  Precise characterization and tailoring of the spatial and temporal evolution
of plasma density within plasma sources is critical for realizing high-quality
accelerated beams in plasma wakefield accelerators. The simultaneous use of two
independent diagnostic techniques allowed the temporally and spatially resolved
detection of plasma density with unprecedented sensitivity and enabled the
characterization of the plasma temperature at local thermodynamic equilibrium
in discharge capillaries. A common-path two-color laser interferometer for
obtaining the average plasma density with a sensitivity of $2\times 10^{15}$
cm$^{-2}$ was developed together with a plasma emission spectrometer for
analyzing spectral line broadening profiles with a resolution of $5\times
10^{15}$ cm$^{-3}$. Both diagnostics show good agreement when applying the
spectral line broadening analysis methodology of Gigosos and Carde{\~n}oso.
Measured longitudinally resolved plasma density profiles exhibit a clear
temporal evolution from an initial flat-top to a Gaussian-like shape in the
first microseconds as material is ejected out from the capillary, deviating
from the often-desired flat-top profile. For plasma with densities of
0.5-$2.5\times 10^{17}$ cm$^{-3}$, temperatures of 1-7 eV were indirectly
measured. These measurements pave the way for highly detailed parameter tuning
in plasma sources for particle accelerators and beam optics.
