The low MN map for single-null divertor tokamaks

Ali, Halima; Punjabi, Alkesh; Boozer, Allen H.; Evans, T.E.

doi:10.1063/1.1691455

Cited by 28 publications

(35 citation statements)

References 31 publications

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“…Then the field line with (ϕ k , h k ) is mapped to the divertor plane using mapping (39). In the latter mapping the increment of the toroidal angle, ϕ, for the geometry of the divertor plates shown in figure 12 is determined by (15), where ξ = X d /R 0 . The radial coordinate R of the footprint can be found using the relation (13) between the relative poloidal flux, h d , and the unperturbed Hamiltonian, i.e.…”

Section: Structure Of Magnetic Footprintsmentioning

confidence: 99%

“…If the divertor plate d is sufficiently close to the X-point the quantity ϕ(h) can be estimated by equation (15).…”

Section: Mappings To the Divertor Platesmentioning

confidence: 99%

“…Mapping approaches to study magnetic field lines near the separatrix in divertor tokamaks have been developed in [10][11][12][13][14][15][16][17][18][19]. The mappings are computationally efficient and they run much faster than the numerical integration of field line equations.…”

Section: Introductionmentioning

confidence: 99%

“…The mappings are computationally efficient and they run much faster than the numerical integration of field line equations. In [10][11][12][13][14][15] the simple mapping models, called tokamak divertor maps, are proposed to describe the field lines in poloidal divertor tokamaks. These areapreserving maps are simple algebraic difference equations.…”

Section: Introductionmentioning

confidence: 99%

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Mappings of stochastic field lines in poloidal divertor tokamaks

et al. 2006

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Two mapping methods to study magnetic field lines near the separatrix of poloidal divertor tokamaks in the presence of external non-axisymmetric magnetic perturbations are proposed. The first mapping method is based on the Hamiltonian formulation of field line equations in the Boozer coordinates and solving it by the canonical transformation of variables (Abdullaev et al 1999 Phys. Plasmas 6 153). The second mapping is a canonical mapping near the separatrix which is constructed using the recently developed method (Abdullaev 2004 Phys. Rev. E 70 064202, Abdullaev 2005 Phys. Rev. E 72 064202). We construct the corresponding mappings for magnetic field lines in divertor tokamaks in the presence of non-axisymmetric magnetic perturbations. The mappings are applied to study the properties of open stochastic field lines near the separatrix for the wire model of the plasma. Poincaré sections, the so-called laminar and magnetic footprint plot (a contour plot of wall to wall connections lengths) in the plasma region and on the divertor plates are obtained. The quasilinear diffusion coefficients of field lines are also estimated.

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Section: Structure Of Magnetic Footprintsmentioning

confidence: 99%

“…If the divertor plate d is sufficiently close to the X-point the quantity ϕ(h) can be estimated by equation (15).…”

Section: Mappings To the Divertor Platesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Mappings of stochastic field lines in poloidal divertor tokamaks

et al. 2006

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“…Due to the flexibility of models based on magnetic fields produced by wires, one can consider different effects by adequately specifying the perturbations. Thus, perturbed wire models have been used to analyze a range of dynamical properties in double-null (two X-points) and single-null (one X-point) diverted tokamaks, such as, the width of the scrape-off layer [12], chaotic layer formation [13][14][15] and particle drift orbits [16].…”

Section: Introductionmentioning

confidence: 99%

Delineating the magnetic field line escape pattern and stickiness in a poloidally diverted tokamak

2014

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We analyze a Hamiltonian model with five wire loops that delineates the magnetic surfaces of the tokamak ITER, including a similar safety factor profile and the X-point related to the presence of a poloidal divertor. Non-axisymmetric magnetic perturbations are added by external coils, similar to the correction coils installed at the tokamak DIII-D and those that will be installed at ITER. To show the influence of magnetic perturbations on the field line escape, we integrate numerically the field line differential equations and obtain the footprints and deposition patterns on the divertor plate.Moreover, we show that the homoclinic tangle describes the deposition patterns in the divertor plate, agreeing with results observed in sophisticated simulation codes. Additionally, we show that while chaotic lines escape to the divertor plates, some of them are trapped, for many toroidal turns, in complex structures around magnetic islands, embedded in the chaotic region, giving rise to the so called stickiness effect characteristic of chaotic Hamiltonian systems. Finally, we introduce a random collisional term to the field line mapping to investigate stickiness alterations due to particle collisions. Within this model, we conclude that, even reduced by collisions, stickiness still influences the field line transport.

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Stochastic Transport of Magnetic Field Lines in the Symmetric Tokamap

Wingen

Spatschek

Abdullaev

2005

Contrib. Plasma Phys.

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The topological structure and the statistical properties of stochastic magnetic fields are investigated on the basis of the so called tokamap. First, a monotonic safety factor (q-profile) is assumed. As it is demonstrated, the transition from the continuous model to the discrete mapping in its symmetric form is essential, not only for the symplectic structure, but also for the precise values characterizing the transition to chaos (e.g. the break-up of the KAM surfaces) in applications. Statistical properties of the symmetric tokamap, such as escape rates and anomalous diffusion properties, are being presented. By a systematic procedure the stable and unstable manifolds of the periodic hyperbolic fixed points and the resulting homoclinic tangles (stochastic layers) are determined. The latter are important for the magnetic field line transport. For a non-monotonic q-profile, the differences between the symmetric and non-symmetric revtokamap become also significant. The symmetric revtokamap represents an open nonlinear dynamical system which is characterized here with the relevant tools.

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The low MN map for single-null divertor tokamaks

Cited by 28 publications

References 31 publications

Mappings of stochastic field lines in poloidal divertor tokamaks

Mappings of stochastic field lines in poloidal divertor tokamaks

Delineating the magnetic field line escape pattern and stickiness in a poloidally diverted tokamak

Stochastic Transport of Magnetic Field Lines in the Symmetric Tokamap

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