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Significant variations in MHD activity and fast-ion transport are observed in the DIIID high-beta, steady-state hybrid discharges with a mixture of Electron Cyclotron (EC) waves and Neutral Beam Injection (NBI). When Electron Cyclotron Heating (ECH) or Current Drive (ECCD) is applied, Alfven Eigenmodes (AEs) are usually suppressed and replaced by low-frequency bursting modes. The analysis of a recently compiled database of hybrid discharges suggests that the change of the fast-ion pressure especially the perpendicular pressure is the main factor responsible for the instability transition although the transition in some discharges can also be explained by a slight drop of the safety factor qmin. The lower ratio of fast-ion injection speed vinj to Alfven speed valfven and slight drop of safety factor qmin during ECCD may also facilitate the transition. The database shows that AEs mainly occur when the fast-ion fraction Pf/Ptotal is less than 0.53 and vinj/valfven is greater than 0.50, while low-frequency bursting modes appear in the opposite regime. Here, Pf and Ptotal are the central fast-ion pressure from classical prediction and total plasma pressure, respectively. The correlation with qmin is weaker and qmin is around unity in all the cases. The reason why the instability transition correlates with Pf/Ptotal and vinj/valfven is that they can significantly modify the drive of low-frequency bursting modes and AEs. The explanation is supported by the observation that low-frequency bursting modes are rarely seen in the hybrids with NBI only, with EC waves and counter-NBI, or with high plasma density. A careful check of the low-frequency bursting modes suggests that they are mainly chirping (neoclassical) tearing modes [referred to as chirping (N)TM], i.e. the mode frequency firstly jumps up from the steady (N)TM frequency, then chirps down, and finally returns to the steady (N)TM frequency. Occasionally, the (N)TMs are fully stabilized and replaced with pure fishbones. The resonance condition calculation and 'Kick' model simulations suggest that (N)TMs and fishbones can interact through modification of the fast ion distribution in phase space, which influences the drive.

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%.

In DIII-D hybrid discharges, the intense Alfven eigenmode (AE) activity driven by Neutral Beam Injection that is typically observed can be suppressed and replaced by fishbone modes when Electron Cyclotron Current Drive (ECCD) is centrally applied. Simulations have been carried out with the kinetic-magnetohydrodynamic hybrid code M3D-K based on DIII-D discharges #161401 without ECCD and #161403 with ECCD, respectively. In both cases, unstable modes are found—the mode frequency and the mode structure indicate that the instability excited in #161403 is of fishbone type, while that in #161401 is identified as the beta-induced Alfven eigenmode-like mode. Moreover, we find that the calculated mode frequencies of these two shots are consistent with experimental observations. A systematic scan has been performed to study the instability region of n=1,2,3 modes in (q0,βhot) parameter space, where n is the toroidal mode number, q0 is the safety factor value at the magnetic axis, and βhot is the energetic particle beta. It is found that the transition between AEs and fishbone modes can occur when q0 is changed. In addition, the modes of n=1,2,3 are stable or weakly unstable in the region of Phot/Ptotal≤0.5 and 1.2

It is shown that nonlinear self-interaction of energetic particle-driven geodesic acoustic mode does not generate a second harmonic in radial electric field using the fluid model. However, kinetic effects of energetic particles can induce a second harmonic in the radial electric field. A formula for the second-order plasma density perturbation is derived. It is shown that a second harmonic of plasma density perturbation is generated by the convective nonlinearity of both thermal plasma and energetic particles. Near the midplane of a tokamak, the second-order plasma density perturbation (the sum of second harmonic and zero frequency sideband) is negative on the low field side with its size comparable to the main harmonic at low fluctuation level. These analytic predictions are consistent with the recent experimental observation in DIII-D.

The ideal magnetohydrodynamic (MHD) stability of the National Compact Stellarator Experiment (NCSX) is extensively analyzed using the most advanced three-dimensional MHD codes. It is shown that the NCSX is stable to finite-n MHD modes, including the vertical mode, external kink modes and ballooning modes. However, high-n external kink modes that peak near the plasma edge are found to be weakly unstable. A global calculation shows that finite-n ballooning modes are significantly more stable than the local infinite-n modes.

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.

Second ballooning stability is examined in quasipoloidally symmetric, compact stellarator configurations. These high-β (volume-average β>4%) free-boundary equilibria are calculated using a reference Quasi-Poloidal Stellarator (QPS) configuration. QPS plasmas have low-shear, stellarator-like rotational transform profile with |B| that is approximately poloidally symmetric. The high-β QPS equilibria are similar in their magnetic configuration to previously studied tokamak-stellarator hybrids which have a high-shear, tokamak-like rotational transform profile. Both types of configurations have strong magnetic wells and consequently high interchange stability β limits. Free-boundary QPS equilibria have regions of second stability at high β. For infinite-n ballooning modes in QPS plasmas, the boundary for first instability is 〈β〉∼2% and the boundary for second stability is 〈β〉∼6%. Finite-n ballooning mode calculations show higher β limits, 〈β〉>5%. Increasing plasma current (for fixed plasma pressure) can lower t...

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.

The damping rate of the n = 1 toroidal Alfven eigenmodes (TAE) mode in Ohmic-heated JET plasmas has been measured and compared with the prediction of the kinetic NOVA-K code, which includes electron and ion Landau damping of the global shear-Alfven wave field, collisional damping, and radiative damping. It was found that the calculated damping rate is too small to account for the measured value under these experimental conditions. A relatively weak dependence of the damping rate on the normalized Larmor radius is observed experimentally.

The multilevel physics, massively parallel plasma simulation code, M3D has been used to study spherical toris (STs) and tokamaks. The magnitude of outboard shift of density profiles relative to electron temperature profiles seen in NSTX under strong toroidal flow is explained. Internal reconnection events in ST discharges can be classified depending on the crash mechanism, just as in tokamak discharges; a sawtooth crash, disruption due to stochasticity, or high-β disruption. Toroidal shear flow can reduce linear growth of internal kink. It has a strong stabilizing effect nonlinearly and causes mode saturation if its profile is maintained, e.g. through a fast momentum source. Normally, however, the flow profile itself flattens during the reconnection process, allowing a complete reconnection to occur. In some cases, the maximum density and pressure spontaneously occur inside the island and cause mode saturation. Gyrokinetic hot particle/MHD hybrid studies of NSTX show the effects of fluid compression on a fast-ion driven n = 1 mode. MHD studies of recent tokamak experiments with a central current hole indicate that the current clamping is due to sawtooth-like crashes, but with n = 0.

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.

Linear and nonlinear simulations of high-order harmonics q = 1 energetic particle modes excited by trapped energetic particles in tokamaks are carried out using kinetic/magnetohydrodynamic hybrid code M3D-K. It is found that with a flat safety factor profile in the core region, the linear growth rate of high-order harmonics ( m = n > 1) driven by energetic trapped particles can be higher than the m / n = 1 / 1 component. The high m = n > 1 modes become more unstable when the pressure of energetic particles becomes higher. Moreover, it is shown that there exist multiple resonant locations satisfying different resonant conditions in the phase space of energetic particles for the high-order harmonics modes, whereas there is only one precessional resonance for the m / n = 1 / 1 harmonics. The fluid nonlinearity reduces the saturation level of the n = 1 component, while it hardly affects those of the high n components, especially the modes with m = n = 3 , 4. The frequency of these modes does not chirp signifi...

The internal structure of the toroidicity-induced Alfven eigenmode (TAE) is studied by comparing soft x-ray profile and beam ion loss data taken during TAE activity in the DIII-D tokamak [W. W. Hei ...

Instabilities with frequency chirping in the frequency range of Alfven eigenmodes have been found in the domain 0.1% < βh < 1% and vb||/vA ~1 with high energy neutral beam injection in JT-60U. One instability with a frequency inside the Alfven continuum spectrum appears and its frequency increases slowly to the toroidicity induced Alfven eigenmode (TAE) gap on the timescale of an equilibrium change ( ≈ 200 ms). Other instabilities appear with a frequency inside the TAE gap and their frequencies change very quickly by 10-20 kHz in 1-5 ms. During the period when these fast frequency sweeping (fast FS) modes occur, abrupt large amplitude events (ALEs) often appear with a drop of neutron emission rate and an increase in fast neutral particle fluxes. The loss of energetic ions increases with a peak fluctuation amplitude of θ/Bθ. An energy dependence of the loss ions is observed and suggests a resonant interaction between energetic ions and the mode.

Toroidicity-induced Alfven eigenmode (TAE) stability in the National Spherical Torus Experiment (NSTX) [S. M. Kaye, M. Ono, Y.-K. M. Peng et al., Fusion Technol. 36, 16 (1999)] is analyzed using the improved NOVA-K code [N. N. Gorelenkov, C. Z. Cheng, and G. Y. Fu, Phys. Plasmas 6, 2802 (1999)], which includes finite orbit width and Larmor radius effects and is able to predict the saturation amplitude for the mode using the quasilinear theory. A broad spectrum of unstable global TAEs with different toroidal mode numbers is predicted. Due to the strong poloidal field and the presence of the magnetic well in NSTX, better particle confinement in the presence of TAEs in comparison with tokamaks is illustrated making use of the ORBIT code [R. B. White and M. S. Chance, Phys. Fluids 27, 2455 (1984)].

Recent stability results of external kink modes and vertical modes in compact stellarators are presented. The vertical mode is found to be stabilized by externally generated poloidal flux. A simple stability criterion is derived in the limit of large aspect ratio and constant current density. For a wall at infinite distance from the plasma, the amount of external flux needed for stabilization is given by F-i = (kappa(2) - kappa)/(kappa(2) + 1), where kappa is the axisymmetric elongation and F-i is the fraction of the external rotational transform. A systematic parameter study shows that the external kink mode in a quasiaxisymmetric stellarator (QAS) can be stabilized at high beta (similar to 5%) without a conducting wall by magnetic shear via three-dimensional (3D) shaping. It is found that external kinks are driven by both parallel current and pressure gradient. The pressure contributes significantly to the overall drive through the curvature term and the Pfirsch-Schluter current. (C) 2000 American Institute of Physics. [S1070-664X(00)91005-X].

The excitation and stabilization of Alfv?n eigenmodes and their impact on energetic ion confinement were investigated with negative ion based neutral beam injection at 330-360?keV into weak or reversed magnetic shear plasmas on JT-60U. Toroidicity induced Alfv?n eigenmodes (TAEs) were observed in weak shear plasmas with ?h ? 0.1% and 0.4 ? vb||/vA ? 1. The stability of TAEs is consistent with predictions by the NOVA-K code. New burst modes and chirping modes were observed in the higher ? regime of ?h ? 0.2%. The effect of TAEs, burst modes and chirping modes on fast ion confinement has been found to be small so far. It was found that a strongly reversed shear plasma with internal transport barrier suppresses AEs.

Non-linear MHD simulation results of pellet injection show that MHD forces can accelerate large pellets injected on the high field side of a tokamak to the plasma centre. Magnetic reconnection can produce a reverse shear q profile. Ballooning instability caused by pellets is also reduced by high field side injection. Studies are also reported of the current quench phase of disruptions, which can cause 3-D halo currents and runaway electrons.

High-frequency modes in the 525-550 kHz range with toroidal mode numbers n = 3-7 were excited after the sawtooth crash during ion cyclotron range of frequency (ICRF) heating. Based on the stability analysis using the NOVA-K code, these modes were found to be consistent with ellipticity-induced Alfven eigenmodes (EAEs) excited in the EAE gap located at the q = 1 surface. A change in the safety factor after the sawtooth crash was essential for the excitation of EAEs in the core region of the plasma. The high-frequency modes were stabilized by the neutral beam injection at 350 keV using negative-ion-based neutral beam (NNB) injectors. Stability analysis using the NOVA-K code has shown that NNB-injected ions enhance the damping of the EAEs and tend to stabilize them.

The effects of finite drift orbit width (FOW) and Larmor radius (FLR) of fast particles on the stability of low-n toroidicity-induced Alfven eigenmodes (TAE) are studied. The formulation is based on the solution of the low frequency gyrokinetic equation (ω≪ωc, where ωc is particle cyclotron frequency). A quadratic form has been derived in terms of invariant variables; energy E, magnetic moment μ, and toroidal angular momentum Pφ. The growth rate of the TAE is computed perturbatively using numerical averaging over the fast particle drift orbit. This new computational capability improves the NOVA-K code [G. Y. Fu, C. Z. Cheng, and K. L. Wong, Phys. Fluids B 5, 4040 (1994)] which included FOW effects in the growth rate calculation based on small radial orbit width approximation. The new NOVA-K version has been benchmarked for different regimes of particle TAE excitation. It is shown that both FOW and FLR effects are typically stabilizing; the TAE growth rate can be reduced by as much as a factor of 2 for tok...

The toroidal Alfven eigenmodes (TAE) in the Tokamak Fusion Test Reactor [K. Young, et al., Plasma Phys. Controlled Fusion 26, 11 (1984)]deuterium-tritium plasmas are analyzed using the NOVA-K code [C.Z. Cheng, Phys. Reports 211, 1 (1992)]. The theoretical results are compared with the experimental measurements in detail. In most cases, the theory agrees with the observations in terms of mode frequency, mode structure, and mode stability. However, one mode with toroidal mode number n = 2 is observed to be poloidally localized on the high field side of the magnetic axis with a mode frequency substantially below the TAE frequency.

On JT-60U, for the first time in negative shear plasmas, toroidicity induced Alfven eigenmodes (TAEs) with frequencies in the range of 90 to 110 kHz and toroidal mode numbers n = 5-8 were observed after a broadening of the density profile due to sequential partial collapses during ion cyclotron range of frequency (ICRF) heating. TAEs are more stable in negative shear plasmas than plasmas with a monotonically increasing q profile. The TAE stability was analysed with the NOVA-K code. It was found that the stability is highly sensitive to the gap alignment just inside qmin and that the theoretical results are consistent with the experimental results. In a weak central magnetic shear discharge, modes with very rapid frequency chirping were observed during ICRF heating. The frequencies of these modes rapidly increased from ~30 kHz up to ~110 kHz in a period of ~150 ms. The large frequency chirping is not well understood by the present theory.

Purely alpha-particle-driven Toroidal Alfven Eigenmodes (TAEs) with toroidal mode numbers n=1-6 have been observed in Deuterium-Tritium (D-T) plasmas on the Tokamak Fusion Test Reactor [D.J. Grove and D.M. Meade, Nucl. Fusion 25, 1167 (1985)]. The appearance of mode activity following termination of neutral beam injection in plasmas with q(0)>1 is generally consistent with theoretical predictions of TAE stability [G.Y. Fu et al., Phys. Plasmas 3, 4036 (1996]. Internal reflectometer measurements of TAE activity is compared with theoretical calculations of the radial mode structure. Core localization of the modes to the region of reduced central magnetic shear is confirmed, however the mode structure can deviate significantly from theoretical estimates. The peak measured TAE amplitude of delta n/n~10(superscript -4) at r/a~0.3-0.4 corresponds to delta B/B~10-5, while dB/B~10(superscript -8) is measured at the plasma edge. Enhanced alpha particle loss associated with TAE activity has not been observed.

For the first time noncircular triangularity induced Alfv\'en eigenmodes (NAE) were observed in combined ion cyclotron resonance frequency and neutral beam injection heated plasmas. Ellipticity induced Alfv\'en eigenmodes (EAE) and toroidicity-induced Alfv\'en eigenmodes (TAE) were also observed in those plasmas. The threshold beta of the energetic ions for exciting the NAE modes was found to be similar to that for exciting TAE modes.

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...

It is found that low-n toroidicity induced Alfven eigenmodes (TAEs) excited by ion cyclotron resonance heating can be stabilized by counter-tangential neutral beam injection in JT-60U. The deformation of the radial structure of the TAE mode due to the shear in toroidal rotation is a plausible stabilizing mechanism. This mechanism is also expected to be effective in suppressing high-n TAE modes. Real time control of TAE mode amplitudes using toroidal rotation control is possible for burn control in fusion reactors

Experiments in the Tokamak Fusion Test Reactor (TFTR) have explored several novel regimes of improved tokamak confinement in deuterium-tritium (D-T) plasmas, including plasmas with reduced or reversed magnetic shear in the core and high-current plasmas with increased shear in the outer region (high-l{sub i}). New techniques have also been developed to enhance the confinement in these regimes by modifying the plasma-limiter interaction through in-situ deposition of lithium. In reversed-shear plasmas, transitions to enhanced confinement have been observed at plasma currents up to 2.2 MA (q{sub a} {approx} 4.3), accompanied by the formation of internal transport barriers, where large radial gradients develop in the temperature and density profiles. Experiments have been performed to elucidate the mechanism of the barrier formation and its relationship with the magnetic configuration and with the heating characteristics. The increased stability of high-current, high-l{sub i} plasmas produced by rapid expansion of the minor cross-section, coupled with improvement in the confinement by lithium deposition has enabled the achievement of high fusion power, up to 8.7 MW, with D-T neutral beam heating. The physics of fusion alpha-particle confinement has been investigated in these regimes, including the interactions of the alphas with endogenous plasma instabilities and externally applied waves in the ion cyclotron range of frequencies. In D-T plasmas with q{sub 0} > 1 and weak magnetic shear in the central region, a toroidal Alfven eigenmode instability driven purely by the alpha particles has been observed for the first time. The interactions of energetic ions with ion Bernstein waves produced by mode-conversion from fast waves in mixed-species plasmas have been studied as a possible mechanism for transferring the energy of the alphas to fuel ions.

Alpha-particle-driven toroidal Alfven eigenmodes (TAEs) have been observed for the first time in deuterium-tritium (D-T) plasmas on the tokamak fusion test reactor (TFTR). These modes are observed 100–200 ms following the end of neutral beam injection in plasmas with reduced central magnetic shear and elevated central safety factor [q(0) > 1]. Mode activity is localized to the central region of the discharge ({lt}0.5) with magnetic fluctuation level B⊥/B∥ ~ 10⁻⁵ and toroidal mode numbers in the range n=2–4, consistent with theoretical calculations of α -TAE stability in TFTR.

Plasmas in spherical and conventional tokamaks, with weakly reversed shear q pro le and minimum q above but close to unity, are susceptible to an non-resonant (m, n ) = (1, 1) internal kink mode. This mode can saturate and persist and can induce a (2; 1) seed island for Neoclassical Tearing Mode (NTMs)1 . The mode can also lead to large energetic particle transport and signi cant broadening of beam-driven current. Motivated by these important e ects, we have carried out extensive nonlinear simulations of the mode with nite toroidal rotation using parameters and pro les of an NTSX plasma with a weakly reversed shear pro le. The numerical results show that, at the experimental level, plasma rotation has little e ect on either equilibrium or linear stability. However, rotation can signi cantly inuence the nonlinear dynamics of the (1, 1) mode and the the induced (2, 1) magnetic island. The simulation results show that a rotating helical equilibrium is formed and maintained in the nonlinear phase at nite plasma rotation. In contrast, for non-rotating cases, the nonlinear evolution exhibits dynamic oscillations between a quasi-2D state and a helical state. Furthermore, the e ects of rotation are found tomore » greatly suppress the (2, 1) magnetic island even at a low level.« less

A 60 GHz microwave scattering system was used to search for kinetic Alfven waves when toroidal Alfven eigenmodes were excited by the energetic hydrogen ions produced during ion cyclotron resonance heating in the tokamak fusion test reactor (TFTR). Scattering signals from the expected location with the correct frequencies and wave wavelengths were observed. These data are presented as the first evidence for the coupling between toroidal Alfven eigenmodes and kinetic Alfven waves.

The toroidal Alfven eigenmodes (TAE) are calculated to be stable in the presently obtained deuterium–tritium plasmas in the Tokamak Fusion Test Reactor (TFTR) [Plasma Phys. Controlled Nucl. Fusion Res. 26, 11 (1984)]. However, the core localized TAE mode can exist and is less stable than the global TAE modes. The beam ion Landau damping and the radiative damping are the two main stabilizing mechanisms in the present calculation. In future deuterium–tritium experiments, the alpha‐driven TAE modes are predicted to occur with a weakly reversed shear profile.

An experiment was performed in TFTR DT plasmas in an attempt to destabilize the alpha particle driven toroidicity-induced Alfven eigenmodes (TAEs) by reducing their thermal ion Landau damping. The thermal ion Landau damping was reduced by transiently lowering the ion temperature using either helium (He) gas puffs or deuterium (D) or lithium (Li) pellet injection during neutral beam injection (NBI) into DT supershots. The ion temperature was successfully lowered from Ti(0) approximately=20 keV to Ti(0) approximately=10 keV in about 0.2 s; however, no alpha driven TAEs were observed. Theoretical analyses of the TAE instability of these DT discharges indicate that the alpha pressure required for TAE stability still remained greater than that actually obtained in this experiment, mainly because of the effects of beam ion Landau damping

The alpha particle effect on the excitation of toroidal Alfv{acute e}n eigenmodes (TAE) was investigated in deuterium-titrium (D-T) plasmas in the Tokamak Fusion Test Reactor. rf power was used to position the plasma near the instability threshold, and the alpha particle effect was inferred from the reduction of rf power threshold for TAE instability in D-T plasmas. Initial calculations indicate that the alpha particles contribute 10{percent}{endash}30{percent} of the total drive in a D-T plasma with 3 MW of peak fusion power. {copyright} {ital 1996 The American Physical Society.}

High frequency fishbone instability driven by passing energetic ions was first reported in the Princeton beta experiment with tangential neutral-beam-injection (Heidbrink et al 1986 Phys. Rev. Lett. 57 835–8). It could play an important role for ITER-like burning plasmas, where α particles are mostly passing particles. In this work, a generalized energetic ion distribution function and finite drift orbit width effect are considered to improve the theoretical model for passing particle driving fishbone instability. For purely passing energetic ions with zero drift orbit width, the kinetic energy is derived analytically. The derived analytic expression is more accurate as compared to the result of previous work (Wang 2001 Phys. Rev. Lett. 86 5286–8). For a generalized energetic ion distribution function, the fishbone dispersion relation is derived and is solved numerically. Numerical results show that broad and off-axis beam density profiles can significantly increase the beam ion beta threshold for instability and decrease mode frequency.

An Alfven frequency mode (AFM) is very often seen in TFTR neutral beam heated plasmas as well as in ohmic plasmas. This quasi-coherent mode has so far only been seen on magnetic fluctuation diagnostics (Mirnov coils). A close correlation between the plasma edge density and the mode activity (frequency and amplitude) has been observed, which indicates that the AFM is an edge localized mode with r/a>0.85. No direct impact of this mode on the plasma global performance or on fast ion loss (e.g., the alpha particles in DT experiments) has been observed. This mode is not the conventional TAE (toroidicity induced Alfven eigenmode). The present TAE theory cannot explain this observation. Other possible explanations are discussed

Experiments with plasmas having nearly equal concentrations of deuterium and tritium have been carried out on TFTR. To date (September 1995), the maximum fusion power has been 10.7 MW, using 39.5 MW of neutral beam heating, in a supershot discharge and 6.7 MW in a high beta P discharge following a current ramp-down. The fusion power density in the core of the plasma has reached 2.8 MW/m3, exceeding that expected in the International Thermonuclear Experimental Reactor (ITER). The energy confinement time tau E is observed to increase in DT, relative to D plasmas, by 20% and the n1(0).T1(0). tau E product by 55%. The improvement in thermal confinement is caused primarily by a decrease in ion heat conductivity in both supershot and limiter H mode discharges. Extensive lithium pellet injection increased the confinement time to 0.27 s and enabled higher current operation in both supershot and high beta P discharges. First measurements of the confined alpha particles have been performed and found to be in good agreement with TRANSP simulations assuming classical confinement. Measurements of the alpha ash profile have been compared with simulations using particle transport coefficients from helium gas puffing experiments. The loss of energetic alpha particles to a detector at the bottom of the vessel is well described by the first-orbit loss mechanism. No loss due to alpha particle driven instabilities has yet been observed. ICRF heating of a DT plasma, using the second harmonic of tritium, has been demonstrated. DT experiments on TFTR will continue both to explore the physics underlying the ITER design and to examine some of the physics issues associated with an advanced tokamak reactor

Experiments to destabilize the toroidicity induced Alfven eigenmode (TAE) by energetic alpha particles were performed on the Tokamak Fusion Test Reactor using deuterium and tritium fuel. To decrease the alpha particle pressure instability threshold, discharges with an elevated value of q(0)>1.5 were used. By raising q(0), the radial location of the low toroidal mode number TAE gaps moves towards the magnetic axis and into alignment with the region of maximum alpha pressure gradient, thereby (in theory) lowering the value of the central alpha particle beta alpha required for instability. No TAE activity was observed when beta alpha (0) reached 0.08% in a discharge with fusion power of 2.4 MW. Calculations predict that the alpha driven TAE was weakly unstable

Linear and nonlinear kinetic-MHD hybrid simulations have been carried out to investigate linear stability and nonlinear dynamics of beam-driven fishbone instability in spherical tokamak plasmas. Realistic NSTX parameters with finite toroidal rotation were used. The results show that the fishbone is driven by both trapped and passing particles. The instability drive of passing particles is comparable to that of trapped particles in the linear regime. The effects of rotation are destabilizing and a new region of instability appears at higher q min (>1.5) values, q min being the minimum of safety factor profile. In the nonlinear regime, the mode saturates due to flattening of beam ion distribution, and this persists after initial saturation while mode frequency chirps down in such a way that the resonant trapped particles move out radially and keep in resonance with the mode. Correspondingly, the flattening region of beam ion distribution expands radially outward. A substantial fraction of initially non-resonant trapped particles become resonant around the time of mode saturation and keep in resonance with the mode as frequency chirps down. On the other hand, the fraction of resonant passing particles is significantly smaller than that of trapped particles. Our analysis shows that trapped particles provide the main drive to the mode in the nonlinear regime.

The toroidicity-induced Alfven eigenmodes (TAE) are found to be stable in the Tokamak Fusion Test Reactor (TFTR) deuterium-tritium plasmas. The dominant stabilizing mechanisms are beam ion Landau damping and radiative damping. A core localized TAE mode is shown to exist near the center of the plasma at small magnetic shear and finite plasma beta, which can be destabilized by energetic alpha particles in future TFTR DT experiments. With additional instability drive from fast minority ions powered by ion cyclotron radio frequency, both the global and core localized TAE modes can be readily destabilized.

TFTR has begun its campaign to study deuterium-tritium fusion under reactor-like conditions. Variable amounts of deuterium and tritium neutral beam power have been used to maximize fusion power, study alpha heating, investigate alpha particle confinement, and search for alpha driven plasma instabilities. Additional areas of study include energy and particle transport and confinement, ICRF heating schemes for DT plasmas, tritium retention, and fusion in high βp plasmas. The majority of this work is done in the TFTR supershot confinement regime. To obtain supershots, extensive limiter conditioning using helium fueled ohmic discharges and lithium pellet injection into ohmic and neutral beam heated plasmas is performed, resulting in a low recycling limiter. The relationship between recycling and core plasma confinement has been studied by using helium, deuterium and high-Z gas puffs to simulate high recycling limiter conditions. These studies show that confinement in TFTR supershots is very sensitive to the influx of neutral particles at the plasma edge.

Peak fusion power production of 6.2 ± 0.4 MW has been achieved in TFTR plasmas heated by deuterium and tritium neutral beams at a total power of 29.5 MW. These plasmas have an inferred central fusion alpha particle density of 1.2 x 1017 m ₋3 without the appearance of either disruptive magnetohydrodynamics events or detectable changes in Alfven wave activity. The measured loss rate of energetic alpha particles agreed with the approximately 5% losses expected from alpha particles which are born on unconfined orbits.

Several techniques were used to excite toroidal Alfven eigenmodes (TAE) in the Tokamak Fusion Test Reactor (TFTR) (Proc. 13th Int. Conf. on Plasma Physics and Controlled Nuclear Fusion Research Vol 1 (Vienna: IAEA, 1990) 9) at magnetic fields above 10 kG. These involved pellet injection to raise the plasma density, variation of the plasma current to change the energetic ion orbit and the q-profile, and ICRF heating to produce energetic hydrogen ions at velocities comparable with 3.5 MeV alpha particles created in deuterium-tritium (d-t) fusion reactions. The amplitude of the TAE modes observed in ICRF-heated plasmas behaves differently from those driven by neutral beams. This can be explained by the difference in the energetic ion orbits. These experimental results are presented and relevance to fusion reactors are discussed.

The stability of toroidicity‐induced Alfven eigenmodes (TAE) is investigated in general tokamak equilibria with finite aspect ratio and finite plasma beta. The finite orbit width of the hot particles and the collisional damping of the trapped electrons are included. For the trapped hot particles, the finite orbit width is found to be stabilizing. For the circulating hot particles, the finite orbit width effect is stabilizing for larger values of vh/vA (≳1) and destabilizing for smaller values of vh/vA (

The stability of high-n toroidicity-induced shear Alfven eigenmodes (TAE) in the presence of fusion alpha particles or energetic ions in tokamaks is investigated. The TAE modes are discrete in nature and thus can easily tap the free energy associated with energetic particle pressure gradient through wave particle resonant interaction. A quadratic form is derived for the high-n TAE modes using gyro-kinetic equation. The kinetic effects of energetic particles are calculated perturbatively using the ideal MHD solution as the lowest order eigenfunction. The finite Larmor radius (FLR) effects and the finite drift orbit width (FDW) effects are included for both circulating and trapped energetic particles. It is shown that, for circulating particles, FLR and FDW effects have two opposite influences on the stability of the high-n TAE modes. First, they have the usual stabilizing effects by reducing the wave particle interaction strength. Second, they also have destabilizing effects by allowing more particles to resonate with the TAE modes. It is found that the growth rate induced by the circulating alpha particles increase linearly with toroidal mode number n for small {kappa}{sub {theta}}{rho}{sub {alpha}}, and decreases as 1/n for {kappa}{sub {theta}}{rho}{sub {alpha}} {much gt} 1. The maximum growth rate is obtained atmore » {kappa}{sub {theta}}{rho}{sub {alpha}} on the order of unity and is nearly constant for the range of 0.7 < {upsilon}{sub {alpha}}/{upsilon}{sub A} < 2.5. On the other hand, the trapped particle response is dominated by the precessional drift resonance. The bounce resonant contribution is negligible. The growth rate peaks sharply at the value of {kappa}{sub {theta}}{rho}{sub {alpha}} such that the precessional drift resonance occurs for the most energetic trapped particles. The maximum growth rate due to the energetic trapped particles is comparable to that of circulating particles.« less

Intense axisymmetric oscillations driven by suprathermal ions injected in the direction counter to the toroidal plasma current are observed in the DIII-D tokamak. The modes appear at nearly half the ideal geodesic acoustic mode frequency, in plasmas with comparable electron and ion temperatures and elevated magnetic safety factor (qmin 2). Strong bursting and frequency chirping are observed, concomitant with large (10%-15%) drops in the neutron emission. Large electron density fluctuations (ne/ne1.5%) are observed with no detectable electron temperature fluctuations, confirming a dominant compressional contribution to the pressure perturbation as predicted by kinetic theory. The observed mode frequency is consistent with a recent theoretical prediction for the energetic-particle-driven geodesic acoustic mode. © 2008 The American Physical Society.

A new energetic particle-induced Geodesic Acoustic Mode (EGAM) is shown to exist. The mode frequency, mode structure, and mode destabilization are determined non-perturbatively by energetic particle kinetic effects. In particular the EGAM frequency is found to be substantially lower than the standard GAM frequency. The radial mode width is determined by the energetic particle drift orbit width and can be fairly large for high energetic particle pressure and large safety factor. These results are consistent with the recent experimental observation of the beam- driven n=0 mode in DIII-D. The new mode is important since it can degrade energetic particle confinement as shown in the DIII-D experiments. The new mode may also affect the thermal plasma confinement via its interaction with plasma micro-turbulence.

A high‐n WKB‐ballooning mode equation is employed to study toroidicity‐induced shear Alfven eigenmodes (TAE) in s‐α space, where s=(r/q)(dq/dr) is the magnetic shear and α=−(2Rq2/B2)(dp/dr) is the normalized pressure gradient for tokamak plasmas. In the ballooning mode first stability region, TAE modes are found to exist only for α less than some critical value αc. It is found that these TAE modes reappear in the ballooning mode second stability region for bands of α values. The global envelope structures of these TAE modes are studied by the Wentzel–Kramers–Brillouin (WKB) method and are found to be bounded radially if the local mode frequency has a maximum in radius.

A new wave particle resonance mechanism is found explaining the first-orbit prompt neutral beam-ion losses induced by shear Alfven Eigenmodes (AEs) in the DIII-D tokamak. Because of the large banana width, a typical trapped beam ion can only interact locally with a core localised Alfven Eigenmode for a fraction of its orbit, i.e. part of its inner leg of the banana orbit. These trapped beam ions can experience substantial radial kick within one bounce as long as the phases of the wave seen by the particles are nearly constant during this local interaction. A wave particle resonant condition is found based on the locally averaged particle orbit frequencies over the interaction part of the particle orbit. It is further found that the frequency width of the local resonance is quite large because the interaction time is short. This implies that particles over a considerable region of phase space can interact effectively with the localised AEs and experience large radial kicks within one bounce orbit. The radial kick size is found numerically and analytically to scale linearly in AE amplitude and is about 5 cm for typical experimental parameters. These results are consistent with experimental measurement.