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We use the 3D magnetohydrodynamic (MHD) code M3D-C1 [Jardin et al., Comput. Sci. Discovery 5, 014002 (2012)] to examine the MHD stability and subsequent evolution of NSTX shot 129169. This discharge had a period with a non-monotonic safety factor profile, q (reversed shear), which was terminated by a MHD event that abruptly lowered the central safety factor, q0, and greatly reduced the peakedness of the pressure profile. We show that the equilibrium just before the MHD event occurred was linearly unstable to many pressure-driven infernal modes. Modes with toroidal mode number n ≥ 3 all had rational surfaces very close to the minimum value of q. However, a non-resonant pressure-driven (1, 1) mode was also present, and this dominated the nonlinear evolution. The final state in the simulation, after the MHD activity subsided, had a reduced and flattened pressure profile and a nearly monotonic q-profile, in qualitative agreement with experimental results. The initial state was also unstable to the resistive interchange criteria in the reversed-shear region, but the final state was stable everywhere. The "double tearing mode" (DTM) does not appear to play a role in the MHD activity of this discharge. In Appendix A, we show that in a torus, the DTM is strongly stabilized by pressure, but it is destabilized in cylindrical geometry (which has been the most extensively analyzed in the literature). [ABSTRACT FROM AUTHOR]

We use a new gyrokinetic threshold model to predict a bifurcation in tokamak pedestal width-height scalings that depends strongly on plasma shaping and aspect-ratio. The bifurcation arises from the first and second stability properties of kinetic-ballooning-modes that yields wide and narrow pedestal branches, expanding the space of accessible pedestal widths and heights. The wide branch offers potential for edge-localized-mode-free pedestals with high core pressure. For negative triangularity, low-aspect-ratio configurations are predicted to give steeper pedestals than conventional-aspect-ratio. Both wide and narrow branches have been attained in tokamak experiments. [ABSTRACT FROM AUTHOR]

This paper extends the analysis first presented in Jardin et al. [Phys. Rev. Lett. 128, 245001 (2022)] to more thoroughly examine the stability of spherical torus equilibrium to ideal magnetohydrodynamic (MHD) infernal modes and their nonlinear consequences. We demonstrate that in a 3D resistive magnetohydrodynamic (MHD) simulation of a NSTX discharge, anomalous transport can occur due to these instabilities. We generate a family of equilibrium of differing β and use this to show that these instabilities could explain the experimentally observed flattening of the electron temperature profile at modest β. The modes studied in this paper are found to occur with poloidal mode number m and toroidal mode number n when the ratio m/n is in the range of 1.2–1.5, when the central safety factor is in this range or slightly lower, and when the central region has very low magnetic shear. Our analysis gives some insight as to why the unstable linear growth rates are oscillatory functions of the toroidal mode number n. We present a simulation of an initially stable configuration that passes through a stability boundary at a critical β as it is heated. We also show that a particular NSTX discharge is unstable to these modes over a timescale of several hundred ms. We conclude that these modes must be taken into account when performing predictive modeling. An appendix shows that similar modes can be found in R / a = 4 tokamaks for certain q-profiles and β values. [ABSTRACT FROM AUTHOR]

A new model for electron temperature gradient (ETG) modes is developed as a component of the multi-mode anomalous transport module [Rafiq et al., Phys Plasmas 20, 032506 (2013)] to predict a time-dependent electron temperature profile in conventional and low aspect ratio tokamaks. This model is based on two-fluid equations that govern the dynamics of low-frequency short- and long-wavelength electromagnetic toroidal ETG driven drift modes. A low collisionality NSTX discharge is used to scan the plasma parameter dependence on the ETG real frequency, growth rate, and electron thermal diffusivity. Electron thermal transport is discovered in the deep core region where modes are more electromagnetic in nature. Several previously reported gyrokinetic trends are reproduced, including the dependencies of density gradients, magnetic shear, β and gradient of β (β ′) , collisionality, safety factor, and toroidicity, where β is the ratio of the plasma pressure to the magnetic pressure. The electron heat diffusivity associated with the ETG mode is discovered to be on a scale consistent with the experimental diffusivity determined by power balance analysis. [ABSTRACT FROM AUTHOR]

Experimental results from the National Spherical Torus Experiment (NSTX), a medium-size spherical tokamak with a compact divertor, and DIII-D, a large conventional aspect ratio tokamak, demonstrate that the snowflake (SF) divertor configuration may provide a promising solution for mitigating divertor heat loads and target plate erosion compatible with core H-mode confinement in the future fusion devices, where the standard radiative divertor solution may be inadequate. In NSTX, where the initial high-power SF experiment was performed, the SF divertor was compatible with H-mode confinement, and led to the destabilization of large Edge Localized Modes (ELMs). However, a stable partial detachment of the outer strike point was also achieved where inter-ELM peak heat flux was reduced by factors 3–5, and peak ELM heat flux was reduced by up to 80% (see standard divertor). The DIII-D studies show the SF divertor enables significant power spreading in attached and radiative divertor conditions. Results include: compatibility with the core and pedestal, peak inter-ELM divertor heat flux reduction due to geometry at lower ne , and ELM energy and divertor peak heat flux reduction, especially prominent in radiative D2 -seeded SF divertor, and nearly complete power detachment and broader radiated power distribution in the radiative D2 -seeded SF divertor at P\text {SOL}=3-4 MW. A variety of SF configurations can be supported by the divertor coil set in NSTX Upgrade. Edge transport modeling with the multifluid edge transport code UEDGE shows that the radiative SF divertor can successfully reduce peak divertor heat flux for the projected P\text {SOL} \simeq 9 MW case. The radiative SF divertor with carbon impurity provides a wider ne operating window, 50% less argon is needed in the impurity-seeded SF configuration to achieve similar q\text {peak} reduction factors (see standard divertor). [ABSTRACT FROM AUTHOR]

This paper presents quasi-linear gyrokinetic predictions of the Coriolis momentum pinch for low aspect-ratio National Spherical Torus Experiment (NSTX) H-modes where previous experimental measurements were focused. Local, linear calculations predict that in the region of interest (just outside the mid-radius) of these relatively high-beta plasmas, profiles are most unstable to microtearing modes that are only effective in transporting electron energy. However, sub-dominant electromagnetic and electrostatic ballooning modes are also unstable, which are effective at transporting energy, particles, and momentum. The quasi-linear prediction of transport from these weaker ballooning modes, assuming they contribute transport in addition to that from microtearing modes in a nonlinear turbulent state, leads to a very small or outward convection of momentum, inconsistent with the experimentally measured inward pinch, and opposite to predictions in conventional aspect ratio tokamaks. Additional predictions of a low beta L-mode plasma, unstable to more traditional electrostatic ion temperature gradient-trapped electron mode instability, show that the Coriolis pinch is inward but remains relatively weak and insensitive to many parameter variations. The weak or outward pinch predicted in NSTX plasmas appears to be at least partially correlated to changes in the parallel mode structure that occur at a finite beta and low aspect ratio, as discussed in previous theories. The only conditions identified where a stronger inward pinch is predicted occur either in the purely electrostatic limit or if the aspect ratio is increased. As the Coriolis pinch cannot explain the measured momentum pinch, additional theoretical momentum transport mechanisms are discussed that may be potentially important. [ABSTRACT FROM AUTHOR]

Highly distinct features of spherical tokamaks (ST), such as National Spherical Torus eXperiment (NSTX) and NSTX-U, result in a different fusion plasma regime with unique physics properties compared to conventional tokamaks. Nonlinear global gyrokinetic simulations critical for addressing turbulence and transport physics in the ST regime have led to new insights. The drift wave Kelvin-Helmholtz (KH) instability characterized by intrinsic mode asymmetry is identified in strongly rotating NSTX L-mode plasmas. While the strong E B shear associated with the rotation leads to a reduction in KH/ion temperature gradient turbulence, the remaining fluctuations can produce a significant ion thermal transport that is comparable to the experimental level in the outer core region (with no "transport shortfall"). The other new, important turbulence source identified in NSTX is the dissipative trapped electron mode (DTEM), which is believed to play little role in conventional tokamak regime. Due to the high fraction of trapped electrons, long wavelength DTEMs peaking around kθρs ~ 0.1 are destabilized in NSTX collisionality regime by electron density and temperature gradients achieved there. Surprisingly, the E B shear stabilization effect on DTEM is remarkably weak, which makes it a major turbulence source in the ST regime dominant over collisionless TEM (CTEM). The latter, on the other hand, is subject to strong collisional and E × B shear suppression in NSTX. DTEM is shown to produce significant particle, energy and toroidal momentum transport, in agreement with experimental levels in NSTX H-modes. Moreover, DTEM-driven transport in NSTX parametric regime is found to increase with electron collision frequency, providing one possible source for the scaling of confinement time observed in NSTX H-modes. Most interestingly, the existence of a turbulence-free regime in the collision-induced CTEM to DTEM transition, corresponding to a minimum plasma transport in advanced ST collisionality regime, is predicted. [ABSTRACT FROM AUTHOR]

Microturbulence is considered to be a major candidate in driving anomalous transport in fusion plasmas, and the equilibrium E x B shear generated by externally driven flow can be a powerful tool to control microturbulence in future fusion devices such as FNSF and ITER. Here we present the first observation of the change in electron-scale turbulence wavenumber spectrum (measured by a high-£ scattering system) and thermal transport responding to continuous E x B shear ramp-up in an NSTX centre-stack limited and neutral beam injection-heated L-mode plasma. It is found that while linear stability analysis shows that the maximum electron temperature gradient mode linear growth rate far exceeds the observed E x B shearing rate in the measurement region of the high-k scattering system, the unstable ion temperature gradient (ITG) modes are susceptible to E x B shear stabilization. We observed that as the E x B shearing rate is continuously ramped up in the high-k measurement region, the ratio between the E x B shearing rate and maximum ITG mode growth rate continuously increases (from about 0.2 to 0.7) and the maximum power of the measured electron-scale turbulence wavenumber spectra decreases. Meanwhile, electron and ion thermal transport is also reduced in the outer half of the plasmas as long as magnetohydrodynamic activities are not important and the L-mode plasmas eventually reach H-mode-like confinement. Linear and nonlinear gyrokinetic simulations are presented to address the experimental observations. [ABSTRACT FROM AUTHOR]

Understanding the dependence of confinement on collisionality in tokamaks is important for the design of next-step devices, which will operate at collisionalities at least one order of magnitude lower than in the present generation. A wide range of collisionality has been obtained in the National Spherical Torus Experiment (NSTX) by employing two different wall conditioning techniques, one with boronization and between-shot helium glow discharge conditioning (HeGDC+B), and one using lithium evaporation (Li EVAP). Previous studies of HeGDC+B plasmas indicated a strong increase of normalized confinement with decreasing collisionality. Discharges with lithium conditioning discussed in the present study generally achieved lower collisionality, extending the accessible range of collisionality by a factor of two. While the confinement dependences on dimensional, engineering variables of the HeGDC+B and Li EVAP datasets differed, collisionality was found to unify the trends, with the lower collisionality lithium conditioned discharges extending the trend of increasing normalized confinement time, BT TE, with decreasing collisionality when other dimensionless variables were held as fixed as possible. This increase of confinement with decreasing collisionality was driven by a large reduction in electron transport in the outer region of the plasma. This result is consistent with gyrokinetic calculations that show microtearing and electron temperature gradient (ETG) modes to be more stable for the lower collisionality discharges. Ion transport, near neoclassical at high collisionality, became more anomalous at lower collisionality, possibly due to the growth of hybrid TEM/KBM modes in the outer regions of the plasma. [ABSTRACT FROM AUTHOR]

A database of toroidal momentum transport on five tokamaks, Alcator C-Mod, DIII-D, JET, NSTX and JT-60U, has been constructed under a wide range of conditions in order to understand the characteristics of toroidal momentum transport coefficients, namely the toroidal momentum diffusivity (χɸ) and the pinch velocity (Vpinch). Through an inter-machine comparison, the similarities and differences in the properties of χɸ and Vpinch among the machines have been clarified. Parametric dependences of these momentum transport coefficients have been investigated over a wide range of plasma parameters taking advantage of the different operation regimes in machines. The approach offers insights into the parametric dependences as follows. The toroidal momentum diffusivity (χɸ) generally increases with increasing heat diffusivity (χi). The correlation is observed over a wide range of χɸ, covering roughly two orders of magnitude, and within each of the machines over the whole radius. Through the inter-machine comparison, it is found that χɸ becomes larger in the outer region of the plasma. Also observed is a general trend for Vpinch in tokamaks; the inward pinch velocity (-Vpinch) increases with increasing χɸ. The results that are commonly observed in machines will support a toroidal rotation prediction in future devices. On the other hand, differences among machines have been observed. The toroidal momentum diffusivity, χɸ, is larger than or equal to χi in JET and JT-60U; on the other hand, χɸ is smaller than or equal to χi in NSTX, DIII-D and Alcator C-Mod. In DIII-D, the ratio -RVpinch/χɸ at r/a = 0.5-0.6 is about 2, which is small compared with that in other tokamaks (-RVpinch/χɸ ≈ 5). Based on these different observations, parametric dependences of χɸ/χi, RVpinch/χɸ and χɸ have been investigated in H-mode plasmas. Across the dataset from all machines, the ratio χɸ/χi tends to be larger in low . νe* at fixed Te/Ti and ρpol*. An increase in χɸ is observed with decreasing ne and/or increasing Te. The pinch number (-RVpinch/χɸ) is observed to increase with increasing R/Lne at both q95 = 5.5-7.2 and q95 = 3.7-4.5. Here νe*, ρpol*, Te, Ti, R/Lne and q95 are, respectively, the normalized effective electron collision frequency, the normalized ion poloidal Larmor radius, the electron and ion temperatures, the inverse ratio of density scale length, Lne, to the major radius, R, and the safety factor at the 95% flux surface. [ABSTRACT FROM AUTHOR]

Experimental results from NSTX indicate that the snowflake divertor (D. Ryutov, Phys. Plasmas 14, 064502 (2007)) may be a viable solution for outstanding tokamak plasma-material interface issues. Steady-state handling of divertor heat flux and divertor plate erosion remains to be critical issues for ITER and future concept devices based on conventional and spherical tokamak geometry with high power density divertors. Experiments conducted in 4-6 MW NBI-heated H-mode plasmas in NSTX demonstrated that the snowflake divertor is compatible with high-confinement core plasma operation, while being very effective in steady-state divertor heat flux mitigation and impurity reduction. A steady-state snowflake divertor was obtained in recent NSTX experiments for up to 600 ms using three divertor magnetic coils. The high magnetic flux expansion region of the scrape-off layer (SOL) spanning up to 50% of the SOL width λq was partially detached in the snowflake divertor. In the detached zone, the heat flux profile flattened and decreased to 0.5-1 MW/m2 (from 4-7 MW/m2 in the standard divertor) indicative of radiative heating. An up to 50% increase in divertor, Prad in the snowflake divertor was accompanied by broadening of the intrinsic C III and C IV radiation zones, and a nearly order of magnitude increase in divertor high-n Balmer line emission indicative of volumetric recombination onset. Magnetic reconstructions showed that the x-point connection length, divertor plasma-wetted area and divertor volume, all critical parameters for geometric reduction of deposited heat flux, and increased volumetric divertor losses were significantly increased in the snowflake divertor, as expected from theory. [ABSTRACT FROM AUTHOR]

Electron-scale turbulence is predicted to drive anomalous electron thermal transport. However, experimental study of its relation with transport is still in its early stage. On the National Spherical Tokamak Experiment (NSTX), electron-scale density fluctuations are studied with a novel tangential microwave scattering system with high radial resolution of ±2 cm. Here, we report a study of parametric dependence of electron-scale turbulence in NSTX H-mode plasmas. The dependence on density gradient is studied through the observation of a large density gradient variation in the core induced by an edge localized mode (ELM) event, where we found the first clear experimental evidence of density gradient stabilization of electron-gyro scale turbulence in a fusion plasma. This observation, coupled with linear gyro-kinetic calculations, leads to the identification of the observed instability as toroidal electron temperature gradient (ETG) modes. It is observed that longer wavelength ETG modes, k⊥ρs<=10 (ρs is the ion gyroradius at electron temperature and k⊥ is the wavenumber perpendicular to local equilibrium magnetic field), are most stabilized by density gradient, and the stabilization is accompanied by about a factor of two decrease in electron thermal diffusivity. Comparisons with nonlinear ETG gyrokinetic simulations show ETG turbulence may be able to explain the experimental electron heat flux observed before the ELM event. The collisionality dependence of electron-scale turbulence is also studied by systematically varying plasma current and toroidal field, so that electron gyroradius (ρe), electron beta (βe), and safety factor (q95) are kept approximately constant. More than a factor of two change in electron collisionality, νe*, was achieved, and we found that the spectral power of electron-scale turbulence appears to increase as νe* is decreased in this collisonality scan. However, both linear and nonlinear simulations show no or weak dependence with the electron-ion collision frequency, νe/i. Instead, other equilibrium parameters (safety factor, electron density gradient, for example) affect ETG linear growth rate and electron thermal transport more than νe/i does. Furthermore, electron heat flux predicted by the simulations is found to have an order-of-magnitude spatial variation in the experimental measurement region and is also found to be much smaller than experimental levels except at one radial location we evaluated. The predicted electron heat flux is shown to be strongly anti-correlated with density gradient, which varies for a factor of three in the measurement region, which is in agreement with the density gradient dependence study reported in this paper. [ABSTRACT FROM AUTHOR]

The National Spherical Torus Experiment (NSTX) [M. Ono et al., Nucl. Fusion 40, 557 (2000)] can achieve high electron plasma confinement regimes that are super-critically unstable to the electron temperature gradient driven (ETG) instability. These plasmas, dubbed electron internal transport barriers (e-ITBs), occur when the magnetic shear becomes strongly negative. Using the gyrokinetic code GYRO [J. Candy and R. E. Waltz, J. Comput. Phys. 186, 545 (2003)], the first nonlinear ETG simulations of NSTX e-ITB plasmas reinforce this observation. Local simulations identify a strongly upshifted nonlinear critical gradient for thermal transport that depends on magnetic shear. Global simulations show e-ITB formation can occur when the magnetic shear becomes strongly negative. While the ETG-driven thermal flux at the outer edge of the barrier is large enough to be experimentally relevant, the turbulence cannot propagate past the barrier into the plasma interior. [ABSTRACT FROM AUTHOR]

Thermal energy confinement times in National Spherical Torus Experiment (NSTX) dimensionless parameter scans increase with decreasing collisionality. While ion thermal transport is neoclassical, the source of anomalous electron thermal transport in these discharges remains unclear, leading to considerable uncertainty when extrapolating to future spherical tokamak (ST) devices at much lower collisionality. Linear gyrokinetic simulations find microtearing modes to be unstable in high collisionality discharges. First non-linear gyrokinetic simulations of microtearing turbulence in NSTX show they can yield experimental levels of transport. Magnetic flutter is responsible for almost all the transport (∼98%), perturbed field line trajectories are globally stochastic, and a test particle stochastic transport model agrees to within 25% of the simulated transport. Most significantly, microtearing transport is predicted to increase with electron collisionality, consistent with the observed NSTX confinement scaling. While this suggests microtearing modes may be the source of electron thermal transport, the predictions are also very sensitive to electron temperature gradient, indicating the scaling of the instability threshold is important. In addition, microtearing turbulence is susceptible to suppression via sheared E × B flows as experimental values of E × B shear (comparable to the linear growth rates) dramatically reduce the transport below experimental values. Refinements in numerical resolution and physics model assumptions are expected to minimize the apparent discrepancy. In cases where the predicted transport is strong, calculations suggest that a proposed polarimetry diagnostic may be sensitive to the magnetic perturbations associated with the unique structure of microtearing turbulence. [ABSTRACT FROM AUTHOR]

Recent experiments on DIII-D [J. L. Luxon, Nucl. Fusion 42, 614 (2002)] and National Spherical Torus Experiment (NSTX) [M. Ono et al., Nucl. Fusion 40, 557 (2000)] have focused on investigating mechanisms of driving rotation in fusion plasmas. The so-called intrinsic rotation is generated by an effective torque, driven by residual stresses in the plasma, which appears to originate in the plasma edge. A clear scaling of this intrinsic drive with the H-mode pressure gradient is observed. Coupled with the experimentally inferred pinch of angular momentum, such an edge source is capable of producing sheared rotation profiles. Intrinsic drive is also possible directly in the core, although the physics mechanisms are much more complex. Another option which is being explored is the use of nonresonant magnetic fields for spinning the plasma. It is found beneficially that the torque from these fields can be enhanced at low rotation, which assists in spinning the plasma from rest, and offers increased resistance against plasma slowing. [ABSTRACT FROM AUTHOR]

The first successful quantitative account of the electron thermal conductivity χe in a tokamak experiment due to imperfect magnetic surfaces is presented. The unstable spectrum of microtearing instabilities is calculated with the GS2 code for a well-behaved H-mode plasma in the National Spherical Tokamak Experiment [M. Ono et al., Nucl. Fusion 40, 557 (2000)], with 6 MW deuterium neutral beam heating at Ip=0.75 MA, Bt=0.5 T. The application of existing nonlinear theory shows that the unstable modes can produce overlapping magnetic islands leading to global stochastic magnetic fields. The calculated χe based on the present theory is in reasonable agreement with the values from transport analysis of the experimental data over the entire region (0.4

There has been a substantial international research effort in the fusion community to identify tokamak operating regimes with either small or no periodic bursts of particles and power from the edge plasma, known as edge-localized modes (ELMs). While several candidate regimes have been presented in the literature, very little has been published on the characteristics of the small ELMs themselves. One such small ELM regime, also known as the Type V ELM regime, was recently identified in the National Spherical Torus Experiment [M. Ono, S. M. Kaye, Y.-K. M. Peng et al., Nucl. Fusion 40, 557 (2000)]. In this paper, the spatial and temporal structure of the Type V ELMs is presented, as measured by several different diagnostics. The composite picture of the Type V ELM is of an instability with one or two filaments that rotate toroidally at ∼5–10 km/s, in the direction opposite to the plasma current and neutral beam injection. The toroidal extent of Type V ELMs is typically ∼5 m, whereas the cross-field (radial) extent is typically ∼10 cm (3 cm), yielding a portrait of an electromagnetic, ribbon-like perturbation aligned with the total magnetic field. The filaments comprising the Type V ELM appear to be destabilized near the top of the H-mode pedestal and drift radially outward as they rotate toroidally. After the filaments come in contact with the open field lines, the divertor plasma perturbations are qualitatively similar to other ELM types, albeit with only one or two filaments in the Type V ELM versus more filaments for Type I or Type III ELMs. Preliminary stability calculations eliminate pressure driven modes as the underlying instability for Type V ELMs, but more work is required to determine if current driven modes are responsible for destabilization. [ABSTRACT FROM AUTHOR]

Electron transport is rapid in most National Spherical Torus Experiment, M. Ono et al., Nucl. Fusion 40, 557 (2000) beam heated plasmas. A regime of improved electron confinement is nevertheless observed in low density L-mode (“low-confinement”) discharges heated by early beam injection. Experiments were performed in this regime to study the role of the current profile on thermal transport. Variations in the magnetic shear profile were produced by changing the current ramp rate and onset of neutral beam heating. An increased electron temperature gradient and local minimum in the electron thermal diffusivity were observed at early times in plasmas with the fastest current ramp and earliest beam injection. In addition, an increased ion temperature gradient associated with a region of reduced ion transport is observed at slightly larger radii. Ultrasoft x-ray measurements of double-tearing magnetohydrodynamic activity, together with current diffusion calculations, point to the existence of negative magnetic shear in the core of these plasmas. Discharges with slower current ramp and delayed beam onset, which are estimated to have more monotonic q-profiles, do not exhibit regions of reduced transport. The results are discussed in the light of the initial linear microstability assessment of these plasmas, which suggests that the growth rate of all instabilities, including microtearing modes, can be reduced by negative or low magnetic shear in the temperature gradient region. Several puzzles arising from the present experiments are also highlighted. [ABSTRACT FROM AUTHOR]

Large ion orbits can produce nonlocal neoclassical effects on ion heat transport, the ambipolar radial electric field, and the bootstrap current in realistic toroidal plasmas. Using a global δf particle simulation, it is found that the conventional local, linear gradient-flux relation is broken for the ion thermal transport near the magnetic axis. With regard to the transport level, it is found that details of the ion temperature profile determine whether the transport is higher or lower when compared with the predictions of standard neoclassical theory. Particularly, this nonlocal feature is suggested to exist in the National Spherical Torus Experiment (NSTX) [M. Ono, S. M. Kaye, Y.-K. M. Peng et al., Nucl. Fusion 40, 557 (2000)], being consistent with NSTX experimental evidence. It is also shown that a large ion temperature gradient can increase the bootstrap current. When the plasma rotation is taken into account, the toroidal rotation gradient can drive an additional parallel flow for the ions and then additional bootstrap current, either positive or negative, depending on the gradient direction. Compared with the carbon radial force balance estimate for the neoclassical poloidal flow, our nonlocal simulation predicts a significantly deeper radial electric field well at the location of an internal transport barrier of an NSTX discharge. [ABSTRACT FROM AUTHOR]

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 Alfvén 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-Alfvénic 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 Alfvén 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 q² and is independent of plasma major radius, where q is the safety factor. This scaling helps validate the predictive capability of the NOVA-K code for studying TAE stability in future burning plasma devices. The subion cyclotron frequency magnetic activities in NSTX are identified as compressional and global shear Alfvén eigenmodes (AEs) (CAEs and GAEs). CAE and GAE instabilities are driven by beam ions via the Doppler shifted cyclotron resonance by the velocity space bump-on-tail distribution function in the perpendicular velocity. Results of the GAE/CAE theoretical and numerical analysis are presented. [ABSTRACT FROM AUTHOR]

The effects of toroidal and poloidal flows on the equilibrium of tokamak plasmas are numerically investigated using the code FLOW. The code is used to determine the changes in the profiles induced by large toroidal flows on NSTX-like equilibria [with NSTX being the National Spherical Torus Experiment, M. Ono, S.M. Kaye, Y.-K.M. Peng et al., Nucl. Fusion 40, 557 (2000)] where flows exceeding the sound speed lead to a considerable outward shift of the plasma. The code is also used to study the effects of poloidal flow when the flow velocity profile varies from subsonic to supersonic with respect to the poloidal sound speed. It is found that pressure and density profiles develop a pedestal structure characterized by radial discontinuities at the transonic surface where the poloidal velocity abruptly jumps from subsonic to supersonic values. These results confirm the conclusions of the analytic theory of R. Betti and J. P. Freidberg [Phys. Plasmas 7, 2439 (2000)], derived for a low-β, large aspect ratio tokamak with a circular cross section. © 2004 American Institute of Physics. [ABSTRACT FROM AUTHOR]

Recent experiments in the low aspect ratio National Spherical Torus Experiment (NSTX) [M. Ono et al., Nucl. Fusion 40, 557 (2000)] have achieved normalized beta values twice the conventional tokamak limit at low internal inductance and with significant bootstrap current. These experimental results have motivated a computational re-examination of the plasma aspect ratio dependence of ideal no-wall magnetohydrodynamic stability limits. These calculations find that the profileoptimized no-wall stability limit in high bootstrap fraction regimes is well described by a nearly aspect ratio invariant normalized beta parameter utilizing the total magnetic field energy density inside the plasma. However, the scaling of normalized beta with internal inductance is found to be strongly aspect ratio dependent at sufficiently low aspect ratio. These calculations and detailed stability analyses of experimental equilibria indicate that the nonrotating plasma no-wall stability limit has been exceeded by as much as 30% in NSTX in a high bootstrap fraction regime. © 2004 American Institute of Physics. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

Edge parameters play a critical role in high confinement mode (H-mode) access, which is a key component of discharge optimization in present day toroidal confinement experiments and the design of next generation devices. Because the edge magnetic topology of a spherical torus (ST) differs from a conventional aspect ratio tokamak, H-modes in STs exhibit important differences compared with tokamaks. The dependence of the National Spherical Torus Experiment (NSTX) [C. Neumeyer et al., Fusion Eng. Des. 54, 275 (2001)] edge plasma on heating power, including the low confinement mode (L-mode) to H-mode (L-H) transition requirements and the occurrence of edge-localized modes (ELMs), and on divertor configuration is quantified. Comparisons between good L-modes and H-modes show greater differences in the ion channel than the electron channel. The threshold power for the H-mode transition in NSTX is generally above the predictions of a recent International Tokamak Experimental Reactor (ITER) [ITER Physics Basis Editors, Nucl. Fusion 39, 2175 (1999)] scaling. Correlations of transition and ELM phenomena with turbulent fluctuations revealed by gas puff imaging and reflectometry are observed. In both single-null and double-null divertor discharges, the density peaks off-axis, sometimes developing prominent "ears" which can be sustained for many energy confinement times, τ[SUBE], in the absence of ELMs. A wide variety of ELM behavior is observed, and ELM characteristics depend on configuration and fueling. [ABSTRACT FROM AUTHOR]

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 βT of 32%. A variety of MHD phenomena have been observed to limit β. NSTX has now begun addressing TE scaling, β limits, and current drive issues. During the NBI heating experiments, a broad Ti profile with Ti up to 2 keV, Ti > Te and a large toroidal rotation were observed. Transport analysis suggests that the impurity ions have diffusivities approaching neoclassical. For L-Mode plasmas, TE 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 TE after the transition in some conditions. During HHFW heating, Te > Ti and Te 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 Ip, high q, and high βp. [ABSTRACT FROM AUTHOR]

Toroidicity-induced Alfvén 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)]. © 2000 American Institute of Physics. [ABSTRACT FROM AUTHOR]

Simple analytic representations of the neoclassical transport coefficients for indented flux surfaces are presented. It is shown that a transport coefficient for an indented flux surface can be expressed in terms of a linear combination of the previously known transport coefficients for two nonindented flux surfaces. Numerical calculations based on actual equilibria from the PBX-M tokamak [Phys. Fluids B 2, 1271 (1990)] indicate that, even for modestly indented flux surfaces, the ion neoclassical thermal transport can be over a factor of 2 smaller than in a circular plasma with the same midplane radius or with the equivalent area. [ABSTRACT FROM AUTHOR]

Empirical scaling expressions, reflecting the parametric dependence of the L-mode energy confinement time, have been used not only as benchmarks for tokamak operation and theories of energy transport, but for predicting the performance of proposed tokamak devices. Several scaling expressions based on data from small and medium sized devices have done well in predicting performance in larger devices, although great uncertainty exists in extrapolating yet further, into the ignition regime. Several approaches exist for developing higher confidence scaling expressions. These include reducing the statistical uncertainty by identifying and filling in gaps in the present database, making use of more sophisticated statistical techniques, and developing scalings for confinement regimes within which future devices will operate. Confidence in the scaling expressions will be increased still further if the expressions can be more directly tied to transport physics theory. This can be done through the use of dimensionless parameters, by better describing the edge and core confinement regimes separately, and by incorporating transport models directly into the scaling expressions. [ABSTRACT FROM AUTHOR]

Studies microinstability properties of small-aspect-ratio tokamaks. Kinetic instabilities analyzed using a toroidal eigenvalue code; Relationship between aspect ratio and magnetic curves; Stabilization of electrostatic and electromagnetic high-n instabilities.

The experimental program of the Princeton Beta Experiment-Modified (PBX-M) tokamak [Phys. Fluids B2, 1271 (1990)] is directed toward tailoring plasma profiles to achieve greater stability and confinement and to gain access to the second stability region. Modification of the current density profile has been achieved with lower-hybrid current drive (LHCD), leading to a regime free of global magnetohydrodynamic modes, while raising the value of q(0) above unity. The diffusion of the fast electrons produced by LHCD has been examined using two-dimensional hard x-ray imaging. Ion Bernstein waves (IBW) have been used for ion heating: a preliminary analysis shows that ion heating was spatially localized and in agreement with theoretical calculations. Divertor biasing has modified the electric field inside the last closed surface, resulting in the formation of a transport barrier, which in turn has reduced the threshold power of neutral beam injection (NBI) for H-mode transition by 25%. [ABSTRACT FROM AUTHOR]

The highly indented plasmas of the PBX-M tokamak experiment [Plasma Physics and Controlled Nuclear Fusion Research (IAEA, Vienna, 1989), Vol. 1, p. 97] have reached plasma regimes of both high volume-averaged beta (β[sub t]), and high-beta poloidal (β[sub p]), and show evidence of the suppression of external surface modes by the passive stabilizing system. Values of β[sub t] up to 4.0 I/aB (% MA/m T) with 'T[sub i] (0) ≈ 4 keV have been obtained. A magnetohydrodynamic analysis of plasmas with β[sub p] = 2.0 indicates that these plasmas are near the threshold of the second stability regime. A value of β[sub t] of 6.8% has been reached with T[sub i] (0) > 5 keV and an indentation of 28%. Control of plasma shape is accomplished with a feedback system that uses a moment expansion about a single equilibrium and is augmented by time-dependent waveforms to redefine plasma shape. Diagnostics to measure the safety factor q have been developed and used to make accurate measurements of q(r) and to verify changes made in q(0). [ABSTRACT FROM AUTHOR]

The effect of current density distribution in tokamak plasmas is examined on the access to the second stability regime of high-n ballooning modes. The main factor in determining access to the second stability regime is to lower shear sufficiently on each flux surface. This is achieved by broadening the current profile. A general method of finding equilibria with access to the second region of stability is presented. The value of on-axis safety factor q0 is found not to be a good measure of the type of profile required for second region access. [ABSTRACT FROM AUTHOR]

During tangential injection of neutral beams into low-density tokamak plasmas with β>1%, instabilities are observed that degrade the confinement of beam ions. Neutron, charge-exchange, and diamagnetic loop measurements are examined in order to identify the mechanism or mechanisms responsible for the beam-ion transport. The data suggest a resonant interaction between the instabilities and the parallel energetic beam ions. Evidence for some nonresonant transport also exists. [ABSTRACT FROM AUTHOR]

This paper describes a detailed examination of the effects of a relatively small pulsed deuterium gas puff on the edge plasma and edge turbulence in NSTX. This gas puff caused little or no change in the line-averaged plasma density or total stored energy, or in the edge density and electron temperature up to the time of the peak of the gas puff. The radial profile of the Dα light emission and the edge turbulence within this gas puff did not vary significantly over its rise and fall, implying that these gas puffs did not significantly perturb the local edge plasma or edge turbulence. These measurements are compared with modeling by DEGAS 2, UEDGE, and with simplified estimates for the expected effects of this gas puff. [ABSTRACT FROM AUTHOR]

The impact of toroidal rotation, energetic ions, and drift-kinetic effects on the tokamak ideal wall mode stability limit is considered theoretically and compared to experiment for the first time. It is shown that high toroidal rotation can be an important destabilizing mechanism primarily through the angular velocity shear; non-Maxwellian fast ions can also be destabilizing, and drift-kinetic damping can potentially offset these destabilization mechanisms. These results are obtained using the unique parameter regime accessible in the spherical torus NSTX of high toroidal rotation speed relative to the thermal and Alfven speeds and high kinetic pressure relative to the magnetic pressure. Inclusion of rotation and kinetic effects significantly improves agreement between measured and predicted ideal stability characteristics and may provide new insight into tearing mode triggering. [ABSTRACT FROM AUTHOR]

Abstract: Recent experiments on the National Spherical Torus eXperiment (NSTX) have shown the benefits of solid lithium coatings on carbon PFC''s to diverted plasma performance, in both L- and H-mode confinement regimes. Better particle control, with decreased inductive flux consumption, and increased electron temperature, ion temperature, energy confinement time, and DD neutron rate were observed. Successive increases in lithium coverage resulted in the complete suppression of ELM activity in H-mode discharges. A liquid lithium divertor (LLD), which will employ the porous molybdenum surface developed for the LTX shell, is being installed on NSTX for the 2010 run period, and will provide comparisons between liquid walls in the Lithium Tokamak eXperiment (LTX) and liquid divertor targets in NSTX. LTX, which recently began operations at the Princeton Plasma Physics Laboratory, is the world''s first confinement experiment with full liquid metal plasma-facing components (PFCs). All materials and construction techniques in LTX are compatible with liquid lithium. LTX employs an inner, heated, stainless steel-faced liner or shell, which will be lithium-coated. In order to ensure that lithium adheres to the shell, it is designed to operate at up to 500–600°C to promote wetting of the stainless by the lithium, providing the first hot wall in a tokamak to operate at reactor-relevant temperatures. The engineering of LTX will be discussed. [Copyright &y& Elsevier]

Abstract: Lithium wall coating techniques have been experimentally explored on National Spherical Torus Experiment (NSTX) for the last five years. The lithium experimentation on NSTX started with a few milligrams of lithium injected into the plasma as pellets and it has evolved to a lithium evaporation system which can evaporate up to ∼100g of lithium onto the lower divertor plates between lithium re-loadings. The unique feature of the lithium research program on NSTX is that it can investigate the effects of lithium in H-mode divertor plasmas. This lithium evaporation system thus far has produced many intriguing and potentially important results; the latest of these are summarized in a companion paper by H. Kugel. In this paper, we suggest possible implications and applications of the NSTX lithium results on the magnetic fusion research which include electron and global energy confinement improvements, MHD stability enhancement at high beta, edge localized mode (ELM) control, H-mode power threshold reduction, improvements in radio frequency heating and non-inductive plasma start-up performance, innovative divertor solutions and improved operational efficiency. [ABSTRACT FROM AUTHOR]

Abstract: Experimental studies of the novel snowflake divertor concept (D. Ryutov, Phys. Plasmas 14 (2007) 064502) performed in the NSTX and TCV tokamaks are reviewed in this paper. The snowflake divertor enables power sharing between divertor strike points, as well as the divertor plasma-wetted area, effective connection length and divertor volumetric power loss to increase beyond those in the standard divertor, potentially reducing heat flux and plasma temperature at the target. It also enables higher magnetic shear inside the separatrix, potentially affecting pedestal MHD stability. Experimental results from NSTX and TCV confirm the predicted properties of the snowflake divertor. In the NSTX, a large spherical tokamak with a compact divertor and lithium-coated graphite plasma-facing components (PFCs), the snowflake divertor operation led to reduced core and pedestal impurity concentration, as well as re-appearance of Type I ELMs that were suppressed in standard divertor H-mode discharges. In the divertor, an otherwise inaccessible partial detachment of the outer strike point with an up to 50% increase in divertor radiation and a peak divertor heat flux reduction from 3–7MW/m2 to 0.5–1MW/m2 was achieved. Impulsive heat fluxes due to Type-I ELMs were significantly dissipated in the high magnetic flux expansion region. In the TCV, a medium-size tokamak with graphite PFCs, several advantageous snowflake divertor features (cf. the standard divertor) have been demonstrated: an unchanged L–H power threshold, enhanced stability of the peeling–ballooning modes in the pedestal region (and generally an extended second stability region), as well as an H-mode pedestal regime with reduced (×2–3) Type I ELM frequency and slightly increased (20–30%) normalized ELM energy, resulting in a favorable average energy loss comparison to the standard divertor. In the divertor, ELM power partitioning between snowflake divertor strike points was demonstrated. The NSTX and TCV experiments are providing support for the snowflake divertor as a viable solution for the outstanding tokamak plasma–material interface issues. [Copyright &y& Elsevier]