Abstract: The confinement of charged particles in toroidal magnetic configurations, such as stellarators, remains a critical challenge for nuclear fusion. Omnigenous magnetic fields, where the bounce-averaged radial drift of trapped particles vanishes, offer superior confinement. Despite being less restrictive than quasisymmetry or axisymmetry, omnigenity has been underexplored due to its inherent complexity. This work introduces a novel optimization method for omnigenity. By mapping the magnetic field onto specific coordinates, excellent omnigenity can be achieved through the reduction of asymmetric components, comparable in simplicity to quasisymmetry optimization. Precisely omnigenous configurations with field-strength contours that close toroidally, poloidally, or along arbitrary directions have been successfully realized, exhibiting low aspect ratios and excellent particle confinement. Moreover, special configurations with pseudosymmetry or piecewise omnigenity have been directly optimized for the first time. These results simplify the exploration of the broad design space of omnigenous stellarators, enabling more efficient discovery of optimized configurations.

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