Longitudinal Spin Transfer to $\Lambda^0$ Hyperons in CLAS12

Using the self analyzing decay of the $\Lambda^0$, the longitudinal spin transfer $D_{LL}$ from a polarized electron beam scattering an unpolarized proton target to the hyperon can be measured. For $\Lambda$'s produced in the current fragmentation region, this quantity is proportional to the helicity dependent fragmentation function $G_1^\Lambda$ and can provide insight into the spin structure of the $\Lambda^0$. Currently, experimental data on $D_{LL}$ is limited and is not able to discriminate between different models of the $\Lambda^0$ spin structure. This contribution will report the status of the ongoing analysis of the longitudinal spin transfer using data taken by the CLAS12 experiment at Jefferson Lab, a large acceptance spectrometer using a 10.6 GeV electron beam.