Design of quasi-axisymmetric stellarators with varying-thickness permanent magnets based on Fourier and surface magnetic charges method

[摘要] To obtain engineering-feasible designs of stellarators with permanent magnets and simplified coils, a new algorithm has been developed based on Fourier decomposition and surface magnetic charges method. The strong toroidal fields in a quasi-axisymmetric stellarator are still generated by coils. The permanent magnets are designed to compensate the normal magnetic fieldB _n on the plasma surface ∂ Pcreated by the coils and plasma. The normal magnetic fields created by the permanent magnetsB _pmn are calculated as the difference between the magnetic fields created by the surface magnetic charges on the inner surface ∂ Dand the outer surface ∂ D _h of the magnets. The Fourier coefficients of the magnet thickness function hleft(heta ,phi right)are computed through matrix division operation based on the least square principle with dominant Fourier components selected through 2D Fourier transformation ofB _pmn. The residual uncompensatedB _n is minimized through iteration to progressively optimize the thickness function. This new algorithm has been successfully applied to design the permanent magnets of anl= 2 quasi-axisymmetric stellarator with background magnetic field created by 12 identical circular planar coils for demonstrations. High accuracy has been achieved, allowing for a flux-surface-averaged residualB _n relative to the total field leftlangle leftvert {B}_{n}/Brightvert rightrangle sim 1.3{imes}1{0}^{-5}and a maximum residualB _n of less than 2 Gs for ∼1 T total field. This new design has some advantages in engineering implementations: all permanent magnet pieces have the same remanenceB _r; only one single layer of magnets are mounted perpendicular to the winding surface; the magnets can be easily inserted into the cells of a gridded frame attached to the winding surface and fixed with springs from the back, which greatly simplifies the manufacture, assembly and maintenance of the magnets, and thus facilitates precision control and cost reduction.

[关键词] quasi-axisymmetric stellarator;permanent magnet;optimization algorithm;Fourier decomposition;coil design;surface magnetic charges