Mapping the intrinsic stochasticity of tokamak divertor configuration

Barocio, S. R.; Chávez-Alarcón, E.; Gutiérrez-Tapia, C.

doi:10.1590/s0103-97332006000400014

Cited by 7 publications

(5 citation statements)

References 24 publications

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“…Consequently, the field line configuration can be represented in Poincaré sections at a fixed toroidal angle, equivalent to two-dimensional area-preserving maps [3,10,11]. Thus, we can use such maps to qualitatively represent the magnetic configurations of tokamak plasmas [14]. In this work, we present maps proposed to investigate the fundamental features of the magnetic field line dynamics in tokamaks with divertor.…”

Section: Introductionmentioning

confidence: 99%

Symplectic Maps for Diverted Plasmas

Caldas

Bartoloni

Ciro

et al. 2018

IEEE Trans. Plasma Sci.

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Nowadays, divertors are used in the main tokamaks to control the magnetic field and to improve the plasma confinement. In this article, we present analytical symplectic maps describing Poincaré maps of the magnetic field lines in confined plasmas with a single null poloidal divertor. Initially, we present a divertor map and the tokamap for a diverted configuration. We also introduce the Ullmann map for a diverted plasma, whose control parameters are determined from tokamak experiments. Finally, an explicit, area-preserving and integrable magnetic field line map for a single-null divertor tokamak is obtained using a trajectory integration method to represent toroidal equilibrium magnetic surfaces. In this method, we also give examples of onset of chaotic field lines at the plasma edge due to resonant perturbations.

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Section: Introductionmentioning

confidence: 99%

Symplectic Maps for Diverted Plasmas

Caldas

Bartoloni

Ciro

et al. 2018

IEEE Trans. Plasma Sci.

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“…Some of these maps have been obtained directly from the magnetic field equations [8][9][10] by means of a procedure that uses generalized Poincaré integrals [11]. Other divertor maps have been obtained by the mathematical construction of appropriate generating functions and canonical transformations [12][13][14][15][16]. Divertor maps using the geometry of the DIII-D tokamak have been obtained by fitting experimental data to find appropriate expressions for equilibrium Hamiltonians [17][18][19].…”

Section: Introductionmentioning

confidence: 99%

Divertor map with freedom of geometry and safety factor profile

Kroetz

Roberto

Caldas

et al. 2012

Plasma Phys. Control. Fusion

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An explicit, area-preserving and integrable magnetic field line map for a single-null divertor tokamak is obtained using a trajectory integration method to represent equilibrium magnetic surfaces. The magnetic surfaces obtained from the map are capable of fitting different geometries with freely specified position of the X-point, by varying free model parameters. The safety factor profile of the map is independent of the geometric parameters and can also be chosen arbitrarily. The divertor integrable map is composed of a nonintegrable map that simulates the effect of external symmetry-breaking resonances, so as to generate a chaotic region near the separatrix passing through the X-point. The composed field line map is used to analyze escape patterns (the connection length distribution and magnetic footprints on the divertor plate) for two equilibrium configurations with different magnetic shear profiles at the plasma edge.

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“…On the other hand, discrete time Poincaré maps are much faster to iterate and can yield reliable results on key features of divertor phenomenology, such as magnetic footprints and escape basins present in outer chaotic magnetic configurations in tokamaks [4,23,25]. In fact, in the past two decades many works on divertor physics have used discrete maps of various types and geometries [11,12,[26][27][28][29]. A series of symplectic maps for divertor fields were proposed in [30][31][32][33][34][35][36][37] to investigate the effect of different kinds of resonant perturbations on the field line topology.…”

Section: Introductionmentioning

confidence: 99%

“…Recently, a field line convection coefficient was added to this approach to estimate the chaotic transport near the magnetic separatrix [12,41]. Another canonical procedure to derive a map from magnetic field line equations was introduced in [26], where it was studied using parameters of the tokamak COMPASS-D.…”

Section: Introductionmentioning

confidence: 99%

Integrable maps with non-trivial topology: application to divertor configurations

Kroetz¹,

Roberto²,

Caldas³

et al. 2010

Nucl. Fusion

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We explore a method for constructing two-dimensional area-preserving, integrable maps associated with Hamiltonian systems, with a given set of fixed points and given invariant curves. The method is used to find an integrable Poincaré map for the field lines in a large aspect ratio tokamak with a poloidal single-null divertor. The divertor field is a superposition of a magnetohydrodynamic equilibrium with an arbitrarily chosen safety factor profile, with a wire carrying an electric current to create an X-point. This integrable map is perturbed by an impulsive perturbation that describes non-axisymmetric magnetic resonances at the plasma edge. The non-integrable perturbed map is applied to study the structure of the open field lines in the scrape-off layer, reproducing the main transport features obtained by integrating numerically the magnetic field line equations, such as the connection lengths and magnetic footprints on the divertor plate.

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Mapping the intrinsic stochasticity of tokamak divertor configuration

Cited by 7 publications

References 24 publications

Symplectic Maps for Diverted Plasmas

Symplectic Maps for Diverted Plasmas

Divertor map with freedom of geometry and safety factor profile

Integrable maps with non-trivial topology: application to divertor configurations

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