  This study documents several correlations observed during the first run of
the plasma wakefield acceleration experiment E300 conducted at FACET-II, using
a single drive electron bunch. The established correlations include those
between the measured maximum energy loss of the drive electron beam and the
integrated betatron x-ray signal, the calculated total beam energy deposited in
the plasma and the integrated x-ray signal, among three visible light emission
measuring cameras, and between the visible plasma light and x-ray signal. The
integrated x-ray signal correlates almost linearly with both the maximum energy
loss of the drive beam and the energy deposited into the plasma, demonstrating
its usability as a measure of energy transfer from the drive beam to the
plasma. Visible plasma light is found to be a useful indicator of the presence
of wake at three locations that overall are two meters apart. Despite the
complex dynamics and vastly different timescales, the x-ray radiation from the
drive bunch and visible light emission from the plasma may prove to be
effective non-invasive diagnostics for monitoring the energy transfer from the
beam to the plasma in future high-repetition-rate experiments.
