“…In the terms of matrix shape, cylindrical magnetic matrices with a circular cross-section are often used in HGMS systems, while magnetic matrices with other special cross-section shapes have also received attention (Zheng et al 2016, Xue et al 2020a, 2020b, Xia et al 2021. For instance, Xue et al (2020a) explored the particle capture performance by magnetic matrices with four cross sections (circular, elliptic, square and diamond cross-section) in an axial HGMS system by using three-dimensional numerical simulations, and made a quantitative comparison, showing that the particle capture cross section of the elliptic and diamond matrices is larger than that of the square and elliptic matrices when the applied magnetic field is less than 1.1 T, while the particle capture cross section of the four types of matrices is similar when the applied magnetic field is greater than 1.1 T. In addition to shape, the effect of matrix size on the capture process was also investigated (Padmanabhan et al 2011, Zheng et al 2015, Zheng et al 2017. For instance, Zheng et al (2015) numerically demonstrated that the capture radius decreases rapidly with the increase of matrices size, where matrices of small size have larger capture radius and present higher capture efficiency under the same packing fraction as matrices of large size.…”