Noble magnetic barriers in the ASDEX UG tokamak

作者：Ali Halima; Punjabi Alkesh^*; Vazquez Justin

来源：Radiation Effects and Defects in Solids, 2010, 165(2): 83-95.

DOI：10.1080/10420150903497265

• Hamiltonian systems
• chaos
• invariant torus
• tokamak
• magnetic perturbation
• magnetic barrier

The second-order perturbation method of creating invariant tori inside chaos in Hamiltonian systems (Ali, H.; Punjabi, A. Plasma Phys. Contr. F. 2007, 49, 1565-1582) is applied to the axially symmetric divertor experiment upgrade (ASDEX UG) tokamak to build noble irrational magnetic barriers inside chaos created by resonant magnetic perturbations (m, n) = (3, 2) + (4, 3), with m and n the poloidal and toroidal mode numbers of the Fourier expansion of the magnetic perturbation. The radial dependence of the Fourier modes is ignored. The modes are considered to be locked and have the same amplitude delta. A symplectic mathematical mapping in magnetic coordinates is used to integrate magnetic field line trajectories in the ASDEX UG. Tori with noble irrational rotational transform are the last ones to be destroyed by perturbation in Hamiltonian systems. For this reason, noble irrational magnetic barriers are built inside chaos, and the strongest noble irrational barrier is identified. Three candidate locations for the strongest noble barrier in ASDEX UG are selected. All three candidate locations are chosen to be roughly midway between the resonant rational surfaces psi(32) and psi(43). psi is the magnetic coordinate of the flux surface. The three candidate surfaces are the noble irrational surfaces close to the surface with q value that is a mediant of q = 3/2 and 4/3, q value of the physical midpoint of the two resonant surfaces, and the q value of the surface where the islands of the two perturbing modes just overlap. These q values of the candidate surfaces are denoted by q(MED), q(MID), and q(OVERLAP). The strongest noble barrier close to q(MED) has the continued fraction representation (CFR) [1; 2,2,1(infinity)] and exists for delta <= 2.6599 x 10(-4); the strongest noble barrier close to q(MID) has CFR [1; 2,2,2,1(infinity)] and exists for delta <= 4.6311 x 10(-4); and the strongest noble barrier close to q(OVERLAP) has CFR [1; 2,2,6,2,1(infinity)] and exists for delta <= 1.367770 x 10(-4). From these results, the strongest noble barrier is found to be close to the surface that is located physically exactly in the middle of the two resonant surfaces.

• 出版日期2010