Session TM10: Mini-Conference on Momentum Transport in Magnetic Fusion and Astrophysical Systems I

Overview of Toroidal Rotation Observations in Alcator C-Mod Plasmas

Spontaneous toroidal rotation, self-generated in the absence of external momentum input, exhibits a rich phenomenology in C-Mod. In Ohmic L-mode plasmas, the rotation is predominantly in the counter-current direction and varies in a complicated fashion with electron density, magnetic configuration and plasma current. Abrupt rotation reversals have been observed, with the magnitude of the reversals typically 10s of km/s, and triggered by slight changes in the electron density or plasma current. In contrast, the rotation in H-mode plasmas is mainly directed co-current, and has a relatively simple parameter dependence, with the magnitude of the core velocity proportional to the stored energy normalized to the plasma current. The co-current rotation is observed to propagate in towards the center from the plasma edge following the H-mode transition, on a time scale similar to the energy confinement time. Similar rotation characteristics are seen in I-mode plasmas. The magnitude of the intrinsic rotation in H- and I-mode is related to the pedestal temperature gradient. ICRF mode conversion flow drive, with co-current velocities as high as 100 km/s, has been demonstrated. In contrast, with LHCD the rotation is strongly peaked in the counter-current direction in the central half of the plasma, with the strong gradient region near r/a=0.3. A variety of velocity profile shapes has been observed, indicating the presence of a momentum pinch.   

Intrinsic Rotation Drive on DIII-D

Recent experiments on \hbox{DIII-D} have focused on understanding the drive mechanisms for intrinsic rotation in tokamak fusion plasmas. At the edge ($\rho >0.8$) of \hbox{H-mode} plasmas, a clear dependence of the ``intrinsic torque'' associated with the intrinsic rotation is observed with the edge pressure gradient. The intrinsic torque in the core ($\rho <0.5$) of \hbox{H-mode} plasmas tends to be small, although some cases have been found where it is sufficient to modify the rotation profile. For example, large core intrinsic torques have been observed in quiescent \hbox{H-mode} plasmas and more recently in hybrid discharges. In such cases, the net result when integrated across the profile is an intrinsic torque that is in the counter current direction, which is the opposite for usual \hbox{H-modes}. Recent studies of the residual stress with the global gyrokinetic code GYRO, suggest that nonlocal profile variations are capable of generating large residual stresses suitable for driving intrinsic rotation.   

Generation of a Sheared Plasma Rotation by Emission, Propagation and Absorption of Drift Wave Packets

Collisional electron drift wave turbulence is shown to nonlinearly generate drift wave packet structures with density and vorticity fluctuations in the central plasma pressure gradient region of a linear plasma device. Tracking these packets reveals that they follow an outward directed spiral shaped trajectory in the $(r,\theta )$ plane, are azimuthally stretched and develop anisotropy as they approach an axisymmetric, radially sheared azimuthal flow located at the plasma boundary. Nonlinear energy transfer measurements and time-delay analysis confirm that structure absorption amplifies the sheared flow. Similar mechanisms likely operate at the edge of confined toroidal plasmas and should lead to the amplification of sheared flows at the boundary of these devices as well.   

Impurity Poloidal Rotation in DIII-D Under Low Toroidal Field Conditions

Predictive understanding of plasma transport is a long-term goal of fusion research. This requires testing models of plasma rotation including poloidal rotation. The present experiment was motivated by recent poloidal rotation measurements on NSTX which show that the poloidal rotation of C$^{+6}$ is much closer to the neoclassical value than results in larger aspect ratio machines such as TFTR, DIII-D and JET working at higher toroidal field $B_{\rm T}$. We investigated whether the difference in aspect ratio (1.44 on NSTX vs 2.7 on DIII-D) could explain this. We performed a poloidal rotation experiment in DIII-D under conditions which matched, as best possible, those in the NSTX experiment; we matched plasma current (0.65 MA), on-axis $B_{\rm T}$ (0.55 T), minor radius (0.6 m), and outer flux surface shape as well as the density and temperature profiles. DIII-D results from this work show reasonable agreement with neoclassical theory. Accordingly, the different aspect ratio does not explain the previously mentioned difference in poloidal rotation results.   

Momentum studies with sources and sinks in fusion

Recent experimental [1,2] as well as numerical [3] studies have started emphasising on the possible non-neoclassical behaviour of poloidal momentum. Correlation between this observed non-neoclassical behaviour and turbulence-induced Reynolds stresses was pointed out in the latter work. Building upon those results, a discussion of the mechanisms through which microturbulence may drive poloidal flows has been proposed [4]. More generally, the role of turbulence in determining rotation profiles and momentum transport is paramount, as exemplified through the chief role of turbulence-induced mean profile dynamics in flux-driven gyrokinetic simulations, including versatile momentum sources. Poloidal and parallel momentum are investigated, as well as their respective transport, in both L--mode-like and enhanced confinement regimes.\\[4pt] [1] K. H. Burrell et al., Phys. Plasmas \textbf{1}:1536 (1994)\\[0pt] [2] K. Cromb\'e et al., Phys. Rev. Lett. \textbf{95}:155003 (2005)\\[0pt] [3] G. Dif-Pradalier et al., Phys. Rev. Lett. \textbf{103}:065002 (2009)\\[0pt] [4] C.J. McDevitt et al., this conference   

Advances in Velocimetry Techniques for Plasma Turbulence Studies

The HOP-V (Hybrid OPtical-flow Velocimetry) code, developed for extracting time-resolved 2-D velocity maps from turbulence imaging diagnostics, combines optical-flow and local pattern-matching techniques to derive ``dense'' velocity fields at the full time resolution and a fraction of the spatial resolution of the underlying image frames, often tens of pixels per side and thousands of timepoints in duration, with resolution sufficient to resolve the relevant turbulent structures. Here we discuss recent advances in the techniques for extracting velocity fields, as well as a number of applications related to analysis of turbulence and its interaction with plasma flow. As part of this study, we have implemented a synthetic diagnostic (similar to the Gas Puff Imaging instrument) to analyze the output of the BOUT and SOLT edge turbulence codes, enabling direct comparison to the known plasma quantities from the simulation, in an attempt to define the connection between the observed velocities and underlying turbulent plasma behavior. In this talk, we discuss recent velocimetry analysis of both numerical simulations and experiments.   

Measurement of Momentum Transport in Magnetic Turbulence

Momentum transport in a hot accretion disk must be much faster than allowed by classical dissipation. The leading candidate for this anomalous transport is the magnetorotational instability (MRI), which produces magnetic turbulence [1]. Anomalous momentum transport is also observed in reversed field pinch (RFP) plasmas. Surprisingly, despite $\beta$ a few percent in MST plasmas, parallel pressure fluctuations correlated with magnetic fluctuations can produce momentum flux comparable to the radial momentum transport that occurs in magnetic relaxation events (sawteeth), thereby implying that kinetic effects are important for momentum transport in a turbulent magnetic field. This result was obtained using advanced interferometry and polarimetry techniques in the hot MST plasma core. Previous measurements in MST identified that both the Reynolds and Maxwell fluid stresses are also large (and oppositely directed) during these relaxation events. Thus multiple momentum transport mechanisms appear to be active in the RFP. We note that the parallel Maxwell stress is identically the Hall dynamo; the self-consistent coupling of momentum transport and dynamo has also been considered for accretion disks [2]. Supported by US DOE and NSF. [1] S.A. Balbus, J.F. Hawley, Rev. Mod. Phys., \textbf{70}, 1 (1998). [2] F. Ebrahimi et al., Phys. Rev. Lett. \textbf{99}, 075003 (2007).   

Characteristics of turbulence nonlinearly driven plasma flow and origins of empirical scalings of intrinsic rotation in experiments

Recent progress made by our global gyrokinetic simulations in understanding the origin of intrinsic rotation and plasma flow formation in tokamaks is reported. Critical issues to be addressed are closely coupled to experimental and theoretical studies. We focus our discussion on: i) nonlinear mechanism for turbulence driving plasma flow; ii) underlying physics governing experimental empirical scalings of the intrinsic rotation with respect to plasma gradients, current and magnetic shear; iii) machine size scaling of the intrinsic rotation; iv) coupling of core rotation to edge (namely, very outer core region) flow via turbulence. Our nonlinear simulation studies are carried out for electrostatic turbulence with emphasis placed on electron transport dominated regimes. Also discussed are possible experimental tests of simulation predictions.   

Intrinsic rotation and residual stress in full-f ITG turbulence simulations

Intrinsic rotation of tokamak plasma is of interest for macroscopic stability and understanding and control of transport. To study the toroidal rotation generated by flux-driven turbulence, we have performed full-f flux-driven ITG simulations using XGC1p code, which self-consistently evolves the profile of ion temperature, parallel flow and poloidal flow. The growth of net co-current flow with values of $u_{||}/v_{th}\sim $5\% is observed with no-slip boundary condition. The residual stress is identified by applying external torque which cancels out the intrinsic rotation. Also, correlation analysis between stress, turbulence intensity, ExB shear, and k-parallel symmetry breaking are performed.   

Intrinsic Rotation and Momentum Transport in Reversed Shear Plasmas with Internal Transport Barriers

The intrinsic rotation in fusion plasmas is believed to be generated via the residual stress without external momentum input. The physical mechanism responsible for the generation and transport of intrinsic rotation in L- and H-mode tokamak plasmas has been studied extensively. However, it is noted that the physics of intrinsic rotation generation and its relationship to the formation of internal transport barriers (ITBs) in reversed shear (RS) tokamak plasmas have not been explored in detail, which is the main subject in the present work. A global gyrofluid code TRB is used for this study. It is found that the large intrinsic rotation ($\sim$10-30\% of the ion sound speed depending on ITB characteristics) is generated near the ITB region and propagates into the core. The intrinsic rotation increases linearly as the temperature gradient at ITB position increases, albeit not indefinitely. Key parameters related to the symmetry breaking, such as turbulent intensity and its gradient, the flux surface averaged parallel wavenumber are evaluated dynamically during the ITB formation. The role of reversed shear and the q-profile curvature is presented in relation to the symmetry breaking mechanism in RS plasmas.   

Gyrokinetic simulation of toroidal momentum transport in ITG and CTEM turbulence

Studies of kinetic electrons effect in the toroidal momentum transport in the ITG turbulence and pioneering global nonlinear gyrokinetic simulations of momentum transport in CTEM turbulence using GTC are presented. The distinct off-diagonal momentum fluxes are observed. Varying the background rotation speed, the toroidal momentum pinch velocity and residual momentum flux is calculated, and used to separate the diffusive momentum flux and to calculate the intrinsic Prandtl number for the first time. The obtained values for ITG and CTEM turbulence are found to be from Pr=0.3 to Pr=0.9, which is consistent with experimental observations and quasilinear estimates. The effect of kinetic electrons leads to the increase of momentum flux in the ITG turbulence. The convective particle flux in this case gives relatively small contribution to the total momentum pinch. In CTEM turbulence particle convection gives significant contribution to the momentum pinch, although the total momentum pinch is relatively small. The volume-averaged residual momentum flux in CTEM turbulence is found to be insignificant. While the diagonal and off-diagonal fluxes are comparable in the ITG turbulence, the dominant contribution to the momentum flux in CTEM case comes from the diffusive term.