W. A. Hornsby

Overview of toroidal momentum transport

Toroidal momentum transport mechanisms are reviewed and put in a broader perspective. The generation of a finite momentum flux is closely related to the breaking of symmetry (parity) along the field. The symmetry argument allows for the systematic identification of possible transport mechanisms. Those that appear to lowest order in the normalized Larmor radius (the diagonal part, Coriolis pinch, E x B shearing, particle flux, and up-down asymmetric equilibria) are reasonably well understood. At higher order, expected to be of importance in the plasma edge, the theory is still under development.

Influence of the centrifugal force and parallel dynamics on the toroidal momentum transport due to small scale turbulence in a tokamak

The paper derives the gyro-kinetic equation in the comoving frame of a toroidally rotating plasma, including both the Coriolis drift effect [A. G. Peeters et al., Phys. Rev. Lett. 98, 265003 (2007)] as well as the centrifugal force. The relation with the laboratory frame is discussed. A low field side gyro-fluid model is derived from the gyro-kinetic equation and applied to the description of parallel momentum transport. The model includes the effects of the Coriolis and centrifugal force as well as the parallel dynamics. The latter physics effect allows for a consistent description of both the Coriolis drift effect as well as the ExB shear effect [R. R. Dominguez and G. M. Staebler, Phys. Fluids B 5, 3876 (1993)] on the momentum transport. Strong plasma rotation as well as parallel dynamics reduce the Coriolis (inward) pinch of momentum and can lead to a sign reversal generating an outward pinch velocity. Also, the ExB shear effect is, in a similar manner, reduced by the parallel dynamics and stronger rotation.

Gyrokinetic simulations including the centrifugal force in a rotating tokamak plasma

Tokamak experiments operate with a rotating plasma, with toroidal velocity which can be driven externally but can also arise spontaneously. In the frame that corotates with the plasma, the effects of the centrifugal force are felt through a centrifugal drift and an enhanced mirror force [Peeters et al., Phys. Plasmas 16, 042310 (2009)]. These inertial terms become important in the case of strong rotation, as is common in spherical devices, and are also important for heavy impurity ions even at small toroidal velocities. In this work, the first gyrokinetic simulations including the centrifugal force in a strongly rotating plasma are presented. The enhanced mirror force redistributes density over a flux surface and modifies the trapping condition, destabilizing trapped electron modes. At intermediate scales this can result in promotion of the trapped electron mode over the ion temperature gradient (ITG) mode as the dominant instability, which under marginal conditions could result in an enhanced electron heat flux. The centrifugal drift acts to damp the residual zonal flow of the geoacoustic mode, while its frequency is increased. For nonlinear ITG dominated turbulence, increased trapped electron drive and reduced zonal flow lead to an increase in ion heat diffusivity if the increased rotation is not accompanied by rotational shear stabilization. An increased fraction of slow trapped electrons enhances the convective particle pinch, leading to an increase in the steady state density gradient with strong rotation. Linear ITG mode results show an increased pinch of heavy trace impurities due to their strong centrifugal trapping.

The nonlinear coupling between gyroradius scale turbulence and mesoscale magnetic islands in fusion plasmas

The interaction between small scale turbulence (of the order of the ion Larmor radius) and mesoscale magnetic islands is investigated within the gyrokinetic framework. Turbulence, driven by background temperature and density gradients, over nonlinear mode coupling, pumps energy into long wavelength modes, and can result in an electrostatic vortex mode that coincides with the magnetic island. The strength of the vortex is strongly enhanced by the modified plasma flow response connected with the change in topology, and the transport it generates can compete with the parallel motion along the perturbed magnetic field. Despite the stabilizing effect of sheared plasma flows in and around the island, the net effect of the island is a degradation of the confinement. When density and temperature gradients inside the island are below the threshold for turbulence generation, turbulent fluctuations still persist through turbulence convection and spreading. The latter mechanisms then generate a finite transport flux ...

Intrinsic rotation driven by the electrostatic turbulence in up-down asymmetric toroidal plasmas

The transport of parallel momentum by small scale fluctuations is intrinsically linked to symmetry breaking in the direction of the magnetic field. In tokamaks, an up-down asymmetry in the equilibrium proves to be an efficient parallel symmetry breaking mechanism leading to the generation of a net radial flux of parallel momentum by the electrostatic turbulence [Y. Camenen et al., Phys. Rev. Lett. 102, 125001 (2009)]. This flux is neither proportional to the toroidal rotation nor to its gradient and arises from an incomplete cancellation of the local contributions to the parallel momentum flux under the flux surface average. The flux of parallel momentum then depends on the asymmetry of the curvature drift and on the extension of the fluctuations around the low field side midplane. In this paper, the mechanisms underlying the generation of the flux of parallel momentum are highlighted and the main dependences on plasma parameters investigated using linear gyrokinetic simulations.

Interaction of turbulence with magnetic islands: effect on bootstrap current

A finite radial temperature gradient has been observed to be maintained within magnetic islands in gyro-kinetic turbulence simulations despite the fast motion along the field, and is related to the trapped particles which do not move along the field around the island. Recent calculations of the interaction of drift-wave turbulence with magnetic islands have shown that turbulence can exist within the separatrix, which in turn allows only the partial flattening of electron temperature profiles. Here we calculate, using a minimal drift-kinetic model, the effect on the bootstrap current in a tokamak. Consequences for the stability of the neoclassical tearing mode are discussed.

The influence of the self-consistent mode structure on the Coriolis pinch effect

This paper discusses the effect of the mode structure on the Coriolis pinch effect [A. G. Peeters, C. Angioni, and D. Strintzi, Phys. Rev. Lett. 98, 265003 (2007)]. It is shown that the Coriolis drift effect can be compensated for by a finite parallel wave vector, resulting in a reduced momentum pinch velocity. Gyrokinetic simulations in full toroidal geometry reveal that parallel dynamics effectively removes the Coriolis pinch for the case of adiabatic electrons, while the compensation due to the parallel dynamics is incomplete for the case of kinetic electrons, resulting in a finite pinch velocity. The finite flux in the case of kinetic electrons is interpreted to be related to the electron trapping, which prevents a strong asymmetry in the electrostatic potential with respect to the low field side position. The physics picture developed here leads to the discovery and explanation of two unexpected effects: First the pinch velocity scales with the trapped particle fraction (root of the inverse aspect ratio), and second there is no strong collisionality dependence. The latter is related to the role of the trapped electrons, which retain some symmetry in the eigenmode, but play no role in the perturbed parallel velocity.

On the dynamics of vortex modes within magnetic islands

Recent work investigating the interaction of magnetic islands with micro-turbulence has uncovered the striking observation of large scale vortex modes forming within the island structure [W. A. Hornsby et al., Phys. Plasmas 17, 092301 (2010)]. These electrostatic vortices are found to be the size of the island and are oscillatory. It is this oscillatory behaviour and the presence of turbulence that leads us to believe that the dynamics are related to the geodesic acoustic mode (GAM), and it is this link that is investigated in this paper. Here, we derive an equation for the GAM in the MHD limit, in the presence of a magnetic island modified three-dimensional axisymmetric geometry. The eigenvalues and eigenfunctions are calculated numerically and then utilised to analyse the dynamics of oscillatory large-scale electrostatic potential structures seen in both linear and non-linear gyro-kinetic simulations.

Toroidal momentum transport in a tokamak caused by symmetry breaking parallel derivatives

A new mechanism for toroidal momentum transport in a tokamak is investigated using the gyro-kinetic model. First, an analytic model is developed through the use of the ballooning transform. The terms that generate the momentum transport are then connected with the poloidal derivative of the ballooning envelope, which are one order smaller in the normalised Larmor radius, compared with the derivative of the eikonal. The mechanism, therefore, does not introduce an inhomogeneity in the radial direction, in contrast with the effect of profile shearing. Numerical simulations of the linear ion temperature gradient mode with adiabatic electrons, retaining the finite ρ* effects in the E × B velocity, the drift, and the gyro-average, are presented. The momentum flux is found to be linear in the normalised Larmor radius (ρ*) but is, nevertheless, generating a sizeable counter-current rotation. The total momentum flux scales linear with the aspect ratio of the considered magnetic surface, and increases with increasi...

Gyrokinetic and gyrofluid investigation of magnetic islands in tokamaks

The evolution of a tearing mode is a multi-scale problem, involving lengths from below the ion gyroradius up to the dimensions of the system. The effects due to finite ion Larmor radius on the island dynamics are investigated by means of numerical gyrokinetic and gyrofluid simulations in tokamak geometry. In gyrokinetic runs, the magnetic island is prescribed. The coupling induced by a static island between small and large scale fluctuations in the case of electrostatic turbulence is discussed and the role of the perturbed magnetic geometry on the electron response is highlighted. Simulations in the presence of a rotating island, excluding background turbulence, allow a clear, self-consistent determination of the electrostatic potential associated with the island rotation and of the relevant plasma profiles for arbitrary island widths. Finally, the first gyrofluid simulations showing the growth of an island in the presence of electromagnetic turbulence for parameters typical of a mid-size tokamak are presented.