Session NM4: Mini-conference on Angular Momentum Transport in Laboratory and Nature III

Spontaneous Rotation in Tokamak Plasmas

Spontaneous toroidal rotation has been observed in Alcator C-Mod tokamak plasmas with no external momentum input. The magnitude of the rotation ranges from --60 km/s in discharges with low energy confinement (L-mode) to +140 km/s in plasmas with good energy confinement (H-mode). The rotation in L-mode plasmas is found to depend strongly and in a complicated fashion on the electron density, the plasma current and the magnetic topology, and is typically in the counter-current direction. In contrast, the rotation velocity in H-mode discharges is observed to scale linearly with the plasma stored energy (or plasma pressure) normalized to the plasma current, a relatively simple dependence, and is directed co-current. Immediately following the abrupt transition from L-mode to H-mode, the co-current rotation appears near the plasma edge and propagates to the center on a time scale similar to the energy confinement time, but anomalously fast compared to the classical (collisional) momentum diffusion time. Very similar scalings in H-mode plasmas have been made on many tokamaks worldwide in a variety of operating conditions, indicating the fundamental nature of spontaneous rotation. A universal scaling is beginning to emerge with an eye toward prediction of the level of rotation expected in future devices such as ITER. At present there is no comprehensive theory which explains this phenomenon.   

Momentum Confinement on DIII-D with Low Net Neutral Beam Torque

Momentum confinement was investigated in ELMing H-mode plasmas with elevated q$_{min}$. Torque scans were performed at constant $\beta_{{\rm N}}$, and the rotation profile was measured using charge exchange recombination (CER) spectroscopy. Studies of the mechanical angular momentum in the plasma show a non-uniform response to the applied neutral beam torque, resulting in a torque dependence of the momentum confinement time. Under nominally balanced neutral beam injection, the plasma maintains a significant rotation in the same direction as the plasma current (co-rotation). The intrinsic rotation can be understood as being due to an offset in the applied torque (i.e. an ``anomalous torque''). Analysis including the effect of anomalous fast ion diffusion shows that the anomalous torque appears to have a magnitude comparable to one neutral beam source, with the torque peaked at the edge of the plasma. Meaningful studies of momentum confinement must account for this intrinsic rotation/anomalous torque.   

Momentum Transport Studies in NSTX

The momentum diffusivity in NSTX is low, $<\chi_{i}$, and it does not scale with the ion thermal diffusivity, as at conventional aspect ratio, possibly due to suppression of ITG modes due to high ExB shear. Dedicated confinement scans show that, if anything, the $\chi_{\phi}$ scales with $\chi _{e}$. Perturbative studies of momentum transport have recently been performed on NSTX using n=3 non-resonant braking as a means of perturbing the rotation profile. Braking was applied for 50 ms during a relatively MHD-quiescent phase of the discharge, after which the evolution of the plasma rotation was measured. The non-local torque perturbation created by the n=3 error field created some distortion to the toroidal rotation profile, allowing the separation of momentum flux caused by diffusion (proportional to the gradient in the toroidal rotation) and a momentum pinch (proportional to the toroidal rotation). Preliminary analysis indicates the necessity of a momentum pinch to explain the profile evolution. The effect of off-diagonal terms in the momentum balance equation (eg grad(Ti), grad(ne)) are also considered.   

Formation and saturation of zonal flows via turbulent momentum transport in a basic magnetized plasma experiment

A radially sheared azimuthal plasma fluid flow is observed in a cylindrical magnetized helicon plasma device with no external sources of momentum input and is sustained against collisional dissipation by the turbulent Reynolds stress. Measurements show that the cross-phase between turbulent velocity components determine the detailed shape of the Reynolds stress profile and the resulting time averaged shear layer profile. Recent work also shows the a-periodic formation of radially outward going plasma transport events which are born near the shear layer and which are associated with the slow evolution of the background plasma fluctuations. The results show a clear demonstration of turbulent-driven shear flows via momentum transport, and suggest that such shear flows may become unstable and thereby generate outward going radial transport events.   

Toroidal Rotation in the Torpex Magnetized Plasmas

Rotation and plasma flow in general are closely tied to transport of heat and particles across field lines. Toroidal velocity measurements obtained with a Mach probe and covering the entire poloidal cross-section of the TORPEX device ($n_e\leq10^{17}$m$^{-3}$, $T_e\leq10$eV, R=1m, a=0.2m) are presented. It is found that the time averaged toroidal velocity profile does not change when the toroidal magnetic field is reversed. In addition, dependencies of the time averaged toroidal velocity on the vertical magnetic field, the neutral gas pressure and the neutral gas type is investigated and will be compared with theoretical predictions. On TORPEX, a regime has been identified, in which a core plasma is produced and confined on the device high field side, separated from an SOL-like region on the low-field-side. Blobs are observed in this regime to carry plasma from the core to the SOL region. We are investigating the possible impact of the blob propagation on the plasma toroidal rotation using time resolved measurements of the toroidal velocity. It is found that the plasma decelerates when a blob is propagating radially.   

Developments in the Theory of Toriodal Momentum Transport

In this talk, we will review and discuss recent developments in the theory of toroidal momentum transport and intrinsic rotation. Special emphasis will be placed on physics mechanisms which underlie the non-diffusive momentum flux, in both its pinch and residual stress components. Electric field shear, toroidicity and wave momentum exchange effects are analyzed. The outlook for future investigations involving energetic particle driven Alfven waves and their effect on momentum transport will be discussed. We also discuss a new class of momentum transport bifurcations.   

Edge flows and their role in intrinsic rotation and the LH transition

As we enter the era of next-step devices like ITER, where external momentum sources may prove insufficient, intrinsic mass flows are becoming increasingly relevant because of their importance in macroscopic stability and transport. There are flows in tokamaks driven purely by the toroidal geometry itself, making them an integral part of all tokamak plasmas. Related to the Pfirsch-Schl\"{u}ter fluxes and dipolar in nature, these flows are localized to the edge region because of temperature gradients. Within the separatrix they are essentially cross-field, accompanied by parallel flows in the scrape-off layer (SOL) that tend to provide global mass conservation. In a symmetric system, the toroidal component of the SOL flows has no net angular momentum; however, asymmetries introduced, for example, by a single-null field geometry, results in a net momentum source at the edge. Coupled with an effective inward momentum transport mechanism (e.g., momentum pinch), this source can drive an intrinsic core rotation in the absence of any external momentum source. These flows also have the correct symmetry properties to account for the increased power threshold for the LH transition when the grad-B drift is in the ``wrong'' direction.   

Angular momentum sources in tokamak plasma edge

Computational study of spontaneous rotation phenomena in a diverted tokamak edge plasma is performed using an edge kinetic code XGC. XGC is capable of simulating the whole edge plasma (including the closed and open magnetic field regions) in the presence of magnetic separatrix and material wall. Full function ions, electrons, and Monte Carlo neutrals are followed in the Lagrangian equation of motion. Conserving Coulomb collisions are used. Three spontaneous rotation sources have been identified in a turbulence-free edge plasma: 1) Electrostatic sheath interaction with material wall in the scrape-off region, 2) Particle orbit loss through the magnetic separatrix and X-point, and 3) steep plasma gradient in the edge pedestal. These three rotation sources combine to produce a 2D spontaneous edge rotation profile. Neutral particle interaction is observed to modify the edge plasma rotation profile. XGC finds that the resonance magnetic perturbation (RMP) can also change the spontaneous edge rotation significantly.