Progress toward a measurement of the shape of the $^{14}$C $\beta$ spectrum

Precision beta-decay experiments can constrain possible extensions to the Standard Model of the weak interaction. We report on progress toward a new measurement of the $^{14}$C beta spectrum shape as a test of the strong form of the Conserved Vector Current hypothesis. This measurement will complement a previous measurement of the shape factor in the $^{14}$O analog transition, which was carried out with a superconducting beta spectrometer\footnote{L.D. Knutson \textit{et al.}, Rev. Sci. Instrum. \textbf{82}, 073302 (2011).} and achieved a relative precision of 3\% on the linear term of the shape factor\footnote{E.A. George \textit{et al.}, Phys. Rev. C \textbf{90}, 065501 (2014).}. A comparable precision is the goal of the $^{14}$C shape measurement. For this measurement we have constructed a new iron-free magnetic beta spectrometer with the same geometry as the $^{14}$O spectrometer but with conventional field coils. Because of the low $^{14}$C endpoint energy (156 keV), scattering within the spectrometer may cause energy-dependent distortions at the target precision. We report on the design of the spectrometer, Monte Carlo simulations aimed at addressing scattering issues, and results from initial test runs.