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Escaping of the chaotic magnetic field lines a tokamak wall


Chaotic field lines can be generated by an ergodic magnetic limiter (EML), which consists of slices of external helical conductors with a suitable pitch. In this project we propose to study the escape of these field lines towards the wall. We use a non-monotonic safety factor profile to obtain the spatial escape patterns at the tokamak wall. These patterns are similar to the measurements of the heat flux patterns in tokamaks such as Textor [1]. It seems that such spatial patterns are determined by the chaotic saddle of the hyperbolic points. We also propose to generate a perturbation using a current ring parallel to plasma current, to create an X point in the most external magnetic surface, such as a poloidal divertor. We will use the same methodology of our preview works with the EML. Moreover, we propose to obtain a conservative map for the MHD equilibrium with an X point, following the methodology described by Morrison [2]. Since the axisymmetric equilibrium magnetic field lines can be interpreted as Hamiltonian dynamic system, we may set the azimuthal angle as a time-like variable. We can start with a Hamiltonian H=y2/2 + V(x), where V(x) presents minimum and maximum points in such a way that the last magnetic surface generated by this Hamiltonian has the divertor shape. The map can be obtained taking the winding number with a radial dependence, since the safety factor (which is just the inverse of the winding number) of a tokamak has a radial dependence. One can choose a safety factor profile with realistic parameters observed in magnetic configurations.[1] Wingen, A., et al. Physics of Plasmas 14, 042502, 2007[2] Abbamonte, P.M., Morrison, P.J. DOE/ET-55088-638, 1994. (AU)

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