Session R2: Invited Session: Angular Momentum Transport in the Laboratory and in Nature

Why Magnetically Confined Plasmas Rotate and Why it is Important

Rotation in tokamak and spherical tokamak magnetic confinement devices has been found to be critical to enhancing the plasma stability to both the electron and ion gyroradius scale-turbulence as well to magnetohydrodynamic (MHD) modes whose characteristic scales can be of order the device size. Suppression of these modes leads to reduced energy and particle transport losses in these plasmas, thus increasing the potential fusion power production. Rotation can also lead to the avoidance of catastrophic MHD events known as ``disruptions.'' This strong impact of the rotation underscores the importance of developing the knowledge of how rotation is generated in these devices and how the momentum is transported through the plasma. Rotation in these plasmas is generated by a number of different torques, including external momentum input from neutral beam injection, and magnetic torques (toroidal viscosity) resulting from a non-axisymmetric magnetic field structure. One leading theory suggests that rotation can also be self-generated from microturbulence. In this strongly coupled, predator-prey-like system, the plasma can self-organize from a turbulent state to one with directed flow in directions both parallel and perpendicular to the magnetic field. The rotation in the perpendicular direction is often seen to have radial structure and is analogous to the Zonal Flows observed in planetary atmospheres. The self-generated, or intrinsic, rotation that flows mainly along the magnetic field, has been measured on virtually all experimental devices. The theory suggests that the intrinsic torque generating the intrinsic rotation is due to long-wavelength (of order the ion gyroradius) modes, and experimental measurements of intrinsic torque and rotation generally follow the trends predicted by theory. Values of the momentum diffusivity and convective pinch term have been determined from perturbation experiments, and their trends indicate that the same modes that drive intrinsic rotation appear to be those responsible for the transport of momentum through the plasma. The results from conventional and spherical tokamaks are quite similar. While these studies offer a window into turbulent processes that can generate the flow as well as transport the momentum, other effects, such as torques due to lost particles and the effect of flows just outside the plasma boundary, can also be important. Developing an understanding of how all these processes interact is crucial for being able to predict rotation profiles and stability in future, fusion power generating devices, such as ITER.   

Turbulent momentum transport and intrinsic rotation in tokamaks

A key physics issue for magnetic confinement fusion is the presence of high levels of turbulent particle and energy transport in magnetized plasmas. This transport is detrimental to fusion because it significantly lowers the plasma density and temperature, both of which must be kept high to increase fusion energy yield. Sheared flows have been shown to strongly reduce this plasma turbulent transport. Many current fusion experiments induce sheared flows by injecting beams of neutral particles, which make the plasma differentially rotate. However, this external momentum injection will be much less effective in the large, dense plasmas that may be required for a fusion reactor. A number of recent fusion experiments have measured significant differential rotation even without external momentum injection. This `intrinsic' rotation is a result of the rearrangement of momentum within the plasma. Since this rotation may determine the extent to which turbulent transport is suppressed, it is critical for the community to understand how momentum transport produces intrinsic rotation profiles. This is challenging, as intrinsic rotation exhibits a complex phenomenology that defies simple empirical scalings or heuristic models. This talk gives a brief overview of the intrinsic rotation phenomenology and elucidates features that any viable model for intrinsic rotation must contain. We propose a fully self-consistent, first-principles model for intrinsic rotation, which is based on an asymptotic expansion in the smallness of the turbulence fluctuation frequency relative to the ion Larmor frequency (known as gyrokinetics). Stringent conditions are placed on this model by a symmetry of the gyrokinetic equations. This model has been implemented in the gyrokinetic turbulence code GS2, from which we present simulation results on turbulent momentum transport. Various physical mechanisms that contribute to the momentum transport are studied to determine their dependences on key plasma parameters and their relative importance for generating intrinsic rotation.   

Momentum Transport in Accretion Disks

The most energetic phenomena in the universe are systems powered by gravity through accretion. Magnetic fields are unstable to the magnetororational instability (MRI) in a differentially rotating system. The MRI, operating in an accretion disk system, leads to magnetic turbulence which, in turn, accounts for the internal stresses that drive the accretion process. MHD turbulence is thus fundamental to the system. The governing equations are those of compressible magnetohydrodynamics (MHD). Accretion disk dynamics can thus be investigated using three-dimensional MHD simulations, both in the local and global domain. The difficulties associated with numerical simulations of MHD turbulence are increased by the action of the MRI which stirs the turbulence on multiple scales. The challenge is to gain a sufficient understanding of the transport properties of MRI-driven turbulence to model accretion systems and jets from a basis that is closer to first-principles.