Building magnetic barriers in tokamaks

Abstract

The second order perturbation method of creating invariant manifold inside chaos in Hamiltonian systems (Ciraolo G et al 2004 J. Phys. A: Math. Gen. 37 3589; Ciraolo G et al 2004 Phys. Rev. E 69 056213; Vittot M 2004 Phys. A: Math. Gen. 37 6337; Chandre C et al 2005 Phys. Rev. Lett. 94 074101) is applied to tokamaks to build magnetic barriers inside the region of magnetic chaos created by resonant magnetic perturbations. A symplectic map in magnetic coordinates is derived for calculation of magnetic field line trajectories in toroidal magnetic confinement configurations for fusion plasmas. A class of safety factor, q, profiles is chosen to represent the Ohmically heated tokamaks (OHT), the DIII-D and the ASDEX UG devices. For OHT, the equilibrium poloidal flux is calculated from the standard safety factor profile. Magnetic perturbation in OHT are poloidal mode number m = 3 and toroidal mode number n = 2 and m = 2, n = 1. A magnetic barrier is created at about midway between these two resonant magnetic surfaces. The barrier reduces the diffusion of magnetic field lines roughly by half. The barrier is fortified by adding up to third order magnetic perturbation for the amplitude of the tearing modes, δ < 2.25 × 10−3. For δ > 2.25 × 10−3, the barrier is not sustainable. A close-by noble barrier is found to be much more robust. For the DIII-D, equilibrium poloidal flux is calculated from the data for shot 115467 at 3000 ms. The magnetic perturbation chosen in the case of the DIII-D q-profile has mode numbers (m, n) equal to (3,1) and (4,1). A magnetic barrier is created inside chaos for the DIII-D q-profile by adding the second order magnetic perturbation to equilibrium poloidal flux. The robustness of this barrier in the DIII-D against topological noise is studied. For the ASDEX UG q-profile, (3,2) and (4,3) modes are chosen and a barrier is created about midway by the second order magnetic perturbation.