Extreme ultraviolet (XUV) frequency combs exhibit promise for enabling high-precision spectroscopic measurements of myriad chemical species for the first time. Coherent XUV radiation can be generated through high harmonic generation (HHG) in femtosecond enhancement cavities. HHG efficiency is limited by nonlinear phase shifts induced by residual intracavity plasma. The goal of this work is to gain insight regarding plasma dynamics in order to allay the detrimental effects of plasma interactions. Our approach is to conduct simulations of cavity pump-probe experiments by probing with higher-order transverse modes. We propose methods for estimating spatial plasma profiles, gas jet velocities, and the plasma recombination coefficient based on measurements of plasma-induced phase shifts. Beam distortion due to plasma interaction is analyzed and used as another reference for plasma dynamics.