  Plasma impedance probes (PIPs) are a type of RF probe that primarily measure
electron density. This work introduces two advancements: a streamlined
analytical model for interpreting PIP-monopole measurements and techniques for
achieving $\geq 1$ MHz time-resolved PIP measurements. The model's improvements
include introducing sheath thickness as a measurement and providing a more
accurate method for measuring electron density and damping. The model is
validated by a quasi-static numerical simulation which compares the simulation
with measurements, identifies sources of error, and provides probe design
criteria for minimizing uncertainty. The improved time resolution is achieved
by introducing higher-frequency hardware, updated analysis algorithms, and a
more rigorous approach to RF calibration. Finally, the new model and high-speed
techniques are applied to two datasets: a 4 kHz plasma density oscillation
resolved at 100 kHz with densities ranging between $2 \times 10^{14}$ to $3
\times 10^{15}$ m$^{-3}$ and a 150 kHz oscillation resolved at 4 MHz with
densities ranging between $4 \times 10^{14}$ to $6 \times 10^{14}$ m$^{-3}$.
