  The Nab collaboration will study free neutron beta decay at the Spallation
Neutron Source at Oak Ridge National Lab. A neutron decays into a proton, an
electron and an anti-neutrino in this process, where the energy of the outgoing
protons and electrons are collected to determine (1) the electron-antineutrino
correlation co-efficient $a$ to the precision of |$\Delta a/a$|<=$10^{-3}$ and
(2) the Fierz interference term $b$ to the precision of |$\Delta
b/b$|<=$3*10^{-3}$. From the measurement of $a$, we can calculate the
axial-vector to vector coupling ratio $\lambda$. Together with the neutron
lifetime measurement, we could also calculate the upper right element of the
Cabbibo-Kobayashi-Maskawa Matrix, and test the unitarity of that matrix. The
measurement of $b$ could shed light on the physics beyond the Standard Model
since $b$ is predicted to be 0 by the $V-A$ structure of weak interaction in
the Standard Model. This thesis presents the design of Nab electrode system,
and the solution to a major systematic effect in the measurement of $a$: the
requirement of having a low electrical field environment in the neutron decay
region. The electrode system has been built and installed successfully, and as
our characterization and its analysis shows, the electrode system meets the
required specifications. This thesis also gives a systematic uncertainty study
for $b$ measurement and provides a table of the requirements for the $b$
measurement...
