《稳定和不稳定流形在扰动下的一阶偏移公式及其在磁约束聚变中的应用》

Author: Wenyin Wei (魏wèi ~ 文wén 崟yín) and Yunfeng Liang (梁liáng ~ 云yún 峰fēng)
Conference: The 49th European Conference on Plasma Physics (2023) EPS48, 欧洲物理年会第 49 届等离子体分会
Poster Number: Tu_MCF33
Time: July 4th 2022, Tuesday, 2:00-4:00 p.m., Poster Session
Abstract pdf: here is the download link.
Poster pdf: please send an email to Wenyin to ask for it: wenyin.wei@ipp.ac.cn .
Research Gate link: https://www.researchgate.net/publication/372364544_First-order_shift_formula_of_stable_and_unstable_manifolds_under_perturbation_and_its_application_in_magnetic_confinement_fusion

Abstract:
In the established theory [1,2] of the global structure of three-dimensional (3D) magnetic fields, we had derived the first-order shift formula of X/O-cycles under perturbation (δB), based on which we further deduce the first-order shift formula of stable and unstable manifolds under perturbation. These two formulae provide a new perspective for controlling the shape of magnetically confined plasma by applying them to the vacuum magnetic fields induced by various magnetic coils. Moreover, it is feasible to control the width of chaotic layers at the plasma edge and island chains. Of particular importance among all the ``perturbing'' fields, the time derivative of a realistic field, ∂B/∂t, can be considered a peculiar one in the formulae (i.e., substituted for the perturbing field δB), which yields the shift velocities of X/O cycles, stable and unstable manifolds. It should be noted the perturbation field δB does not need to be axisymmetric and the field to be perturbed does not need to be divergence-free.

  
For a typical divertor configuration, the connection lengths of magnetic field lines in the scrape-off layer (SOL) are greatly influenced by the Jacobian matrix eigenvalues of the Poincaré map of the outmost X-cycle(s). The Jacobian matrix is denoted by DP^m for a cycle of m toroidal turns, where P denotes the Poincaré map of one toroidal turn. Adjusting the eigenvalues of DP^m of the X-cycle(s) to be close to unity can significantly increase the connection lengths in the SOL. The first-order change of DP^m under perturbation is revealed by a formula deduced in the same manner as that of X/O-cycles and (un)stable manifolds. It is expected that pushing the two eigenvalues of DP^m towards unity will facilitate the achievement of edge plasma detachment due to the resulting increase in radiation loss from the longer connection lengths.