Session NI2: Transport of Momentum and Particles

Turbulent momentum transport in tokamaks

Momentum transport has become an active area of research in tokamaks in recent years because velocity shear has been shown theoretically to regulate turbulence levels. Thus, predicting and controlling the rotation in tokamaks has become an attractive goal, even more so with the increasing experimental evidence of different spontaneous rotation regimes. This talk reviews the requirements that gyrokinetic simulations must satisfy in order to self-consistently provide the correct rotation profile. Special emphasis on the up-down symmetry of the gyrokinetic equations is made because it places stringent conditions on the required accuracy. Different approaches to gyrokinetic simulations (full f vs. delta f, global vs. local) are examined. Finally, the first fully self-consistent, first-principles model for spontaneous rotation is presented. To simplify this description we expand in the small ratio of the poloidal to toroidal magnetic field amplitudes. This reduced model is now implemented in a local delta f gyrokinetic code, from which preliminary results will be presented.   

Flow, current, and electric field in omnigenous stellarators

An omnigenous magnetic field is one in which all collisionless drift orbits are confined. Omnigenity is a less restrictive condition than quasisymmetry, for a magnetic field can be omnigenous without being quasisymmetric [1], whereas all quasisymmetric fields are omnigenous [2]. Even though an omnigenous stellarator is generally fully three-dimensional, we have derived concise, explicit expressions for the bootstrap current, ion flow, and radial electric field in these devices in the long-mean-free-path regime [3], as well as expressions for the collisionality-independent Pfirsch-Schl\"uter current and flow in these devices. The radial electric field is determined in a manner that is consistent with intrinsic ambipolarity in the quasisymmetric limit. This electric field turns out to be independent of the details of the magnetic field geometry. The flow and current expressions involve only one more term than known expressions for quasisymmetric plasmas [2], but our results apply to a much larger class of stellarators. If the $B$ contours of an omnigenous field close poloidally, the bootstrap current vanishes [3, 4]. As a result, the drive for MHD instability is reduced, and the magnetic field optimization is less sensitive to the pressure profile. Stellarators that are optimized for maximal alpha-particle confinement will be approximately omnigenous, so our analytic results may give new insight into the physics of advanced stellarators.\\[4pt] [1] J. R. Cary \& S. G. Shasharina, Phys. Plasmas 4, 3323 (1997).\\[0pt] [2] A. Boozer, Phys. Fluids 26, 496 (1983).\\[0pt] [3] M. Landreman \& P. J. Catto, Plasma Phys. Control. Fusion 53, 015044 (2011).\\[0pt] [4] P. Helander \& J. Nuhrenberg, Plasma Phys. Control. Fusion 51, 055004 (2009).   

Measurement and Gyrokinetic Simulation of Impurity Transport in the Core of Alcator C-Mod

Measurements of impurity transport in the core of tokamak plasmas are compared with nonlinear gyrokinetic simulations for the first time. At Alcator C-Mod, a novel multi-pulse laser blow-off system introduces a \underline {measured} source of trace, non-intrinsic impurity (calcium) with precise timing. Unique measurements provided by a high resolution x-ray crystal spectrometer allow for precise characterization of the time evolving \underline {profile} of a single charge state (Ca$^{+18})$ of the trace impurity over the radial region 0.0 $<$ r/a $<$ 0.6. Simulated emission by the trace impurity is obtained using the STRAHL code. A chi squared minimization of the difference in measured and simulated emission is used to determine time-independent transport coefficients and perform rigorous error analysis. Presented here are results from two experimental scans: a scan of plasma current (I$_{p}$ = 0.6 -- 1.2 MA) and a scan of ICRH input power (P$_{in}$ =1.0 - 3.3 MW). Plasma current is well correlated with increased impurity confinement time and reduction in the density gradient scale length, a/L$_{n}$, and safety factor, q. Experimental values of diffusion and inward convection are found to decrease with I$_{p}$. This trend is well reproduced in global, nonlinear GYRO simulations and shown to be the result of reduced core safety factor (and magnetic shear) at high values of I$_{p}$. Addition of ICRH power results in decreased Ion Temperature Gradient (ITG) turbulence drive and a transition to Trapped Electron Mode (TEM) dominated core turbulence. During this scan, diffusion decreases and inward convection increases modestly, in contrast to initial gyrokinetic results which predict significant reduction of diffusion and inward convection. Extended analysis which includes high fidelity GYRO simulations and critical comparison between measured and predicted impurity transport will be presented.   

Classical confinement and outward convection of impurity ions in the MST RFP

Impurity ion dynamics measured with simultaneous high spatial and temporal resolution reveal evidence of classical ion transport for the first time in the reversed field pinch (RFP). The boron, carbon, oxygen and aluminum impurity ion density profiles are obtained in MST using a fast, active charge-exchange recombination spectroscopy (CHERS) diagnostic. The impurity ion density profile evolution is measured during improved-confinement RFP plasmas obtained using inductive control of tearing instability to mitigate stochastic transport (PPCD technique). At the onset of the transition to improved confinement, the profiles become hollow, with a slow decay of the impurity density in the core region concurrent with an increase in impurity density in the outer region. The high electron temperature ($\sim $ 2 keV) attained with improved confinement implies that the impurities are fully stripped, and that the source is small in most of the plasma. Hence, an outward convection of impurities is implied. A hollow profile and outward convection are favorable for impurity removal in a fusion plasma. Impurity transport from Coulomb collisions in the RFP is ``classical'' for all collisionality cases, and analysis shows that the observed hollow profile can be explained by the classical ``temperature screening'' mechanism. The profiles agree well with classical expectations. ``Neoclassical'' corrections are small in the RFP because the safety factor is small (poloidal field dominates), even though the trapped particle fraction is similar to that in high toroidal field configurations. Experiments have also been performed with impurity pellet injection and provide further evidence for classical impurity ion confinement. This work further establishes good confinement characteristics for the RFP when tearing instabilities are suppressed.   

Measurements of the Deuterium Ion Toroidal Rotation in the DIII-D Tokamak and Comparison to Neoclassical Theory

Bulk ion toroidal rotation in tokamak plays a critical role in controlling microturbulence and MHD stability as well as yielding important insights into angular momentum transport and intrinsic rotation. So far, our understanding of the bulk plasma flow in hydrogenic plasmas has been inferred from impurity charge exchange measurements and neoclassical theoretical calculations. However, the validity of these inferences has not been tested rigorously through direct measurement, particularly in regions with steep pressure gradients where very large differences (up to 100$\,$km/s) can be expected between bulk ion and impurity rotation. New advances in the analysis of wavelength-resolved D$_\alpha$ emission on the DIII-D tokamak have enabled accurate measurements of the main ion (deuteron) temperature and toroidal rotation. The D$_\alpha$ emission spectrum is accurately fit using a model that incorporates thermal deuterium charge exchange, beam emission and fast-ion emission (FIDA) spectra. Simultaneous spectral measurements of counter current injected and co current injected neutral beams enable a direct determination of the deuteron toroidal velocity, in quantitative agreement with time-dependent collisional-radiative modeling of photo-emission process in three-dimensional geometry. Discharges with low beam ion pressure and broad thermal pressure profiles exhibit deuteron temperature and toroidal velocities similar to carbon measurements. However, in conditions with internal transport barriers, large differences between the core deuteron and carbon rotation are observed which do not match the neoclassical predictions. First profile measurements of simultaneous carbon and deuterium rotation profiles will be presented, and the progress on edge pedestal measurements of bulk ion rotation will be discussed.   

Rotation Reversal and Energy Confinement Saturation in Alcator C-Mod Ohmic L-mode Plasmas: A Novel Transport Bifurcation

Direction reversals of intrinsic toroidal rotation have been observed in Alcator C-Mod Ohmic L-mode plasmas following modest electron density or toroidal magnetic field ramps. Rotation reversals exhibit both a threshold and hysteresis, and thus constitute a momentum transport bifurcation. The reversal process occurs in the plasma interior, inside of the q = 3/2 surface. For low density diverted plasmas, the rotation is in the co-current direction, and can reverse to the counter-current direction following an increase in the electron density above a certain threshold. Reversals from the co- to counter-current direction are correlated with a sharp decrease in density fluctuations with 2 cm$^{-1} \quad <$ k$_{q} \quad <$ 11 cm$^{-1}$ and with frequencies above 70 kHz. The density at which the rotation reverses increases linearly with plasma current, and decreases with increasing magnetic field. There is a strong correlation between the reversal density and the density at which the global Ohmic L-mode energy confinement changes from the linear to the saturated regime. Taken together, these results suggest that reversals result from a change in the sign of the turbulence driven intrinsic torque density, proportional to the radial gradient of the residual stress. This change is predicted to accompany the evolution from TEM turbulence in LOC to ITG driven turbulence in SOC, and is a consequence of the scaling of the residual stress with the mode diamagnetic velocity.