A method for managing the broad band microwave and TeraHertz (THz) radiation in a free electron laser (FEL) having a wiggler producing power in the electromagnetic spectrum. The method includes placement of broadband microwave and TeraHertz (THz) radiation absorbers on the upstream end of the wiggler. The absorbers dampen the bounced back, broad band microwave and THz radiation returning from the surfaces outside the nose of the cookie-cutter and thus preventing broadening of the electron beam pulse's narrow longitudinal energy distribution. Broadening diminishes the ultimate laser power from the wiggler. The broadband microwave and THz radiation absorbers are placed on either side of the slot in the cookie-cutter that shapes the wake field wave of the electron pulse to the slot shape of the wiggler chamber aperture. The broad band microwave and THz radiation absorber is preferably a non-porous pyrolytic grade of graphite with small grain size.