Precision Measurement of the Neutron Asymmetry $A_1^n$ at Large Bjorken $x$ at 12 GeV JLab

The virtual photon asymmetry $A_1$ is one of the fundamental quantities that provide information on the spin structure of the nucleon. The value of $A_1$ at high $x_{Bj}$ is of particular interest because valence quark dominate in this region, which makes it a relatively clean region to study the nucleon spin structure. There are several theoretical calculations that apply to the high $x$ valence quark region, and here we will focus on the neutron $A_1^n$. With the 12 GeV upgrade of JLab, a new experiment on $A_1^n$ is being carried out using a 10.4 GeV beam, a polarized $^3He$ target, and the HMS and the Super-HMS (spectrometers) in Hall C. This measurement will reach a deeper valence quark region: $x\sim 0.75$. And once combined with expected data from the upgraded CLAS12 experiment on the proton $A_1^p$, we will finally be able to reveal whether $\Delta d/d$ turns positive (as in pQCD) or remain negative at high $x$ (as in RCQM). We will present the physics of $A_1^n$ and present preliminary analysis results of the experiment. Performance of an upgraded polarized $^3He$ target will be presented.