Abstract explicit expressions for the neoclassical poloidal and toroidal rotation speeds of primary ion and impurity species are derived via the hirshman and sigmar moment approach. Experimental evidence on contemporary tokamaks shows that the near central absorption of rf heating power ich and ech and current drive in presence of. Moreover, the measurements of the poloidal rotation have been compared with neoclassical theory in many tokamaks. To roidal rotation velocity is of the same order as poloidal rotation velocity at the plasma edge. Broken symmetry in tokamak equilibrium is caused by the toroidal field ripples and the external magnetic perturbations applied to mitigate the edgelocalized modes. Toroidal rotation impacts a variety of important plasmas physics topics. A new theory of spontaneous toroidal rotation and some thoughts page numberon neoclassical poloidal rotation in tokamaks m.
Perturbation field penetration is shielded by plasma rotation. Plasma equilibrium in presence of the poloidal flow in. There are several diagnostic systems designed to measure tokamak plasma rotation. When the axisymmetry of tokamak magnetic eld is broken, the toroidal canonical momentum p ivk is no longer a constant of motion, and guiding centers of trapped particles drift across the const. On steady poloidal and toroidal flows in tokamak plasmas. In conditions of ideal axisymmetry, for a magnetized plasma in a generic bounded domain, necessarily toroidal, the uniform absorption of external energy e. Solomon1 1princeton plasma physics laboratory, princeton university, princeton, nj 08543, usa 2general atomics, p. Structure of the radial electric field toroidalpoloidal flow. Some of the possible plasma particle and mo1 small gyroradius expansion, which to zeroth order. In accordance with torque mechanism it can be divided for middle size tokamaks into two types. Toroidal and poloidal flows in singlefluid and twofluid tokamak equilibria phys. This toroidal torque is represented as a toroidal viscosity, which is called the neoclassical toroidal plasma viscosity 4.
Stacey fusion research center georgia institute of technology atlanta, ga 30332, usa october, 2003 abstract a model for the calculation of toroidal rotation velocities and the radial electric field in the edge pedestal of tokamaks is described. Note some figures may be in color only in the electronic version. Many effects influence the evolution of toroidal rotation in tokamak plasmas. Electromagnetic torque in tokamaks with toroidal asymmetries. The effects of poloidal and toroidal flows on tokamak plasma equilibria are. Intrinsic plasma rotation determined by neoclassical. Rotation in tokamaks and stellarators university of oxford. Fluids b 3, 2050 1991 article pdf available in physics of fluids b plasma physics 49 september 1992 with 47.
The same phenomenon has also been observed in stellarator experiments 14. Hayashi 1 1 japan atomic energy agency, naka, japan 2 national institute for fusion science, toki, japan abstract. The neoclassical theory employed here is described in neoclassical poloidal and toroidal rotation in tokamaks, y. A new theory of spontaneous toroidal rotation and some. Note that the poloidal rotation is independent of the radial electric field. Theory for neoclassical toroidal plasma viscosity in tokamaks. Box 85608, san diego, ca 921865608, usa corresponding author. Experimental tests of the theory of poloidal rotation in the.
Plasma rotation in tokamaks university of texas at austin. Toroidal plasma rotation in the tcv tokamak citeseerx. In addition, the toroidal rotation can be a ected by magnetic eld errors, which this work concentrates on. With the toroidal rotation generally outranking the poloidal rotation by an order of magnitude, this in itself can be a substantial offset. Driftkinetic simulation studies on neoclassical toroidal. It can be used to control toroidal plasma rotation in fusion grade tokamak experiments such as iter. It is known that the neoclassical toroidal plasma viscosity results in a steady state toroidal rotation even without momentum sources. Rotating nonlinear magnetic islands in a tokamak plasma. Explicit expressions for the neoclassical poloidal and toroidal rotation speeds of primary ion and impurity species are derived via the hirshman and sigmar moment approach. Toroidal rotation driven by the neoclassical toroidal. Comparison of deuterium toroidal and poloidal rotation to. Low collisionality neoclassical toroidal viscosity in tokamaks and quasisymmetric stellarators using an integraltruncation technique a. The contribution of toroidal rotation velocity to the electric field is much.
Neoclassical poloidal and toroidal rotation in tokamaks. Second, it is unlikely that rotation in the core of large and dense tokamaks can be produced by means of neutral beam momentum injection 6. This recalibration method is valid only in the weak rotation limit applicable to most diiid plasmas, since then the neoclassical ow coe cient does not depend on the radial electric eld. We make a number of assumptions to facilitate determining comprehensive equations for the particle. Structure of the radial electric field and toroidalpoloidal flow in high temperature toroidal plasma drift orbit is small enough compared with the neoclassical non ambipolar loss.
Pdf neoclassical poloidal and toroidal rotation in tokamaks. Neoclassical poloidal and toroidal rotation in tokamaks phys. Comparison of neoclassical predictions with measured flows. This diagnostic uses charge exchange recombination spectroscopy to measure toroidal rotation on the high and lowfield side of the tokamak midplane to determine the poloidal rotation from a divergencefree description of flow within fluxsurfaces. By comparing the measured rotational velocities, and using the radial force balance relation, the mainion poloidal rotation can be inferred and compared to the neoclassical values. Momentum sources and radial plasma transport due to axisymmetric neoclassical and paleoclassical as well as microturbulenceinduced anomalous processes are usually considered. Simulations of toroidal rotation driven by the neoclassical. In the steady state in the absence of momentum sources and sinks it is explicitly evaluated by the condition that radial ux of toroidal angular momentum vanishes. Neoclassical poloidal flow damping frequency is of the form. In tokamaks, due to the importance of toroidal rotation that suppresses magnetohydrodynamic mhd instabilities and turbulence, extensive research has been done from the aspects of theory, modelling and experiments in recent years and it brings better physical understanding of toroidal rotation and toroidal momentum transport. Callen university of wisconsin, madison, wi 537061609 dated. Toroidal rotation is critical to the experimental control of tokamaks.
Neoclassical poloidal and toroidal rotation in tokamaks article pdf available in physics of fluids b plasma physics 38. Poloidal flow damping produces parallel plasma flow. Atoms free fulltext poloidal rotation and edge ion. But a toroidally rotating plasma in the axisymmetric tokamaks does not suffer the magnetic pumping effect since the neoclassical transport. For tokamaks, the poloidal rotation is generally damped due to the magnetic pumping effects, which transfer the plasma kinetic energy into thermal energy, and eventually, towards the neoclassical value. A neoclassical model for toroidal rotation and the radial electric field in the edge pedestal w. With the toroidal rotation generally outranking the poloidal rotation by. The tokamak is one of several types of magnetic confinement devices being developed to produce controlled thermonuclear fusion power.
The broken symmetry in tokamaks gives rise to the neoclassical toroidal viscosity ntv which has a potential to change the toroidal rotation profile substantially. Evaluation of the neoclassical radial electric field in a. The poloidal component of the velocity is given by ti and rotation velocity is. Liang4 1 institute of plasma physics, chinese academy of sciences, po box 1126, hefei 230031, peoples republic of china 2 institute for space, astrophysical and plasma sciences, national cheng kung unversity. Intrinsic plasma rotation determined by neoclassical toroidal. Neoclassical calculation of poloidal rotation and poloidal density asymmetries in tokamaks article pdf available in physics of plasmas 99 september 2002 with 11 reads how we measure reads. Mit plasma science and fusion center, cambridge, ma, usa. Turbulent momentum transport due to neoclassical ows arxiv.
This method of comparison is done by forward modeling with neoclassical codes, as well as deducing the. In accordance with the conventional orderings of neoclassical theory, poloidal and toroidal accelerations with constant parallel flow can be driven by heat transport in the absence of external momentum input and with vanishing parallel viscous stress. Understanding and controlling plasma rotation in tokamaks. Instead, we suppose that poloidal flow is present in our discussion.
In previous experiments 1721, the transition from ion root to electron root was observed only in plasmas with ech. The rotation speeds of the primary ion can be significantly different from those of impurities in various interesting cases. Comparison of measured poloidal rotation in mast plasmas with. On top of these poloidal and toroidal field components radial and. Centrifugal and fastion effects on poloidal impurity density. Theoretical study of ion toroidal rotation in the presence of lower hybrid current drive in a tokamak by jungpyo lee submitted to the department of nuclear science. A general comparison between tokamak and stellarator plasmas. Intrinsic plasma rotation determined by neoclassical toroidal plasma viscosity in tokamaks y. Haines imperial college, london sw7 2az, blackett laboratory for an axisymmetric, magnetically confined toroidal plasma, the rate of change of angular momentum density is given by 1 here p. Extension and comparison of neoclassical models for.
Radial transport of toroidal angular momentum in tokamaks. Previous efforts to handle the gyroorbit correction on tftr 5 have concentrated on using extensive and complicated atomic physics calculations to model the effective lifetime of the excited state. Plasma rotation measurement in small tokamaks using an. Several neoclassical models for the calculation of poloidal rotation in tokamaks were rederived within a common framework, extended to include additional physics and numerically compared. Neoclassical offset toroidal velocity and auxiliary ion. Neoclassical toroidal viscosity calculations in tokamaks. In a transient phase in which the heat transport is the primary source of the time dependence, the torque generating the rotation is provided. Describing toroidal rotation in tokamaks is a transport problem to date, most treatments describing toroidal rotation evolution rely on. Phase locking of multihelicity neoclassical tearing modes in. Eulerian simulations of neoclassical flows and transport in. Plasma equilibrium in presence of the poloidal flow in tokamaks.
The new poloidal rotation diagnostic has been developed on the diiid tokamak. Poloidal spin up and electricfield generation related to. Neoclassical predictions of the poloidal velocity qualitatively were found to disagree with recent measurements at the. Pdf neoclassical calculation of poloidal rotation and. Accurate calculation method for ntv is required to predict control the. Simulations of toroidal rotation driven by the neoclassical toroidal viscosity in tokamaks m. The poloidal component of the velocity is given by ti and rotation velocity is derived from width and shift of cxrs spectral lines. Neoclassical poloidal plasma rotation in an ion cyclotron heated tokamak revisited. Introduction recognition of both the importance of plasma rotation to the stable magnetic confinement of plasmas in tokamaks e.
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