  Plasma wakefield acceleration is a method for accelerating particle beams
using electromagnetic fields that are orders of magnitude larger than those
found in conventional radio frequency cavities. The core component of a plasma
wakefield accelerator is the plasma source, which ranges from millimeter-scale
gas jets used in laser-driven experiments, to the ten-meter-long rubidium cell
used in the AWAKE experiment. The density of the neutral gas is a controlled
input to the experiment, but the density of the plasma after ionization depends
on many factors. AWAKE uses a high-energy proton beam to drive the plasma
wakefield, and the wakefield acts back on the proton bunch by modulating it at
the plasma frequency. We infer the plasma density by measuring the frequency of
modulation of the proton bunch, and we measure the evolution of the density
versus time by varying the arrival of the proton beam with respect to the
ionizing laser pulse. Using this technique, we uncover a microsecond-long
period of a stable plasma density followed by a rapid decay in density. The
stability of the plasma after ionization has implications for the design of
much longer vapor cells that could be used to accelerate particle beams to
extremely high energies.
