Permanent-magnet discretization error in stellarators scales linearly with magnetization tolerance

Résumé fourni par la source

Abstract Stellarator permanent-magnet concepts discretize a continuously optimized magnetization distribution into a finite number of physical blocks, yet an analytical framework for predicting how the resulting normal-field error scales with the block partitioning parameter has been lacking. Starting from the Biot-Savart integral of the equivalent magnetization currents, this letter derives the power-law scaling of the normalized root-mean-square error (NMSE, defined as the root-mean-square normal-field error on the plasma surface divided by the peak-to-peak normal field of the toroidal-field coils) with the magnetization similarity threshold phi_max (the upper bound on the magnetization-direction angle between any two points within one block). The analysis shows that assigning the volume-weighted average as the equivalent magnetization vector of each block causes the zeroth-order moment of the block error to vanish exactly. When the block linear size l_k is much smaller than the magnet-to-plasma distance r (Regime 1), NMSE ~ C_1 phi_max^2; when l_k ~ r (Regime 2), NMSE ~ C_2 phi_max, where C_1 and C_2 depend only on the configuration geometry. Finite-element simulations of the NCSX quasi-axisymmetric stellarator yield a power-law exponent alpha = 0.94 from a fit to four data points over phi_max = 30-75 degrees, in quantitative agreement with the Regime 2 prediction (alpha = 1). The derived scaling provides a quantitative basis for selecting block partitioning parameters in stellarator and similar tailored-field permanent-magnet systems.

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