{'fraction_non_alphanumeric': 0.01708150317227916, 'fraction_numerical': 0.005368472425573451, 'mean_word_length': 5.231003039513678, 'pattern_counts': {'":': 0, '<': 0, '<?xml version=': 0, '>': 0, 'https://': 0, 'lorem ipsum': 0, 'www.': 0, 'xml': 0}, 'pii_count': 0, 'substrings_counts': 0, 'word_list_counts': {'cursed_substrings.json': 0, 'profanity_word_list.json': 0, 'sexual_word_list.json': 0, 'zh_pornsignals.json': 0}}
Design of quasi-axisymmetric stellarators with varying-thickness permanent magnets based on Fourier and surface magnetic charges method

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 field B n on the plasma surface ∂P created by the coils and plasma. The normal magnetic fields created by the permanent magnets B pmn are calculated as the difference between the magnetic fields created by the surface magnetic charges on the inner surface ∂D and the outer surface ∂D h of the magnets. The Fourier coefficients of the magnet thickness function hθ,ϕ are computed through matrix division operation based on the least square principle with dominant Fourier components selected through 2D Fourier transformation of B pmn. The residual uncompensated B n is minimized through iteration to progressively optimize the thickness function. This new algorithm has been successfully applied to design the permanent magnets of an l = 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 residual B n relative to the total field Bn/B∼1.3×10−5 and a maximum residual B 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 remanence B 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.