You are asking to power magnetrons from a mobile power source. "30 seconds to a minute" is effectively CW (continuous wave), no chance to take the energy out of a capacitor.
Magnetrons have about 70% efficiency, in the first place you are asking for a battery that can supply 140% of the required RF power, secondly for a respective DC/DC converter.
You didn't yet mention RF power amount or the purpose of RF power application.
Just in case let me mention that we don't allow discussions about weapon design or similar dangerous topics at Edaboard.