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The University of Maryland Electron Ring (UMER) is a dedicated research accelerator facility for studying the physics of high-intensity charged particle beams. Advancing the capabilities of the longitudinal confinement system paves the way for multi-bunch electron confinement, allowing UMER to extend its performance and modes of operation for various experiments on longitudinal dynamics. The research reported here employs an existing induction cell [1], and a radiofrequency (RF) amplifier to mimic traditional RF cavity confinement. By applying sinusoidal RF waves at the revolution frequency with synchronous phase angle equal to zero, we can confine an electron beam in the wave's linear regions. To additionally combat particle loss, we calculated the separatrices-the areas of phase space within which the beam is longitudinally confined-with a central synchronous particle.