Mappings of stochastic field lines in poloidal divertor tokamaks

Abstract

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.

Experimental and numerical studies of separatrix splitting and magnetic footprints in DIII-D

“…The application of invariant manifold theory to magnetic field lines in realistic poloidally diverted tokamaks is most directly facilitated by using numerical field line integration and mapping codes such as TRIP3D [4] and TRIP3D_MAP [5] where the unperturbed axisymmetric field is derived from experimentally constrained equilibria, calculated with the EFIT Grad-Shafranov code [6], that includes the effects of the plasma pressure and current density. In addition, mapping codes used to study simplified wire models of poloidally diverted tokamaks [7] are valuable for comparing the properties of field line trajectories to a broader class generic behaviors defined by the dynamics of conservative vector fields Hamiltonian systems.…”

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

“…decreases exponentially while increasing p [10]. Therefore, the perturbing Hamiltonian is reduced to …”

“…In this appendix we present the unperturbed Hamiltonian equation, in ) , , (  Z R coordinates (see figure 1), introduced in [10], and used in the present article. Accordingly, the magnetic field line equations are:…”

“…Moreover, a Hamiltonian with three loop wires was analyzed in [10], to describe two mapping methods and to study the stochastic field lines in poloidal divertor tokamak plasmas affected by external non-axisymmetric magnetic perturbations.…”

“…Following reference [10], in the present work we analyze a Hamiltonian model with five loop wires that enables the choice of magnetic axis position, triangularity and elongation. The versatility of the model allows us to delineate equilibrium magnetic surfaces that reproduce ITER like magnetic topology, including a similar safety factor profile.…”