The turbulent convective flux of the toroidal angular momentum density is derived using the nonlinear toroidal gyrokinetic equation which conserves phase space density and energy [T. S. Hahm, Phys. Fluids, 31, 2670 (1988)]. A novel pinch mechanism is identified which originates from the symmetry breaking due to the magnetic field curvature. A net parallel momentum transfer from the waves to the ion guiding centers is possible when the fluctuation intensity varies on the flux surface, resulting in imperfect cancellation of the curvature drift contribution to the parallel acceleration. This mechanism is inherently a toroidal effect, and complements the k∥ symmetry breaking mechanism due to the mean E×B shear [O. Gurcan, Phys. Plasmas 14, 042306 (2007)] which exists in a simpler geometry. In the absence of ion thermal effects, this pinch velocity of the angular momentum density can also be understood as a manifestation of a tendency to homogenize the profile of "magnetically weighted angular momentum density," n mi R2 ω∥ B2. This part of the pinch flux is mode-independent (whether it is trapped electron mode or ion temperature gradient mode driven), and radially inward for fluctuations peaked at the low- B -field side, with a pinch velocity typically, V Ang TEP ∼-2 φ R0. Ion thermal effects introduce an additional radial pinch flux from the coupling with the curvature and grad- B drifts. This curvature driven thermal pinch can be inward or outward, depending on the mode-propagation direction. Explicit formulas in general toroidal geometry are presented. © 2007 American Institute of Physics.

The mode-independent part of the magnetic curvature driven turbulent convective (TurCo) pinch of the angular momentum density [Hahm, Phys. Plasmas 14, 072302 (2007)], which was originally derived from the gyrokinetic equation, can be interpreted in terms of the turbulent equipartition (TEP) theory. It is shown that the previous results can be obtained from the local conservation of "magnetically weighted angular momentum density," n mi U R B2, and its homogenization due to turbulent flows. It is also demonstrated that the magnetic curvature modification of the parallel acceleration in the nonlinear gyrokinetic equation in the laboratory frame, which was shown to be responsible for the TEP part of the TurCo pinch of angular momentum density in the previous work, is closely related to the Coriolis drift coupling to the perturbed electric field. In addition, the origin of the diffusive flux in the rotating frame is highlighted. Finally, it is illustrated that there should be a difference in scalings between the momentum pinch originated from inherently toroidal effects and that coming from other mechanisms that exist in a simpler geometry. © 2008 American Institute of Physics.

This response demonstrates that the comment by Peeters contains an incorrect and misleading interpretation of our paper [T. S. Hahm, Phys. Plasmas 15, 055902 (2008)] regarding the density gradient dependence of momentum pinch and the turbulent equipartition theory. © 2009 American Institute of Physics.

Global gyrokinetic simulations have revealed an important nonlinear flow generation process due to the residual stress produced by electrostatic turbulence of ion temperature gradient (ITG) modes and trapped electron modes (TEMs). In collisionless TEM (CTEM) turbulence, nonlinear residual stress generation by both the fluctuation intensity and the intensity gradient in the presence of broken symmetry in the parallel wavenumber spectrum is identified for the first time. Concerning the origin of the symmetry breaking, turbulence self-generated low frequency zonal flow shear has been identified to be a key, universal mechanism in various turbulence regimes. Simulations reported here also indicate the existence of other mechanisms beyond E×B shear. The ITG turbulence driven "intrinsic" torque associated with residual stress is shown to increase close to linearly with the ion temperature gradient, in qualitative agreement with experimental observations in various devices. In CTEM dominated regimes, a net toroidal rotation is driven in the cocurrent direction by intrinsic torque, consistent with the experimental trend of observed intrinsic rotation. The finding of a "flow pinch" in CTEM turbulence may offer an interesting new insight into the underlying dynamics governing the radial penetration of modulated flows in perturbation experiments. Finally, simulations also reveal highly distinct phase space structures between CTEM and ITG turbulence driven momentum, energy, and particle fluxes, elucidating the roles of resonant and non-resonant particles. © 2010 American Institute of Physics.

A significant inward flux of toroidal momentum is found in global gyrokinetic simulations of ion temperature gradient turbulence, leading to core plasma rotation spin-up. The underlying mechanism is identified to be the generation of residual stress due to the k parallel symmetry breaking induced by global quasistationary zonal flow shear. Simulations also show a significant off-diagonal element associated with the ion temperature gradient in the neoclassical momentum flux, while the overall neoclassical flux is small. In addition, the residual turbulence found in the presence of strong E x B flow shear may account for neoclassical-level ion heat and anomalous momentum transport widely observed in experiments.

One of the nagging, unresolved questions in fusion theory is concerned with the extent of the edge. Gyrokinetic particle simulations of toroidal ion temperature gradient turbulence spreading using the gyrokinetic toroidal code [Z. Lin, T. S. Hahm, W. W. Lee, W. M. Tang, and R. B. White, Science 281, 1835 (1998)] and its related dynamical model have been extended to a system with radially varying ion temperature gradient, in order to study the inward spreading of edge turbulence toward the core plasma. Due to such spreading, the turbulence intensity in the core region is significantly enhanced over the value obtained from the simulations of the core region only, and the precise boundary of the edge region is blurred. Even when the core gradient is within the Dimits shift regime (i.e., dominated by self-generated zonal flows which reduce the transport to a negligible value), a significant level of turbulence can penetrate to the core due to spreading from the edge. The scaling of the turbulent front propagation speed is closer to the prediction from a nonlinear diffusion model than from the one based on linear toroidal coupling. © 2005 American Institute of Physics.

Toroidal plasma flow driven by turbulent torque associated with nonlinear residual stress generation is shown to recover the observed key features of intrinsic rotation in experiments. Specifically, the turbulence-driven intrinsic rotation scales close to linearly with plasma gradients and the inverse of the plasma current, qualitatively reproducing empirical scalings obtained from a large experimental data base. The effect of magnetic shear on the symmetry breaking in the parallel wavenumber spectrum is identified. The origin of the current scaling is found to be the enhanced k symmetry breaking induced by increased radial variation of the safety factor as the current decreases. The physics origin for the linear dependence of intrinsic rotation on the pressure gradient comes from the fact that both turbulence intensity and the zonal flow shear, which are two key ingredients for driving the residual stress, are increased with the strength of the turbulence drives, which are R /L Te and R/Lne for the collisionless trapped electron mode (CTEM). Highlighted results also include robust radial pinches in toroidal flow, heat and particle transport driven by CTEM turbulence, which emerge in phase, and are shown to play important roles in determining plasma profiles. Also discussed are the experimental tests proposed to validate findings from these gyrokinetic simulations. © 2011 American Institute of Physics.

Steady-state and perturbative transport analysis are complementary techniques for the study of transport in tokamaks. These techniques are applied to the investigation of auxiliary-heated L-mode and supershot plasmas in the tokamak fusion test reactor (TFTR) [R. J. Hawryluk et al., Plasma Physics and Controlled Nuclear Fusion Research, Proceedings of the 11th International Conference, Kyoto, 1986 (IAEA, Vienna, 1987), Vol. 1, p. 51.]. In the L mode, both steady-state and perturbative transport measurements reveal a strong temperature dependence that is consistent with electrostatic microinstability theory and the degradation of confinement with neutral beam power. Steady-state analysis of the ion heat and momentum balance in supershots indicates a reduction and a significant weakening of the power-law dependence on the transport in the center of the discharge. © 1991 American Institute of Physics.

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 βt with 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.