  The AWAKE experiment requires an automated online rubidium (Rb) plasma
density and gradient diagnostic for densities between 1 and 10$\cdot$10$^{14}$
cm$^{-3}$. A linear density gradient along the plasma source at the percent
level may be useful to improve the electron acceleration process. Because of
full laser ionization of Rb vapor to Rb$^{+}$ within a radius of 1 mm, the
plasma density equals the vapor density. We measure the Rb vapor densities at
both ends of the source, with high precision using, white light interferometry.
At either source end, broadband laser light passes a remotely controlled
Mach-Zehnder interferometer built out of single mode fibers. The resulting
interference signal, influenced by dispersion in the vicinity of the Rb D1 and
D2 transitions, is dispersed in wavelength by a spectrograph. Fully automated
Fourier-based signal conditioning and a fit algorithm yield the density with an
uncertainty between the measurements at both ends of 0.11 to 0.46 $\%$ over the
entire density range. These densities used to operate the plasma source are
displayed live in the control room.
