The transport of magnetized beams is intricate given the coupling between the two transverse degrees of freedom. Exploring the impact of various transformations on the preservation of these correlations is quintessential to insure the beam remained magnetized up to the cooling-section solenoid. Yet, in a high-energy electron cooler the beam is subjected to various transverse- and longitudinal-phase-space transformations. The purpose of the present task is to explore experimentally the evolution of the beam’s magnetization as it undergoes manipulations similar to those foreseen in the EIC electron-cooling scheme. The experimental investigations will make extensive use of the FAST/IOTA facility available at Fermilab. Given the pulse format of the FAST injector (a bunch train consists of 3000 bunches distributed over 1 ms and the train are repeated at up to 5 Hz), our study will focus on the single-bunch dynamics.