We present the development of high-performance polarized $^3\mathrm{He}$targets for use in electron scattering experiments that utilize the techniqueof alkali-hybrid spin-exchange optical pumping. We include data obtained duringthe characterization of 24 separate target cells, each of which was constructedwhile preparing for one of four experiments at Jefferson Laboratory in NewportNews, Virginia. The results presented here document dramatic improvement in theperformance of polarized $^3\mathrm{He}$ targets, as well as the targetproperties and operating parameters that made those improvements possible.Included in our measurements were determinations of the so-called $X$-factorsthat quantify a temperature-dependent and as-yet poorly understoodspin-relaxation mechanism that limits the maximum achievable $^3\mathrm{He}$polarization to well under 100%. The presence of this spin-relaxation mechanismwas clearly evident in our data. We also present results from a simulation ofthe alkali-hydrid spin-exchange optical pumping process that was developed toprovide guidance in the design of these targets. Good agreement with actualperformance was obtained by including details such as off-resonant opticalpumping. Now benchmarked against experimental data, the simulation is usefulfor the design of future targets. Included in our results is a measurement ofthe $\mathrm{K}$-$^3\mathrm{He}$ spin-exchange rate coefficient$k^\mathrm{K}_\mathrm{se} = \left ( 7.46 \pm 0.62 \right )\!\times\!10^{-20}\\mathrm{cm^3/s}$ over the temperature range 503 K to 563 K.
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