodynamic and turbulent fluctuations in fusion plasmas. Conditions specific to the core of tokamak plasmas, such as small amplitude of density irregularities and the uniformity of the background plasma, have enabled progress in the quantitative interpretation of reflectometer signals. In particular the extent of applicability of the one-dimensional (1-D) geometric optics description of the reflected field is investigated by direct comparison to 1-D full wave analysis. Significant advances in laboratory experiments are discussed which are paving the way toward a thorough understanding of this important measurement technique. Data are presented from the Tokamak Fusion Test Reactor [R. Hawryluk, Plasma Phys. Controlled Fusion 33, 1509 (1991)] identifying the validity of the geometric optics description of the scattered field and demonstrating the feasibility of imaging turbulent fluctuations in fusion scale devices.

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

Microwave backscattering experiments have been performed on the Alcator C-Mod tokamak in order to investigate the propagation of lower hybrid (LH) waves in reactor-relevant, high-density plasmas. When the line-averaged density is raised above 1 × 1020 m–3, lower hybrid current drive efficiency is found to be lower than expected [Wallace et al., Phys. Plasmas 19, 062505 (2012)] and LH power is thought to be dissipated at the plasma edge. Using a single channel (60 GHz) ordinary-mode (O-mode) reflectometer system, we demonstrate radially localized LH wave measurements in the scrape-off layer of high density plasmas (n¯e ≳ 0.9×1020 m−3). Measured backscattered O-mode power varies depending on the magnetic field line mapping, suggesting the resonance cone propagation of LH waves. Backscattered power is also sensitive to variations in plasma density and the launched parallel refractive index of the LH waves. LH ray-tracing simulations have been carried out to interpret the observed variations. To understand th...

A second Neutral Beam (NB) injection line is being installed on the NSTX Upgrade device, resulting in six NB sources with different tangency radii that will be available for heating and current drive. This work explores the properties of instabilities in the frequency range of the Toroidal Alfven Eigenmode (TAE) for NSTX-U scenarios with various NB injection geometries, from more perpendicular to more tangential, and with increased toroidal magnetic field with respect to previous NSTX scenarios. Predictions are based on analysis through the ideal MHD code NOVA-K. For the scenarios considered in this work, modifications of the Alfven continuum result in a frequency up-shift and a broadening of the radial mode structure. The latter effect may have consequences for fast ion transport and loss. Preliminary stability considerations indicate that TAEs are potentially unstable with ion Landau damping representing the dominant damping mechanism.

Characterization of the spatial structure of turbulence fluctuations during the edge localized mode cycle in the pedestal region is reported. Using the beam emission spectroscopy and the correlation reflectometry systems, measurements show spatial structure—k⊥ρiped—ranging from 0.2 to 0.7 propagating in the ion diamagnetic drift direction at the pedestal top. These propagating spatial scales are found to be anisotropic and consistent with ion-scale microturbulence of the type ion temperature gradient and/or kinetic ballooning modes.

Non-axisymmetric magnetic perturbations can fundamentally change neoclassical transport in tokamaks by distorting particle orbits on deformed or broken flux surfaces. This so-called non-ambipolar transport is highly complex, and eventually a numerical simulation is required to achieve its precise description and understanding. A new delta#14;f particle code (POCA) has been developed for this purpose using a modi ed pitch angle collision operator preserving momentum conservation. POCA was successfully benchmarked for neoclassical transport and momentum conservation in axisymmetric con guration. Non-ambipolar particle flux is calculated in the non-axisymmetric case, and results show a clear resonant nature of non-ambipolar transport and magnetic braking. Neoclassical toroidal viscosity (NTV) torque is calculated using anisotropic pressures and magnetic fi eld spectrum, and compared with the generalized NTV theory. Calculations indicate a clear #14;B2 dependence of NTV, and good agreements with theory on NTV torque pro les and amplitudes depending on collisionality.

A reversed shear Alfven eigenmodes (RSAEs) theory has been developed for reversed magnetic field shear plasmas when the safety factor minimum, q min , is at or above a rational value. The modes we study are known sometimes as either the bottom of the frequency sweep or the down sweeping RSAEs. We show that, strictly speaking, the ideal MHD theory is not compatible with the eigenmode solution in the reversed shear plasma with q min above integer values. Corrected by a special analytic finite Larmor radius (FLR) condition, MHD dispersion of these modes nevertheless can be developed. Numerically, MHD structure can serve as a good approximation for the RSAEs.The large radial scale part of the analytic RSAE solution can be obtained from ideal MHD and expressed in terms of the Legendre functions. The kinetic equation with FLR effects for the eigenmode is solved numerically and agrees with the analytic solutions. Properties of RSAEs and their potential implications for plasma diagnostics are discussed.

Experiments on the National Spherical Torus Experiment [M. Ono et al., Nucl. Fusion 40, 557 (2000)] found strong bursts of toroidal Alfven eigenmode (TAE) activity correlated with abrupt drops in the neutron rate. A fairly complete data set offers the opportunity to benchmark the NOVA [C. Z. Cheng, Phys. Rep. 211, 1 (1992)] and ORBIT [R. B. White and M. S. Chance, Phys. Fluids 27, 2455 (1984)] codes in the low aspect ratio tokamak (ST) geometry. The internal structure of TAE was modeled with NOVA and good agreement is found with measurements made with an array of five fixed-frequency reflectometers. The fast-ion transport resulting from these bursts of multiple TAE was then modeled with the ORBIT code. The simulations are reasonably consistent with the observed drop in neutron rate, however, further refinements in both the simulation of the TAE structure and in the modeling of the fast-ion transport are needed. Benchmarking stability codes against present experiments is an important step in developing the...

Fast-ion transport induced by Alfven eigenmodes (AEs) is studied in beam-heated plasmas on the National Spherical Torus Experiment [Ono et al., Nucl. Fusion 40, 557 (2000)] through space, time, and energy resolved measurements of the fast-ion population. Fast-ion losses associated with multiple toroidicity-induced AEs (TAEs), which interact nonlinearly and terminate in avalanches, are characterized. A depletion of the energy range >20 keV, leading to sudden drops of up to 40% in the neutron rate over 1 ms, is observed over a broad spatial range. It is shown that avalanches lead to a relaxation of the fast-ion profile, which in turn reduces the drive for the instabilities. The measured radial eigenmode structure and frequency of TAEs are compared with the predictions from a linear magnetohydrodynamics stability code. The partial disagreement suggests that nonlinearities may compromise a direct comparison between experiment and linear theory.

Reversed shear Alfven eigenmodes (RSAEs) have been observed with the phase contrast imaging diagnostic and Mirnov coils during the sawtooth cycle in Alcator C-mod [M. Greenwald et al., Nucl. Fusion 45, S109 (2005)] plasmas with minority ion-cyclotron resonance heating. Both down-chirping RSAEs and up-chirping RSAEs have been observed during the sawtooth cycle. Experimental measurements of the spatial structure of the RSAEs are compared to theoretical models based on the code NOVA [C. Z. Cheng and M. S. Chance, J. Comput. Phys. 71, 124 (1987)] and used to derive constraints on the q profile. It is shown that the observed RSAEs can be understood by assuming a reversed shear q profile (up chirping) or a q profile with a local maximum (down chirping) with q≈1.

Core localized Alfven eigenmodes in DIII-D [J. L. Luxon, Nucl. Fusion 42, 614 (2002)] and Joint European Torus (JET) [P. H. Rebut and B. E. Keen, Fusion Technol. 11, 13 (1987)] plasmas are driven by deuterium neutral beam ions traveling well below the Alfven speed. Modes are observed in reverse magnetic shear discharges with deuterium ion velocities as low as 0.23 and 0.16 of the Alfven speed parallel to the magnetic field in DIII-D and JET plasmas, respectively. Ellipticity-induced Alfven eigenmodes in DIII-D and toroidicity-induced Alfven eigenmodes in JET are excited by deuterium ions traveling well below the fundamental passing ion resonance condition, indicating the role of high-order resonances in driving these modes. NOVA-K analysis reveals many high-order resonances as contributing to the mode drive at high central safety factor due to the correspondingly large poloidal orbit width and the decrease in the perpendicular scale length of the modes.

Reversed shear Alfv́n eigenmodes (RSAEs) are typically thought of as being localized near the minima in the magnetic safety factor profile, however, their spatial coupling to global toroidal Alfv́n eigenmodes (TAEs) has been observed in DIII-D discharges. For a decreasing minimum magnetic safety factor, the RSAE frequency chirps up through that of stable and unstable TAEs. Coupling creates a small gap at the frequency degeneracy point forming two distinct global modes. The core-localized RSAE mode structure changes and becomes temporarily global. Similarly, near the mode frequency crossing point, the global TAE extends deeper into the plasma core. The frequency splitting and spatial structure of the two modes throughout the various coupling stages, as measured by an array of internal fluctuation diagnostics, are in close agreement with linear ideal MHD calculations using the NOVA code. The implications of this coupling for eigenmode stability is also investigated and marked changes are noted throughout the coupling process. © 2007 American Institute of Physics.

Reversed shear Alfven eigenmodes (RSAE) that were observed in the Joint European Torus (JET) [P. H. Rebut and B. E. Keen, Fusion Technol.11, 13 (1987)] and DIII-D [J. L. Luxon, Nucl. Fusion42, 614 (2002)] are studied with the ideal magnetohydrodynamic code NOVA-K [C. Z. Cheng, Phys. Rep.211, 1 (1992)]. It was found that the frequency behavior of the RSAEs can be described accurately by the NOVA-K code when plasma compressibility effects and toroidal plasma rotation are taken into account. For the mode activity on JET, the calculated drive exceeds the mode damping rate, consistent with experimental observations, while on DIII-D the growth rate from neutral beam ions for modes with high toroidal mode numbers is insufficient to account for the excitation of the modes and a major part of the drive comes from the background plasma.

The dynamics of runaway electrons in tokamak plasmas is studied in momentum space. In this analysis the electrons are accelerated by an electric field while they are decelerated by collisional drag, synchrotron radiation, and bremsstrahlung radiation. It is shown that the inclusion of bremsstrahlung losses into the calculations is important for the interpretation of disruption-mitigation experiments where large amounts of high Z are injected into the plasma. The inclusion of bremsstrahlung reduces the maximum energy that the runaway electrons can gain from the electric field.

Rapid frequency sweeping modes observed in reversed magnetic shear (RS) plasmas on the Japan Atomic Energy Research Institute Tokamak 60 Upgrade (JT-60U) [H. Ninomiya and the JT-60 Team, Phys. Fluids B 4, 2070 (1992)] have been identified as reversed-shear-induced Alfven eigenmodes (RSAEs), which are ideal magnetohydrodynamic Alfven eigenmodes (AEs) localized to the region of minimum safety factor, qmin, and are excited by negative-ion-based neutral beam injection. The chirping and subsequent saturation of the mode frequency are consistent with theoretical predictions for the transition from RSAEs to toroidal Alfven eigenmodes (TAEs). The previously observed rapid frequency sweeping modes in ion cyclotron wave heated plasmas in JT-60U can also be similarly explained. The observed AE amplitude is largest during the transition from RSAEs to TAEs, and fast ion loss is observed when the AE amplitude is largest at this transition. It is preferable to operate outside the transition range of qmin, e.g., 2.4

The recently upgraded phase-contrast imaging (PCI) diagnostic is used to characterize the transition from the low (L) to the enhanced Dα (EDA) high (H) confinement mode in Alcator C-Mod [I. H. Hutchinson, R. Boivin, F. Bombarda et al., Phys. Plasmas 1, 1511 (1994)] plasmas. PCI yields information on line integrated density fluctuations along vertical chords. The number of channels has been increased from 12 to 32 and the sampling rate from 1 MHz to 10 MHz. This expansion of diagnostic capabilities is used to study broadband turbulence in L and EDA H mode and to analyze the quasicoherent (QC) mode associated with EDA H mode. Changes in broadband turbulence at the transition from L to EDA H mode can be interpreted as an effect of the Doppler rotation of the bulk plasma. Additional fluctuation measurements of Dα light and the poloidal magnetic field show features correlated with PCI in two different frequency ranges at the transition. The backtransition from EDA H to L mode, the so-called enhanced neutron (E...