Genetic algorithm optimization of low aspect ratio Halbach arrays with explicit control of orthogonal field component

Conventional optimization of compact dipole Halbach magnets is typically based on the homogeneity of the dominant transverse magnetic field component B_y. However, finite-length effects in short Halbach arrays can generate non-negligible orthogonal magnetic field components, primarily B_x along the cylinder axis, that are not captured by these scalar metrics and may accelerate signal dephasing. This study develops a design and optimization strategy that explicitly controls orthogonal components and evaluates their effect on signal coherence.

A dipole Halbach array for adult head MRI (aspect ratio (AR): length-to-diameter = 1.167) was optimized using a multi-objective genetic algorithm (GA), with and without explicit constraints on orthogonal components. Spherical harmonic (SH) and parametric geometry analysis were used to guide the magnet design, and free induction decay (FID) simulations of the optimized field maps were performed to estimate the corresponding effective T₂^∗.

The configuration obtained from unconstrained optimization achieved lower B_y inhomogeneity (10,307 ppm) than the constrained one (14,750 ppm), but generated substantially larger orthogonal components, with local B_x/B_y approaching 20% in parts of the DSV. This resulted in faster FID and shorter T₂^∗. In contrast, the configuration obtained from constrained optimization (B_x/B_y<1%) preserved signal coherence and produced T₂^∗ values close to those of an ideal field without orthogonal components.

Magnetic field maps with similar homogeneity metrics do not necessarily produce comparable FID. For certain compact dipole Halbach geometries (AR < 1.4) finite length effects can generate orthogonal components that become a significant source of signal dephasing. Therefore, these components need to be evaluated and, where necessary, explicitly controlled during the design and optimization of compact Halbach MRI magnets.