Numerical simulation of the plasma equilibrium in a Tokamak

Blum, Jacques

doi:10.1016/0167-7977(87)90015-3

Cited by 15 publications

(23 citation statements)

References 14 publications

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“…In this method, it is possible to evaluate anisotropic stored energy using diamagnetic coils and saddle coils. On the other hand, the reconstruction of a current profile from external magnetic data only is a mathematically ill-posed problem [7]. Therefore, such a plasma pressure profile is required to solve this problem.…”

Section: Introductionmentioning

confidence: 99%

Principles for local measurement of anisotropic electron temperature of plasma using incoherent Thomson scattering

2011

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Anisotropic electron temperature can be measured by utilizing two Thomson scattering spectra from different scattering angles. The ideal conditions for measurement are as follows: the sum of the two scattering angles is 180°, and the magnetic field is parallel to the bisector of the angle formed by the direction of laser propagation and the line of sight or is perpendicular to this bisector. When these conditions are satisfied, one of the spectra predominantly reflects the parallel electron temperature, and the other spectrum predominantly reflects the perpendicular electron temperature. A deviation in the direction of magnetic field of the order of approximately a few tens of degrees from the ideal direction is acceptable in terms of the deviation obtained by both rotating parallel to and tilting from the scattering plane.

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Section: Introductionmentioning

confidence: 99%

Principles for local measurement of anisotropic electron temperature of plasma using incoherent Thomson scattering

2011

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“…From an assumption of axial symmetry, the problem is reduced to a plane section. Then, it follows from the Grad-Shafranov equation, a second-order elliptic nonlinear partial differential equation, see [24,25], that the magnetic flux in the vacuum between the plasma and the circular boundary of the chamber satisfies the homogeneous equation (5). Note, that in this instance, the conductivity equation (5) takes place in an annular domain, that is a doubly connected domain.…”

Section: Introduction and Main Resultsmentioning

confidence: 99%

A Boundary Value Problem for Conjugate Conductivity Equations

2016

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We give explicit integral formulas for the solutions of planar conjugate conductivity equations in a circular domain of the right half-plane with conductivity σ (x, y) = x p , p ∈ Z * . The representations are obtained via the so-called unified transform method or Fokas method, involving a RiemannHilbert problem on the complex plane when p is even and on a two-sheeted Riemann surface when p is odd. They are given in terms of the Dirichlet and Neumann data on the boundary of the domain. For even exponent p, we also show how to make the conversion from one type of conditions to the other by using the global relation that follows from the closedness of some differential form. The method used to derive our integral representations could be applied in any bounded simply connected domain of the right half-plane with a smooth boundary.

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“…We refer to standard text books, e.g. (Freidberg 1987), (Blum 1987), (Wesson 2004), (Goedbloed & Poedts 2004), (Goedbloed et al 2010) and (Jardin 2010) for the details and state in the following paragraphs only the final equations describing the static and evolution problems solved in CEDRES++.…”

Section: )mentioning

confidence: 99%

“…In particular the second term on the right hand side seems to blow up if ψ reaches a critical point. Also in (Blum 1987), it is shown that the derivative of J p (ψ, ξ) in the direction ψ vanishes: D ψ J p (ψ, ξ)(ψ) = 0. Then the Newton scheme for solving Problem 10 is the following iteration: Let (ψ n , λ n ) be the solution at the n-th iteration.…”

Section: )mentioning

confidence: 99%

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Quasi-static free-boundary equilibrium of toroidal plasma with CEDRES++: Computational methods and applications

et al. 2015

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We present a comprehensive survey of the various computational methods in CEDRES++ for finding equilibria of toroidal plasma. Our focus is on free-boundary plasma equilibria, where either poloidal field coil currents or the temporal evolution of voltages in poloidal field circuit systems are given data. Centered around a piecewise linear finite element representation of the poloidal flux map, our approach allows in large parts the use of established numerical schemes. The coupling of a finite element method and a boundary element method gives consistent numerical solutions for equilibrium problems in unbounded domains. We formulate a new Newton method for the discretized nonlinear problem to tackle the various non-linearities, including the free plasma boundary. The Newton method guarantees fast convergence and is the main building block for the inverse equilibrium problems that we can handle in CEDRES++ as well. The inverse problems aim at finding either poloidal field coil currents that ensure a desired shape and position of the plasma or at finding the evolution of the voltages in the poloidal field circuit systems that ensure a prescribed evolution of the plasma shape and position. We provide equilibrium simulations for the tokamaks ITER and WEST to illustrate the performance of CEDRES++ and its application areas.Here again, this is a straightforward and simple calculation for all mappings except one: the mapping J P,h that is related to the non-linear current profile in the plasma domain. The mapping J P,h is given by

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Numerical simulation of the plasma equilibrium in a Tokamak

Cited by 15 publications

References 14 publications

Principles for local measurement of anisotropic electron temperature of plasma using incoherent Thomson scattering

Principles for local measurement of anisotropic electron temperature of plasma using incoherent Thomson scattering

A Boundary Value Problem for Conjugate Conductivity Equations

Quasi-static free-boundary equilibrium of toroidal plasma with CEDRES++: Computational methods and applications

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