Spherical Fused Silica Cells Filled with Pure Helium for NMR-Magnetometry

High magnetic fields (> 1 T) are measured by NMR magnetometers with un-rivaled precision if the precessing spin sample provides long coherence times. The longest coherence times are found in diluted ${}^{3}$He samples, which can be hyperpolarized for sufficient signal strength. In order to have minimal influence on the homogeneity and value of the measured magnetic field the optimal container for the ${}^{3}$He should be a perfect sphere. A fused silica sphere with an inner diameter of 8 mm and an outer diameter of 12 mm was made from two hemispheres by diffusion bonding leaving only a small hole for cleaning and evacuation. This hole was closed in vacuum by a CO${}_{2}$ laser and the inner volume was filled with a few mbars of ${}^3$He via wall permeation. NMR-measurements on such a sample had coherence times of 5 min. While the hemispheres were produced with < 1 $\mu$m deviation from sphericity, the bonding left a step of ca. 50 $\mu$m at maximum. The influence of such a mismatch, its orientation and materials in the direct vicinity of the sample are analyzed by FEM-simulations and discussed in view of coherence times and absolute fields.