The interaction of passing-ion drift orbits with spatially-inhomogeneous but purely diffusive radial transport is demonstrated to cause spontaneous toroidal spin-up to experimentally-relevant values in the tokamak edge. Physically, major-radial orbit shifts cause orbit-averaged diffusivities to depend on parallel velocity, including its sign, leading to residual stress. The resulting intrinsic rotation scales with ion temperature over poloidal magnetic field strength, resembling typical experimental scalings. Additionally, an inboard (outboard) X-point is expected to enhance co- (counter-) current rotation.
Toroidal rotation is well known to play significant roles in the edge transport and L-H transition dynamics of tokamaks. Our recent calculation finds that a sufficiently strong localized toroidal rotation can directly bring out the formation of edge pressure pedestal with reversed magnetic shear that is reminiscent of an H-mode plasma, purely through the effects of toroidal rotation on the tokamak MHD equilibrium itself. In particular, the enhanced edge toroidal rotation enables a substantial peaking of the parallel current profile near edge in higher $β$ regimes, which leads to the flattening…
Calculation of large-aspect-ratio tokamak and toroidally-averaged stellarator equilibria of high-beta reduced magnetohydrodynamics via simulated annealing
The Grad-Shafranov equation is solved using spectral elements for tokamak equilibrium with toroidal rotation. The Grad-Shafranov solver builds upon and extends the NIMEQ code [Howell and Sovinec, Comput. Phys. Commun. 185 (2014) 1415] previously developed for static tokamak equilibria. Both geometric and algebraic convergence are achieved as the polynomial degree of the spectral-element basis increases. A new analytical solution to the Grad-Shafranov equation is obtained for Solov'ev equilibrium in presence of rigid toroidal rotation, in addition to a previously obtained analytical solution fo…
We analyze an axisymmetric equilibrium of a plasma endowed with toroidal and poloidal velocity fields, with the aim to characterize the influence of the global motion on the morphology of the magnetic confinement. We construct our configuration assuming that the poloidal velocity field is aligned with the poloidal magnetic field lines and, furthermore, we require that the plasma mass density depend on the magnetic flux function (or equivalently, that the plasma fluid be incompressible). We then derive a sort of Grad-Shafranov equation for such an equilibrium and implement it to tokamak relevan…
In the presence of energetic particles (EPs), the Long-Lived Mode (LLM) frequency multiplication with n = 1,2,3 or higher is often observed on HL-2A, where n is the toroidal mode number. Hybrid kinetic-MHD model simulations of the energetic particle (EP) driven kink/fishbone modes on a static HL-2A-like tokamak using NIMROD code find that, when the background plasma pressure is relatively high, and the EP pressure and the beam energy are relatively low, the mode frequency increases almost linearly with EP pressure, and the frequency is proportional to n ("frequency multiplication"), even in ab…
The shear Alfvén continuum spectrum is studied for a tokamak with a single island chain using the ideal Magnetohydrodynamics (MHD) theory. We have taken into account the toroidal geometry and toroidal mode coupling with the island considered as a highly-shaped stellarator. Various new frequency gaps open up inside the island due to its asymmetry both poloidally and toroidally, such as the Mirror-induced Alfvén Eigenmode (MAE) gap and the Helicity-induced Alfvén Eigenmode (HAE) gap. We have shown that the MAE gap acts as the continuation of the outside Toroidal Alfvén Eigenmode (TAE) gap into t…
We show that zonal flow can be preferentially excited by intermediate-scale toroidal electron temperature gradient (ETG) turbulence in tokamak plasmas. Previous theoretical studies that yielded an opposite conclusion assumed a fluid approximation for ETG modes. Here, we carry out a gyrokinetic analysis which ultimately yields a nonlinear Schrödinger equation for the ETG dynamics with a Navier-Stokes type nonlinearity. For typical tokamak parameters, it is found that zonal flow generation plays an important role in the intermediate-scale ETG turbulence. This finding offers an explanation for re…
Hollow toroidal rotation profiles in strongly electron heated H-mode plasmas in the ASDEX Upgrade tokamak
Max Planck Institute for Plasma Physics（马克斯·普朗克等离子体物理研究所）；Department of Applied Physics and Applied Mathematics, Columbia University（哥伦比亚大学应用物理与应用数学系）；VTT（芬兰技术研究中心VTT）
Conceptual study on using Doppler backscattering to measure magnetic pitch angle in tokamak plasmas
Future Energy Acceleration and Translation Programme, Agency of Science, Technology and Research (A*STAR)（未来能源加速与转化计划，科学与技术研究局）；Department of Physics, University of Oxford（牛津大学物理系）；Department of Physics and Astronomy, University of California, Los Angeles（加州大学洛杉矶分校物理与天文学系）；Lawrence Livermore National Laboratory（劳伦斯利弗莫尔国家实验室）；Department of Physics, National University of Singapore（新加坡国立大学物理系）；Commonwealth Fusion Systems（联邦聚变系统）；Princeton Plasma Physics Laboratory（普林斯顿等离子体物理实验室）；Rudolf Peierls Centre for Theoretical Physics, University of Oxford（牛津大学鲁道夫·佩尔斯理论物理中心）
I present the results of the analytic plane strain optimization of the structure and conductor grading in the inner leg of a Tokamak toroidal field coil. The coil is assumed to be made of regions of soft conductor inside a stiff grid of conduit. Calculus of variations is used to determine the optimal profile of this structure. The optimal solution is found to be two-layered. An outer layer is bucked only, not wedged, and the structure fraction is graded so that all structure is at a uniform stress. An inner layer is an advanced bucking cylinder, similar to a Florida Bitter plate, whose radial …
The paper presents a relativistic mechanism that can create a poloidal non-uniformity of a radial electric field on a magnetic surface in a tokamak plasma. This mechanism is associated with a significant current velocity of electrons in plasma for many experimental modes of tokamak operations. It is important that electric fields arise without the traditional separation of charges in plasma. The presented mechanism can explain the previously experimentally measured poloidal non-uniformity of the C+6 carbon ion toroidal rotation velocity in the TORE-SUPRA tokamak plasma
Spontaneous spin-up are widely observed in tokamak plasmas, which is crucially important for plasma confinement. A kinetic theory is proposed to show that a toroidal rotation of core plasma is induced by the topological transition of orbits driven by turbulent diffusion in a collisionless tokamak plasma. The theoretical prediction agrees well with the well-known Rice-scaling of intrinsic core plasma flow. This new theory predicts an intrinsic core parallel flow of $\sim 100km/s$ for the International Thermonuclear Experimental Reactor.
