Calculation of Hamada coordinates for a large-aspect-ratio tokamak

Coronado, M.; Trejo, Jesús Galindo

doi:10.1063/1.859343

Cited by 16 publications

(9 citation statements)

References 8 publications

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“…To calculate the flux surface averages noted above and to compare these neoclassical flow direction predictions to labframe measurements, it is necessary to know the Hamada coordinate basis vectors. In previous modeling, the basis vectors for a large aspect ratio circular tokamak 39 were used to approximate the stellarator basis vectors. Given that HSX has essentially no toroidal curvature, the use of the tokamak basis vector approximation is not justified.…”

Section: -mentioning

confidence: 99%

Measurements and modeling of plasma flow damping in the Helically Symmetric eXperiment

et al. 2005

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Fusion Technology 27, 273 ͑1995͔͒ using a biased electrode to impulsively spin the plasma and Mach probes to measure the rotation. There is a distinct asymmetry between the spin-up when the bias is initiated and relaxation when the electrode current is broken. In each case, two time-scales are observed in the evolution of the plasma flow. These observations motivate the development of new neoclassical modeling techniques, including a new model where the fast increment of the electric field initiates the spin-up process. The flow in the quasisymmetric configuration rises more slowly and to a higher value than in a configuration with the quasisymmetry broken, and the rise time-scale is in reasonable agreement with the neoclassical spin-up model. The flows decay more slowly in the quasisymmetry configuration than in the configuration with the quasisymmetry broken, although the decay rates are significantly faster than the neoclassical prediction.

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Section: -mentioning

confidence: 99%

Measurements and modeling of plasma flow damping in the Helically Symmetric eXperiment

et al. 2005

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“…The Hamada coordinate system has a Jacobian J = 1 and and in this case the term n k u·(b×t) is equal to the local radial particle flux times b t or b p depending on the choice of the tangential base vector. How to compute the Hamada coordinate system in tokamak geometry has been demonstrated in [24], [27]. Further driving terms are the tangential inertial forces and the tangential electric field.…”

Section: Spin-up Equationsmentioning

confidence: 99%

“…m e n 0 ν ee (24) ν ee (T 0 , n 0 ) is the electron collision frequency at the reference point n 0 , T 0 . Using these definitions the momentum balance and the equation of continuity in non-dimensional formulation become (25) and…”

Section: Spin-up Equationsmentioning

confidence: 99%

Rotation of a multi-species plasma in a cylinder

Sünder¹,

Wobig²

2006

Plasma Phys. Control. Fusion

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The paper investigates the momentum balance of a multi-species plasma in a cylinder with helical magnetic field. The main magnetic field is oriented in the z-direction. Starting from the macrocopic equations, a steady-state solution is obtained which includes the effect of centrifugal forces and Coriolis forces. The poloidal rotation and axial flow of each particle species is governed by the balance between spin-up, viscous damping, turbulent forces and the v × B driving term. In cylindrical geometry, classical viscous effects are very small and can easily be dominated by the turbulent viscosity. The effect of turbulent Reynolds stresses and the turbulent viscosity is investigated. Under quite general assumptions about the dependence of the anomalous transport coefficients on the velocity shear, criteria on the existence of the bifurcation points and multiple solution can be formulated. The shaping of the velocity shear and the transport barrier depend strongly on the eddy viscosity. Numerical solutions of the differential equations for a two-component plasma support the analytical results. The viscosity is considered as a variable parameter simulating the effect of turbulent eddy viscosity. These computations will be compared with the experimental results found in the HDH-mode experiments in Wendelstein 7-AS.

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“…In this paper, we define the poloidal and toroidal Hamada coordinates ␣ and , to vary between 0 and 2, not between 0 and 1 as in Ref. 7. Also, we use the flux function as the Hamada radial coordinate rather than the volume.…”

Section: Large-aspect-ratio Tokamak Approximationmentioning

confidence: 99%

“…Finally, we convert the results in Ref. 7 to the same R, Z, coordinate system in which the basis vectors for HSX are calculated, rather than the original r, , . The toroidal angle in both coordinate systems increases in the clockwise direction, looking down.…”

Section: Large-aspect-ratio Tokamak Approximationmentioning

confidence: 99%

Numerical calculation of the Hamada basis vectors for three-dimensional toroidal magnetic configurations

Talmadge

Gerhardt

2005

Physics of Plasmas

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The moment equation approach to neoclassical transport is used to calculate neoclassical particle and heat fluxes, impurity transport, the ambipolar electric field, and momentum damping rates. These equations are often written in Hamada coordinates which makes it easier to obtain analytic solutions. However, previous simplifying assumptions used to evaluate the basis vectors analytically are often invalid for advanced stellarator configurations. In this paper, a numerical method is presented by which the Hamada basis set can be determined for an arbitrary three dimensional toroidal confinement device by integrating along a magnetic field line. The method is applied to the magnetic configuration in the Helically Symmetric Experiment ͓F. S. B. Anderson, A. F. Almagri, D. T. Anderson, P. G. Matthews, J. N. Talmadge, and J. L. Shohet, Fusion Technol. 27, 273 ͑1995͔͒ and compared to the large-aspect-ratio tokamak approximation to the basis set. The results indicate that the numerical technique is a more accurate method to specify the basis vectors, especially in a device with negligible toroidal curvature.

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Calculation of Hamada coordinates for a large-aspect-ratio tokamak

Cited by 16 publications

References 8 publications

Measurements and modeling of plasma flow damping in the Helically Symmetric eXperiment

Measurements and modeling of plasma flow damping in the Helically Symmetric eXperiment

Rotation of a multi-species plasma in a cylinder

Numerical calculation of the Hamada basis vectors for three-dimensional toroidal magnetic configurations

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