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It is well documented that the central electron temperature in the national spherical torus experiment (NSTX) remains largely unchanged as the external heating power, and hence the normalized volume averaged plasma pressure β increases [Stutman, Phys. Rev. Lett. 102, 115002 (2009)PRLTAO0031-900710.1103/PhysRevLett.102.115002]. Here we present a hypothesis that low n, pressure driven ideal magnetohydrodynamic (MHD) instabilities that are nondisruptive, can break magnetic surfaces in the central region and thereby flatten the electron temperature profiles. We demonstrate this mechanism in a 3D resistive MHD simulation of a NSTX discharge. By varying the toroidal magnetic field strength, and/or the heating power, we show that there is a critical value of β, above which the central temperature profile no longer peaks on axis.

The efficiency of two lithium (Li) injection methods used on the National Spherical Torus Experiment (NSTX) are compared in terms of the amount of Li used to produce equivalent plasma performance improvements, namely, Li evaporation over the divertor plates, prior to the initiation of the discharge, and real-time Li injection directly into the plasma scrape-off layer during the discharge. The measurements show that the real-time method can affect the energy confinement and the edge stability of NSTX plasmas in a more efficient way than the Li evaporation method, as it requires only a fraction of the amount of Li used by the evaporation method to produce similar improvements.

The National Spherical Torus eXperiment (NSTX) is a medium-sized, low-aspect ratio, spherical tokamak (ST) whose aims are to study 1) the unique physics properties of the ST, 2) complement higher aspect ratio tokamak physics and support ITER, and 3) establish attractive ST operating regimes for future ST-based fusion energy producing devices. Research on NSTX over the past 15 years has been broadly based. Transport and turbulence studies focused on identifying the source of the highly anomalous and dominant electron energy transport, as well as electromagnetic effects on turbulence, in neutral beam and radio frequency heated L- and H-mode plasmas. Macrostability research has identified the importance of kinetic effects in determining high-b T stability, and a multi-parameter-based algorithm was developed capable of predicting plasma disruptions with a near 95% success rate. Energetic particle driven Alfven Eigenmodes were found to have a significant effect on the fast ion population and resulting beam-driven non-inductive current drive profiles. High heat fluxes were mitigated successfully by operating in a “snowflake” divertor configuration, and test stand studies revealed the surface chemistry necessary to understand lithium wall conditioning, a technique used routinely during the last half of NSTX’s operational lifetime. Finally, solenoid-free operation studies explored non-inductive generation and maintenance of the plasma current; non-inductive operation is a critical component of future ST devices. NSTX has just undergone a major upgrade, which allows for an expanded operating and physics parameter range. The Upgrade also includes the addition of a second, more tangentially directed, neutral beam injector for added power and pressure and current profile control. NSTX-Upgrade operation commenced in 2015.

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 this paper we report on observations and interpretations of a new class of global MHD eigenmode solutions arising in gaps in the low frequency Alfven-acoustic continuum below the geodesic acoustic mode frequency. These modes have been just reported (Gorelenkov et al 2007 Phys. Lett. 370 70-7) where preliminary comparisons indicate qualitative agreement between theory and experiment. Here we show a more quantitative comparison emphasizing recent NSTX experiments on the observations of the global eigenmodes, referred to as beta-induced Alfven-acoustic eigenmodes (BAAEs), which exist near the extrema of the Alfven-acoustic continuum. In accordance to the linear dispersion relations, the frequency of these modes may shift as the safety factor, q, profile relaxes. We show that BAAEs can be responsible for observations in JET plasmas at relatively low beta 20%. In NSTX plasma observed magnetic activity has the same properties as predicted by theory for the mode structure and the frequency. Found numerically in NOVA simulations BAAEs are used to explain the observed properties of relatively low frequency experimental signals seen in NSTX and JET tokamaks.

Predictions of the recently developed paleoclassical transport model are compared with data from many toroidal plasma experiments: electron heat diffusivity in DIII-D, C-Mod and NSTX ohmic and near-ohmic plasmas; transport modeling of DIII-D ohmic-level discharges and of the RTP ECH 'stair-step' experiments with eITBs at low order rational surfaces; investigation of a strong eITB in JT-60U; H-mode Te edge pedestal properties in DIII-D; and electron heat diffusivities in non-tokamak experiments (NSTX/ST, MST/RFP, SSPX/spheromak). The radial electron heat transport predicted by the paleoclassical model is found to agree with a wide variety of ohmic-level experimental results and to set the lower limit (within a factor {approx} 2) for the radial electron heat transport in most resistive, current-carrying toroidal plasmas -- unless it is exceeded by fluctuation-induced transport, which often occurs in the edge of L-mode plasmas and when the electron temperature is high ({approx}>T{sub e}{sup crit} {approx}B{sup 2/3}{bar {alpha}}{sup 1/2} keV) because then paleoclassical transport becomes less than gyro-Bohm-level anomalous transport.

Modifications to the plasma control capabilities and poloidal field coils of the National Spherical Torus Experiment (NSTX) have enabled a significant enhancement in shaping capability which has led to the transient achievement of a record shape factor (S≡q95(Ip/aBt)) of ∼41 (MA m−1 T−1) simultaneous with a record plasma elongation of κ ≡b/a∼ 3. This result was obtained using isoflux control and real-time equilibrium reconstruction. Achieving high shape factor together with tolerable divertor loading is an important result for future ST burning plasma experiments as exemplified by studies for future ST reactor concepts, as well as neutron producing devices, which rely on achieving high shape factors in order to achieve steady state operation while maintaining MHD stability. Statistical evidence is presented which demonstrates the expected correlation between increased shaping and improved plasma performance. Plasmas with high shape factor have been sustained for pulse lengths which correspond to τpulse= 1.6s∼ 50 τE∼ 5 τCR, where τCRis the current relaxation time and τEis the energy confinement time. Plasmas with higher βt∼ 20% have been sustained for τpulse= 1.2s∼ 25 τE∼ 3 τCRwith non-inductive current fractionsfNI∼ 50%, with ∼40% pressure driven current and ∼10% neutral beam driven current. An interesting feature of these discharges is the observation that the central value of the safety factorq(0) remains elevated and constant for several current diffusion times without sawteeth, similar to the ‘hybrid mode’. Calculations of the profiles of inductive and non-inductive current are compared with measurements of the total current profile and are shown to be in quantitative agreement. Results are shown from experiments which investigate the applicability of high harmonic fast waves (HHFWs) and electron Bernstein waves (EBWs) as current drive and heating sources, and the possibility of LHCD for future ST devices is raised. A calculated scenario which provides 100% non-inductive current drive is described. NSTX operates with peak divertor heat fluxes which are in the same range as those expected for the ITER device, i.e. with. High triangularity, high elongation plasmas on NSTX have been demonstrated to have reduced peak heat flux to the divertor plates to −2.

The NSTX operates at low aspect ratio (R/a ~ 1.3) and high beta (up to 40%), allowing tests of global confinement and local transport properties that have been established from higher aspect ratio devices. The NSTX plasmas are heated by up to 7 MW of deuterium neutral beams with preferential electron heating as expected for ITER. Confinement scaling studies indicate a strong BT dependence, with a current dependence that is weaker than that observed at higher aspect ratio. Dimensionless scaling experiments indicate a strong increase in confinement with decreasing collisionality and a weak degradation with beta. The increase in confinement with BT is due to reduced transport in the electron channel, while the improvement with plasma current is due to reduced transport in the ion channel related to the decrease in the neoclassical transport level. Improved electron confinement has been observed in plasmas with strong reversed magnetic shear, showing the existence of an electron internal transport barrier (eITB). The development of the eITB may be associated with a reduction in the growth of microtearing modes in the plasma core. Perturbative studies show that while L-mode plasmas with reversed magnetic shear and an eITB exhibit slow changes in across the profile after the pellet injection, H-mode plasmas with a monotonic q-profile and no eITB show no change in this parameter after pellet injection, indicating the existence of a critical gradient that may be related to the q-profile. Both linear and non-linear simulations indicate the potential importance of electron temperature gradient (ETG) modes at the lowest BT. Localized measurements of high-k fluctuations exhibit a sharp decrease in signal amplitude levels across the L–H transition, associated with a decrease in both ion and electron transport, and a decrease in calculated linear microinstability growth rates across a wide k-range, from the ion temperature gradient/TEM regime up to the ETG regime.

The Mega Ampère Spherical Tokamak (MAST) programme is strongly focused on addressing key physics issues in preparation for operation of ITER as well as providing solutions for DEMO design choices. In this regard, MAST has provided key results in understanding and optimizing H-mode confinement, operating with smaller edge localized modes (ELMs), predicting and handling plasma exhaust and tailoring auxiliary current drive. In all cases, the high-resolution diagnostic capability on MAST is complemented by sophisticated numerical modelling to facilitate a deeper understanding. Mitigation of ELMs with resonant magnetic perturbations (RMPs) with toroidal mode number n RMP = 2, 3, 4, 6 has been demonstrated: at high and low collisionality; for the first ELM following the transition to high confinement operation; during the current ramp-up; and with rotating n RMP = 3 RMPs. n RMP = 4, 6 fields cause less rotation braking whilst the power to access H-mode is less with n RMP = 4 than n RMP = 3, 6. Refuelling with gas or pellets gives plasmas with mitigated ELMs and reduced peak heat flux at the same time as achieving good confinement. A synergy exists between pellet fuelling and RMPs, since mitigated ELMs remove fewer particles. Inter-ELM instabilities observed with Doppler backscattering are consistent with gyrokinetic simulations of micro-tearing modes in the pedestal. Meanwhile, ELM precursors have been strikingly observed with beam emission spectroscopy (BES) measurements. A scan in beta at the L–H transition shows that pedestal height scales strongly with core pressure. Gyro-Bohm normalized turbulent ion heat flux (as estimated from the BES data) is observed to decrease with increasing tilt of the turbulent eddies. Fast ion redistribution by energetic particle modes depends on density, and access to a quiescent domain with ‘classical’ fast ion transport is found above a critical density. Highly efficient electron Bernstein wave current drive (1 A W−1) has been achieved in solenoid-free start-up. A new proton detector has characterized escaping fusion products. Langmuir probes and a high-speed camera suggest filaments play a role in particle transport in the private flux region whilst coherence imaging has measured scrape-off layer (SOL) flows. BOUT++ simulations show that fluxes due to filaments are strongly dependent on resistivity and magnetic geometry of the SOL, with higher radial fluxes at higher resistivity. Finally, MAST Upgrade is due to begin operation in 2016 to support ITER preparation and importantly to operate with a Super-X divertor to test extended leg concepts for particle and power exhaust.

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.

A 3-D field line integration code, TRIP3D, has been modified to model stochastic magnetic perturbation produced by a resistive wall mode, error field (RWMEF) coil in the NSTX tokamak with very low aspect ratio. Multiple field lines with a uniform poloidal angle interval on each flux surface are automatically traced for the first time to follow the lines with large elongation plasmas. Each RWMEF coil can be configured to produce perturbation fields with dominant toroidal mode numbers of n = 1 or 3. In this study, it is found that the strongest stochastic layer is produced by the n = 3 configuration rather than n = 1 for the same coil current. Two NSTX divertor discharges, a lower single null and a double null have been modelled with different RWMEF-coil currents and toroidal modes. RWMEF currents of 2 kAt are sufficient to produce a strong stochastic field and significantly perturb the plasma boundary due to weak toroidal field in the spherical tokamak. The edge electron thermal diffusivity due to stochastic magnetic field is estimated to be 1 m 2 s −1 with a 2 kAt current, which is comparable to that in DIII-D with an 8 kAt C-coil current. Currents of this magnitude, when used in the DIII-D I-coil configured for n = 3 perturbations suppress large edge localized modes (ELMs) and thus may have an impact on ELMs in NSTX. The result has been verified by the initial experiments.

Systematic and statistical studies have been conducted in order to develop an understanding of the parametric dependences of both the global and thermal energy confinement times at low aspect ratio in high power National Spherical Torus Experiment discharges. The global and thermal confinement times of both L- and H-mode discharges can exceed values given by H-mode scalings developed for conventional aspect ratio. Results of systematic scans in the H-mode indicate that the confinement times exhibit a nearly linear dependence on plasma current and a power degradation weaker than that observed at conventional aspect ratio. In addition, the dependence on the toroidal magnetic field is stronger than that seen in conventional aspect ratio tokamaks. This latter trend is also evident in statistical analyses of the available dataset. These statistical studies also indicate a weaker parametric dependence on plasma current than found in the systematic scans, due to correlations among the predictor variables. Regressions based on engineering variables, when transformed to dimensionless physics variables, indicate that the dependence of BτE on βt can range from being negative to null. Regressions based directly on the dimensionless physics variables are inexact because of large correlations among these variables. Scatter in the confinement data, at otherwise fixed operating parameters, is found to be due to variations in ELM activity, low frequency density fluctuations and plasma shaping.

The National Spherical Torus Experiment (NSTX) has demonstrated the advantages of low aspect ratio geometry in accessing high toroidal and normalized plasma beta, and βN ≡ 10 8〈βt〉 aB0/Ip. Experiments have reached βt = 39% and βN = 7.2 through boundary and profile optimization. High βN plasmas can exceed the ideal no-wall stability limit, βNno-wall, for periods much greater than the wall eddy current decay time. Resistive wall mode (RWM) physics is studied to understand mode stabilization in these plasmas. The toroidal mode spectrum of unstable RWMs has been measured with mode number n up to 3. The critical rotation frequency of Bondeson-Chu, Ωcrit = ωA/(4q2), describes well the RWM stability of NSTX plasmas when applied over the entire rotation profile and in conjunction with the ideal stability criterion. Rotation damping and global rotation collapse observed in plasmas exceeding βNno-wall differs from the damping observed during tearing mode activity and can be described qualitatively by drag due to neoclassical toroidal viscosity in the helically perturbed field of an ideal displacement. Resonant field amplification of an applied n = 1 field perturbation has been measured and increases with increasing βN. Equilibria are reconstructed including measured ion and electron pressure, toroidal rotation and flux isotherm constraint in plasmas with core rotation ω/ωA up to 0.48. Peak pressure shifts of 18% of the minor radius from the magnetic axis have been reconstructed.

In order to reduce recirculating power fraction to acceptable levels, the spherical torus concept relies on the simultaneous achievement of high toroidal β and high bootstrap fraction in steady state. In the last year, as a result of plasma control system improvements, the achievable plasma elongation on NSTX has been raised from κ ∼ 2.1 to κ ∼ 2.6 - approximately a 25% increase. This increase in elongation has led to a substantial increase in the toroidal β for long pulse discharges. The increase in β is associated with an increase in plasma current at nearly fixed poloidal β, which enables higher βtwith nearly constant bootstrap fraction. As a result, for the first time in a spherical torus, a discharge with a plasma current of 1 MA has been sustained for 1 s (0.8 s current flat-top). Data are presented from NSTX correlating the increase in performance with increased plasma shaping capability. In addition to improved shaping, H-modes induced during the current ramp phase of the plasma discharge have been used to reduce flux consumption and to delay the onset of MHD instabilities. Based on these results, a modelled integrated scenario, which has 100% non-inductive current drive with very high toroidal β, will also be discussed. The NSTX poloidal field coils are currently being modified to produce the plasma shape which is required for this scenario, which requires high triangularity (δ ∼ 0.8) at elevated elongation (κ ∼ 2.5). The other main requirement of steady state on NSTX is the ability to drive a fraction of the total plasma current with RF waves. The results of high harmonic fast wave heating and current drive studies as well as electron Bernstein wave emission studies will be presented. © 2006 IAEA, Vienna.

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.

H-mode operation plays a crucial role in National Spherical Torus Experiment (NSTX) research, allowing higher beta limits due to reduced plasma pressure peaking, and long pulse operation due to high bootstrap current fraction. Here, new results are presented in the areas of edge localized modes (ELMs), H-mode pedestal physics and power threshold studies. ELMs of several types as reported by higher aspect ratio tokamaks have been observed: (1) large, Type I ELMs, (2) intermediate-sized Type III ELMs and (3) tiny ELMs. Many high performance discharges in NSTX have the tiny ELMs (recently termed Type V), which have some differences as compared with small-magnitude ELM types in the published literature. A divertor multifaceted axisymmetric radiation from the edge (MARFE) on the inboard leg provides an effective light source to examine the effect of the ELMs on the divertor plasma; it is clear that only the large ELMs burn through the MARFE. The time difference between observation of the ELM flux at the outer and inner targets is substantially longer for the smallest ELMs as compared with the large ELMs. In addition, the visible light patterns show 'finger-like' striations during the tiny ELMs. H-mode pedestal studies have commenced, with the observation that the pedestal contains between 25% and 33% of the total stored energy, and the NSTX pedestal energy agrees reasonably well with a recent international multi-machine scaling. A power threshold identity experiment between NSTX and the Mega-Amp Spherical Tokamak shows comparable loss power at the L?H transition in balanced double-null discharges. Both machines require more power for the L?H transition as the balance is shifted toward lower-single null. High-field side gas fuelling enables more reliable H-mode access in NSTX, but does not always lead to a lower power threshold, e.g. with a reduction of the duration of early heating.

The condition of the latest version of the ELMy H-mode database has been re-examined. It is shown that there is bias in the ordinary least squares regression for some of the variables. To address these shortcomings three different techniques are employed: (a) principal component regression, (b) an error in variables technique and (c) the selection of a better conditioned dataset with fewer variables. Scalings in terms of the dimensionless physics variables, as well as the standard set of engineering variables, are also derived. The new scalings give a very similar performance for existing scalings for ITER at the standard beta(n) of 1.6, but a much improved performance at higher beta n.

We report the observation of a high performance scenario in the National Spherical Torus Experiment with very small edge-localized modes (ELMs). These ELMs, individually, have no measurable impact on the stored energy and are observed by several diagnostics. The small ELMs have clear differences as compared with the ELM types reported in the literature, and this operating mode has distinct features compared with other high performance tokamak scenarios with little or no ELMs. The ELM is termed as 'type V', and it has a short-lived n = 1 magnetic precursor oscillation rotating counter to the plasma current and a distinct signature on the soft x-ray system. If we could extrapolate it, this scenario would provide an attractive operating regime for next step fusion experiments.

We report on the behavior of ELMs in NBI-heated H-mode plasmas in NSTX. It is observed that the size of Type I ELMs, characterized by the change in plasma energy, decreases with increasing line-average density, as observed at conventional aspect ratio. It is also observed that the Type I ELM size decreases as the plasma equilibrium is shifted from a symmetric double-null toward a lower single-null configuration. Type II/III ELMs have also been observed in NSTX, as well as a high-performance regime with small ELMs which we designate Type V. The Type V ELMs are characterized by an intermittent n = 1 magnetic pre-cursor oscillation rotating counter to the plasma current; the mode vanishes between Type V ELMs crashes. Without active pumping, the density rises continuously through the Type V phase, albeit at a slower rate than ELM-free discharges.

Power balance accountability was investigated for neutral beam heated plasmas in NSTX. Measurements of heat to the divertor strike plates and radiation in the divertor and the core were made as a function of heating power in lower single-null (LSN) and double-null (DN) configurations. Up to 70% of the net input power is accounted in the LSN discharges with ≈15–20% of power lost as fast ions, ≈25–35% incident on the divertor plates, ≈5% radiated in the core, and ≈5–10% radiated in the divertor. In DN discharges, the fast ion loss is comparable to LSN discharges, the core radiated power fraction is ≈10%, and the power deposited in the lower divertor as radiation and heat flux is ≈20–25% of the total. Assuming up/down symmetry, the power accountability in DN is ≈85–90%.

An overview of the research capabilities and the future plans on the MA-class National Spherical Torus Experiment (NSTX) at Princeton is presented. NSTX research is exploring the scientific benefits of modifying the field line structure from that in more conventional aspect ratio devices, such as the tokamak. The relevant scientific issues pursued on NSTX include energy confinement, MHD stability at high beta, non-inductive sustainment, solenoid-free start-up, and power and particle handling. In support of the NSTX research goal, research tools are being developed by the NSTX team. In the context of the fusion energy development path being formulated in the US, an ST-based Component Test Facility (CTF) and, ultimately a high beta Demo device based on the ST, are being considered. For these, it is essential to develop high performance (high beta and high confinement), steady-state (non-inductively driven) ST operational scenarios and an efficient solenoid-free start-up concept. We will also briefly describe the Next-Step-ST (NSST) device being designed to address these issues in fusion-relevant plasma conditions.

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...

An analysis of the international tokamak physics activity (ITPA) H-mode power threshold database is advanced to study the roles of the aspect ratio, A, the absolute magnetic field and the effective charge number, Z eff . A new scaling expression for the power threshold, P thr , is presented. The absolute B at the outer surface is used instead of B t in the scaling, and the I p dependence of Pair in low-A tokamaks is described without the explicit use of the Ip variable. A clear and strong dependence on Z eff is found; P thr Z 0.7 eff. Both the scattering nature in the data fitting and the 'low-density anomaly' can be reduced. A nonlinear A dependence is also suggested. The P thr in ITER is predicted on the basis of the present scaling.

A major research goal of the national spherical torus experiment is establishing long-pulse, high beta, high confinement operation and its physics basis. This research has been enabled by facility capabilities developed during 2001 and 2002, including neutral beam (up to 7?MW) and high harmonic fast wave (HHFW) heating (up to 6?MW), toroidal fields up to 6?kG, plasma currents up to 1.5?MA, flexible shape control, and wall preparation techniques. These capabilities have enabled the generation of plasmas with of up to 35%. Normalized beta values often exceed the no-wall limit, and studies suggest that passive wall mode stabilization enables this for H mode plasmas with broad pressure profiles. The viability of long, high bootstrap current fraction operations has been established for ELMing H mode plasmas with toroidal beta values in excess of 15% and sustained for several current relaxation times. Improvements in wall conditioning and fuelling are likely contributing to a reduction in H mode power thresholds. Electron thermal conduction is the dominant thermal loss channel in auxiliary heated plasmas examined thus far. HHFW effectively heats electrons, and its acceleration of fast beam ions has been observed. Evidence for HHFW current drive is obtained by comparision of the loop voltage evolution in plasmas with matched density and temperature profiles but varying phases of launched HHFW waves. Studies of emissions from electron Bernstein waves indicate a density scale length dependence of their transmission across the upper hybrid resonance near the plasma edge that is consistent with theoretical predictions. A peak heat flux to the divertor targets of 10?MW?m?2 has been measured in the H mode, with large asymmetries being observed in the power deposition between the inner and outer strike points. Non-inductive plasma startup studies have focused on coaxial helicity injection. With this technique, toroidal currents up to 400?kA have been driven, and studies to assess flux closure and coupling to other current drive techniques have begun.

Research on the spherical torus (or spherical tokamak) (ST) is being pursued to explore the scientific benefits of modifying the field line structure from that in more moderate aspect ratio devices, such as the conventional tokamak. The ST experiments are being conducted in various US research facilities including the MA-class National Spherical Torus Experiment (NSTX) at Princeton, and three medium sized ST research facilities: PEGASUS at University of Wisconsin, HIT-II at University of Washington, and CDX-U at Princeton. In the context of the fusion energy development path being formulated in the US, an ST-based Component Test Facility (CTF) and, ultimately a Demo device, are being discussed. For these, it is essential to develop high performance, steady-state operational scenarios. The relevant scientific issues are energy confinement, MHD stability at high beta (?), non-inductive sustainment, Ohmic-solenoid-free start-up, and power and particle handling. In the confinement area, the NSTX experiments have shown that the confinement can be up to 50% better than the ITER-98-pby2 H-mode scaling, consistent with the requirements for an ST-based CTF and Demo. In NSTX, CTF-relevant average toroidal beta values ?T of up to 35% with a near unity central ?T have been obtained. NSTX will be exploring advanced regimes where ?T up to 40% can be sustained through active stabilization of resistive wall modes. To date, the most successful technique for non-inductive sustainment in NSTX is the high beta poloidal regime, where discharges with a high non-inductive fraction (~60% bootstrap current+NBI current drive) were sustained over the resistive skin time. Research on radio-frequency (RF) based heating and current drive utilizing high harmonic fast wave and electron Bernstein wave is also pursued on NSTX, PEGASUS, and CDX-U. For non-inductive start-up, the coaxial helicity injection, developed in HIT/HIT-II, has been adopted on NSTX to test the method up to Ip ~ 500?kA. In parallel, start-up using a RF current drive and only external poloidal field coils are being developed on NSTX. The area of power and particle handling is expected to be challenging because of the higher power density expected in the ST relative to that in conventional aspect-ratio tokamaks. Due to its promise for power and particle handling, liquid lithium is being studied in CDX-U as a potential plasma-facing surface for a fusion reactor.

H-modes are routinely obtained in the National Spherical Torus Experiment (NSTX) and have become a standard operational scenario. L–H transitions triggered by NBI heating have been obtained over a wide parameter range in Ip, Bt, and e in either lower-single-null (LSN) or double-null (DN) diverted discharges. Edge localized modes are observed in both configurations but the characteristics differ between DN and LSN, which also have different triangularities (δ). An H-mode duration of 500 ms was obtained in LSN, with a total pulse length of ~1 s. Preliminary power threshold studies indicate that the L–H threshold is between 600 kW and 1.2 MW, depending on the target parameters. Gas injector fuelling from the centre stack (i.e. the high toroidal field side) has enabled routine H-mode access, and comparisons with low-field side (LFS) fuelled H-mode discharges show that the LFS fuelling delays the L–H transition and alters the pre-transition plasma profiles. Gas puff imaging and reflectometry show that the H-mode edge is usually more quiescent than the L-mode edge. Divertor infrared camera measurements indicate up to 70% of available power flows to the divertor targets in quiescent H-mode discharges.

Two different physical models of the H-mode pedestal are tested against the joint pedestal–core database. The first is a confinement model in which the transport down the steep edge gradient is assumed to be dominated by thermal conduction. The second model is a magnetohydrodynamics (MHD) limit model in which it is assumed that the dominant loss mechanism is by the edge localized modes (ELMs), the pressure gradient being determined by a MHD stability limit. These models are then combined with models for the core and shown to give a good fit to the ELMy H-mode database. The resulting two-term scaling expressions are shown to give very similar predictions for the confinement time, in the next step machines ITER and FIRE, to that of the one-term model IPB98(y,2). The predicted stored energy in the pedestal is 28–50% of the total stored energy.

New efficient methods are developed for the determination of the confined fraction of beam ions in standard and spherical tokamaks. The particle motion is described in the guiding center approximation and finite Larmor radius effects are included in the determination of the prompt orbit losses. A new code, CONBEAM, utilizes these methods and provides rapid evaluation of the beam confinement. Losses due to nonadiabatic changes in the magnetic moment are also evaluated. Due to the conservation of the canonical angular momentum, it is shown that changes in magnetic moment will not lead to a significant reduction in the confinement of co-injected beam ions.

New observations of sub-cyclotron frequency instability in low aspect ratio plasmas in national spherical torus experiments are reported. The frequencies of observed instabilities correlate with the characteristic Alfven velocity of the plasma. A theory of localized compressional Alfven eigenmodes (CAE) and global shear Alfven eigenmodes (GAE) in low aspect ratio plasmas is presented to explain the observed high frequency instabilities. CAEs/GAEs are driven by the velocity space gradient of energetic super-Alfvenic beam ions via Doppler shifted cyclotron resonances. One of the main damping mechanisms of GAEs, the continuum damping, is treated perturbatively within the framework of ideal MHD. Properties of these cyclotron instability ions are presented.

The National Spherical Torus Experiment (NSTX) at Princeton University, Princeton, NJ, is designed to assess the potential of the low-aspect-ratio spherical torus concept for magnetic plasma confinement. The plasma has been heated by up to 7 MW of neutral beam injection (NBI) at an injection energy of 100 keV and up to 6 MW of high harmonic fast wave (HHFW) at 30 MHz. NSTX has achieved /spl beta//sub T/ of 32%. A variety of MHD phenomena have been observed to limit /spl beta/. NSTX has now begun addressing /spl tau//sub E/ scaling, /spl beta/ limits, and current drive issues. During the NBI heating experiments, a broad T/sub i/ profile with T/sub i/ up to 2 keV, T/sub i/>T/sub e/ and a large toroidal rotation were observed. Transport analysis suggests that the impurity ions have diffusivities approaching neoclassical. For L-Mode plasmas, /spl tau//sub E/ is up to two times the ITER97L L-Mode scaling and exceeds the ITER98pby2 H-Mode scaling in some cases. Transitions to H-Mode have been observed which result in an approximate doubling of /spl tau//sub E/ after the transition in some conditions. During HHFW heating, T/sub e/>T/sub i/ and T/sub e/ up to 3.5 keV were observed. Current drive has been studied using both coaxial helicity injection with up to 390 kA of toroidal current and HHFW. HHFW has produced H-modes with significant bootstrap current fraction at low I/sub p/, high q, and high /spl beta//sub p/.

Recent observations of instabilities in MHz frequency range in the National Spherical Torus experiments (NSTX) and their analysis are reported. The instability frequency is correlated with the characteristic Alfven velocity of the plasma, vA. The observed instabilities are explained as compressional Alfven eigenmodes (CAEs) driven by energetic beam ions. Based on a localized CAE solution, mode frequencies are essentially the compressional Alfven frequency at the mode location and are given by ωCAE = vAm/r, where m is the poloidal mode number, and r is the minor radius. Energetic ions that are in Doppler shifted cyclotron resonance with CAEs provide free energy to destabilize CAEs. Properties of CAE instability driven by different neutral-beam injection ion distributions are presented.

The dynamic evolution of the first National Spherical Torus Experiment (NSTX) H-modes will be discussed. The H-modes were obtained in lower-single null divertor discharges with various forms of plasma heating. The exact timing of divertor formation and also the NBI power level affects both whether or not the discharge exhibits ELMs and the duration of the ELM-free phase. ELM-free discharges had energy confinement as high as 120 ms, whereas the few discharges with ELMs had confinement times ∼50-70 ms. Buildup of a steep edge density gradient and formation of ears' on the density profile were observed within a few ms of the L-H transition, yielding broader density and pressure profiles. The L-H transition was marked by a decrease in edge visible light and simultaneous increase in electron Bernstein wave emission, reflecting a steepening of the edge density gradient. Gas puff imaging of He-i light during the H-mode phase showed rapid formation of a narrow emission layer ∼2 cm wide in the H-mqde phase, which returned within 20 microseconds at termination of the H-mode phase to a broader turbulent emission layer. All of the H-modes were terminated by an MHD reconnection event. The first power threshold (P th ) study showed the neutral beam injection power (P b ) component of P th to be ≤0.84 MW, higher than that predicted by the ITER database scaling.

High $$\beta$$ plasma response to the rotating n=1 external magnetic perturbations is numerically studied and compared with National Spherical Torus eXperiment (NSTX). The hybrid magnetohydrodynamic(MHD)-kinetic modeling shows the drift kinetic effects are important to resolve the disagreement of plasma response between the ideal MHD prediction and the NSTX experimental observation when plasma pressure reaches and exceeds the no-wall limit [F. Troyon et al., Plasma Phys. Control. Fusion 26, 209 (1984)]. Thus, since the external rotating fields and high plasma rotation are presented in NSTX experiments, the importance of resistive wall effect and plasma rotation on determining the plasma response is also identified, where the resistive wall suppresses the plasma response through the wall eddy current. The inertial energy, due to plasma rotation, destabilizes the plasma. Finally, the complexity of plasma response, in this study, indicates that MHD modeling, including comprehensive physics e.g. the drift kinetic effects, resistive wall and plasma rotation, is essential to reliably predict the plasma behavior in high beta spherical tokamak device.

This paper presents for the first time a statistical validation of predictive TRANSP simulations of plasma temperature using two transport models, GLF23 and TGLF, over a database of 80 baseline H-m ...

The main aim of the National Spherical Torus Experiment (NSTX) is to establish the fusion physics principles of the spherical torus (ST) concept. The NSTX device began plasma operations in February 1999 and the plasma current Ip was successfully brought up to the design value of 1 MA on 14 December 1999. The planned plasma shaping parameters, elongation κ = 1.6-2.2 and triangularity δ = 0.2-0.4, were achieved in inner wall limited, and single null and double null diverted configurations. The coaxial helicity injection (CHI) and high harmonic fast wave (HHFW) experiments were also initiated. CHI current of 27 kA produced up to 260 kA toroidal current without using an ohmic solenoid. With the injection of 2.3 MW of HHFW power, using 12 antennas connected to six transmitters, electrons were heated from a central temperature of 400 eV to 900 eV at a central density of 3.5 × 1013 cm-3, increasing the plasma energy to 59 kJ and the toroidal β, βT, to 10%. The NBI system commenced operation in September 2000. The initial results with two ion sources (PNBI = 2.8 MW) show good heating, producing a total plasma stored energy of 90 kJ corresponding to βT ≈ 18% at a plasma current of 1.1 MA.

The national spherical torus experiment (NSTX) started plasma operations in February 1999. In the first extended period of experiments, NSTX achieved high current, inner wall limited, double null, and single null plasma discharges, initial Coaxial Helicity Injection, and high harmonic fast wave results. As expected, discharge reproducibility and performance were strongly affected by wall conditions. In this paper, we describe the internal geometry, and initial plasma discharge, impurity control, wall conditioning, erosion, and deposition results.

The five ARIES designs, which correspond to five different tokamak operating modes, are reviewed and compared. Physics figures of merit are introduced that quantify the major parameters of a tokamak design in a physics operating space. The five operating modes are compared to one another and to the existing tokamak data base in terms of these physics parameters. While the steady-state first stability design [ARIES-I] and the pulsed first stability design [PULSAR] are closest, no design has yet been completely prototyped in existing tokamaks.

The scientific parameters and the technology issues for a modest size spherical torus (ST) at 10 MA plasma current are discussed. This class of devices includes a DT-capable ST experiment (DTST, R0 = 1.2 m) for extended plasma performance tests for limited pulse lengths and neutron fluences, and a volume neutron source (VNS, R0 = 1.1 m) for steady state energy technology testing to high neutron fluences. The scientific issues of interest for DTST include non-inductive ramp-up of plasma current on a limited timescale (~30 s), the confinement needed for high Q burn, the behaviour of energetic particles, the physics and techniques to handle intense plasma exhaust, and the possibility of high performance plasma regimes free of disruptions or large disruption impact. Of further interest for the VNS would be steady state operation using large external current drive, possibly at a modest Q (~1-2), achieving significant neutron wall loading (~1 MW/m2) and a configuration relatively amenable to remote maintenance. A much longer timescale would be permitted in a VNS for non-inductive current ramp-up. The centre leg of the toroidal field coils, possibly multiturn for DTST and necessarily single turn for a VNS without significant nuclear shielding, presents technical and material issues of unique importance to the ST. Positive ion neutral beam injection and high harmonic fast wave (~80 MHz) heating and current drive systems already available are likely to be adequate for DTST following pulse length extension to ~50 s. Given an adequate physics database, the remaining enabling technologies needed for the VNS appear largely similar in nature to those of the ITER EDA design.

The mission of the National Spherical Torus Experiment (NSTX) is to prove the principles of spherical torus physics by producing high-beta toroidal plasmas that are non-inductively sustained, and whose current profiles are in steady-state. NSTX will be one of the first ultra low a[P(input) up to 11 MW] in order to produce high-beta toroidal (25 to 40%), low collisionality, high bootstrap fraction (less than or equal to 70%) discharges. Both radio-frequency (RF) and neutral-beam (NB) heating and current drive will be employed. Built into NSTX is sufficient configurational flexibility to study a range of operating space and the resulting dependences of the confinement, micro- and MHD stability, and particle and power handling properties. NSTX research will be carried out by a nationally based science team.

This special topic describes the contents of an L mode database that has been compiled with data from Alcator C-Mod, ASDEX, DIII, DIII-D, FTU, JET, JFT-2M, JT-60, PBX-M, PDX, T-10, TEXTOR, TFTR and Tore Supra. The database consists of a total of 2938 entries, 1881 of which are in the L phase while 922 are ohmically heated only (ohmic). Each entry contains up to 95 descriptive parameters, including global and kinetic information, machine conditioning and configuration. The special topic presents a description of the database and the variables contained therein, and it also presents global and thermal scalings along with predictions for ITER. The L mode thermal confinement time scaling, determined from a subset of 1312 entries for which the τE,th are provided, is τE,th = 0.023Ip0.96BT0.03R1.83(R/a)0.06 κ0.64ne0.40Meff0.20P-0.73 in units of seconds, megamps, teslas, metres, -, -, 10-9 m-1

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.

The ITER H-mode threshold database, which currently includes data from nine divertor tokamaks is presented. The results obtained for single devices and for the combined data set are given. The similarities and differences between the different devices are shown. Possible expressions for the H-mode threshold in agreement with the data are given and the extrapolation to ITER is discussed.

Experimental and theoretical results from around the world point to the possibility of high confinement, high- beta , and high-bootstrap-fraction steady-state tokamak operating modes. These modes of operation, if fully developed and extended to steady-state, could lead to much less expensive tokamak demonstration power reactors and to a significantly reduced cost-of-electricity from fusion, as compared to projections based on low- beta N, pulsed operating modes. Present results have clear implications in the areas of particle control, plasma shaping, and current-profile control. Thus they have strongly influenced the design of the steady-state advanced tokamak TPX, which has the mission to combine the best results from present experiments and extend them to steady-state. These results also have important implications for follow-up tests in ITER, which have the goal of studying advanced-tokamak operation in an ignited plasma, as well as for the eventual configuration of an advanced-tokamak fusion reactor.

The ITER-EDA(93) design has been analyzed to evaluate the physics basis for: (i) size and design trade-off issues, (ii) confinement capability, (iii) power levels, and (iv) burn control.

This paper describes an update of the H mode confinement database that has been assembled for the ITER project. Data were collected from six machines of different sizes and shapes: ASDEX, DIII-D, JET, JFT-2M, PBX-M and PDX. The updated database contains better estimates of fast ion energy content and thermal energy confinement times, discharges with RF heating, data using boronization, beryllium and pellets, more systematic parameter scans, and other features. The list of variables in the database has been expanded, and the selection criteria for the standard dataset have been modified. We also present simple scalings of the total and thermal energy confinement time to the new dataset

The spherical tokamak (ST) is a leading candidate for a fusion nuclear science facility (FNSF) due to its compact size and modular configuration. The National Spherical Torus eXperiment (NSTX) is a MA-class ST facility in the U.S. actively developing the physics basis for an ST-based FNSF. In plasma transport research, ST experiments exhibit a strong (nearly inverse) scaling of normalized confinement with collisionality, and if this trend holds at low collisionality, high fusion neutron fluences could be achievable in very compact ST devices. A major motivation for the NSTX Upgrade (NSTX-U) is to span the next factor of 3–6 reduction in collisionality. To achieve this collisionality reduction with equilibrated profiles, NSTX-U will double the toroidal field, plasma current, and NBI heating power and increase the pulse length from 1–1.5s to 5s. In the area of stability and advanced scenarios, plasmas with higher aspect ratio and elongation, high β N , and broad current profiles approaching those of an ST-based FNSF have been produced in NSTX using active control of the plasma β and advanced resistive wall mode control. High non-inductive current fractions of 70% have been sustained for many current diffusion times, and the more tangential injection of the 2nd NBI of the Upgrade is projected to increase the NBI current drive by up to a factor of 2 and support 100% non-inductive operation. More tangential NBI injection is also projected to provide non-solenoidal current ramp-up (from I P = 0.4MA up to 0.8–1MA) as needed for an ST-based FNSF. In boundary physics, NSTX and higher-A tokamaks measure an inverse relationship between the scrape-off layer heat-flux width and plasma current that could unfavorably impact next-step devices. Recently, NSTX has successfully demonstrated very high flux expansion and substantial heat-flux reduction using a snowflake divertor configuration, and this type of divertor is incorporated in the NSTX-U design. The physics and engineering design supporting NSTX Upgrade are described.

Determination of the profiles of the ion temperature and the plasma toroidal rotation has been accomplished by charge exchange recombination spectroscopy in PBX-M. The angular momentum and the thermal ion energy transport have been studied mainly during the H mode phase of a high βp discharge (Ip ≈ 330 kA, 3.5 × 1019 ≤ ne ≤ 6.5 × 1019 m-3) having different heating beam configurations (combination of two perpendicular and two tangential neutral beam injections, abbreviated as 2 perp. NBI and 2 parall. NBI). The toroidal rotation velocity V rises substantially in the region of r/a ≥ 0.5 after the L-H transition, and the V profile (peakedness) is more highly dependent on the beam configuration than the Ti profile. The angular momentum confinement time varies from 147 ms (rigid rotation for 2 perp. NBI) to 39 ms (viscous rotation for 2 parall. NBI). In contrast, the thermal energy confinement time is 44-48 ms and is almost independent of the configuration. The transport analysis shows that the radial angular momentum diffusion is caused mainly by the viscous losses and that the angular momentum diffusivity χ is reduced substantially in the outer minor radius region during the 2 perp. NBI H mode. The neoclassical friction effect between the bulk ions and the impurities may influence the χ profiles locally, where the ion temperature gradient is steep