Having been affiliated with the Directed Energy Directorate of Air Force Research Laboratory for the most of his career, he was a professor at the Department of Electrical and Computer Engineering at University of New Mexico from 2005 until his death.

He completed his high school education at Christian Brothers Academy in Syracuse, and was subsequently admitted to California Institute of Technology, where he played college football in addition to his studies.

[5] In 1984, he established SUMMA Foundation, a nonprofit organization that awards grants to young scientists in the field of electromagnetics, as well as sponsoring short courses, symposia, and the book publications.

[9] Baum is known for his contribution to theory, applications and testing of electromagnetic pulses (EMP) and high-power microwaves (HPM), authoring numerous journal articles, technical notes, and books on these subjects.

[10] His research also involved the design of various nuclear EMP sensors and simulators for the military such as ATLAS-I;[1][11] Weapons Effects Buoy System, in particular, was deployed and tested in the Bahamas in the 1960s.