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The Heavy Ion Fusion (HIF) program is progressing through a series of physics and technology demonstrations leading to an inertial fusion power plant. The High Current Experiment (HCX) at Lawrence Berkeley National Laboratory is exploring the physics of intense beams with high line-charge density. Superconducting focusing quadrupoles were developed for magnetic transport studies at the HCX. A baseline design was selected following several pre-series models. Optimization of the baseline design led to the development of a first prototype that achieved a conductor-limited gradient of 132 T/m in a 70 mm bore, without training, with measured field errors at the 0.1% level. Based on these results, the magnet geometry and fabrication procedures were adjusted to improve the field quality. These modifications were implemented in a second prototype. In this paper, the optimized design is presented and comparisons between the design harmonics and magnetic measurements performed on the new prototype are discussed. [ABSTRACT FROM AUTHOR]