TECHNOLOGY FOCUS - INORGANIC CHEMISTRY - Preferred Method: The step of quenching comprises: quenching the radicals to a level that is no longer detectable with an electron spin resonance spectrometer, e.g. a level of less than 1014 spins; an application of pressure to the biomass e.g. a pressure greater than 1000 psi optionally applied together with the application of heat; contacting the biomass with a gas capable of reacting with radicals or contacting the biomass with a fluid capable of penetrating into the biomass and reacting with the radicals; and contacting the antioxidant dispersed in the biomass feedstock with the radicals. The radiation is in the form of an electron beam e.g. applied at a total dosage of 10-50 MRad. The methods further comprise processing the quenched and the re-irradiated biomass feedstock respectively to make a combustible fuel, where processing comprises converting the irradiated material and the re-irradiated biomass feedstock (pretreated biomass feedstock) respectively utilizing a microorganism having the ability to convert at least 1 wt.% of the biomass to the fuel. The step of irradiating comprises irradiating with ionizing radiation. The step of cooling the biomass comprises contacting the biomass with a fluid at a temperature below the temperature of the biomass immediately prior to irradiation. Preferred Components: The biomass feedstock comprises a dispersed antioxidant.    TECHNOLOGY FOCUS - INSTRUMENTATION AND TESTING - Preferred Components: The systems (X1) and (Y1) further comprise a biomass feedstock positioned to be ionized by the irradiating device(s).    TECHNOLOGY FOCUS - ORGANIC CHEMISTRY - Preferred Method: The methods further comprise: preparing the biomass feedstock by reducing one or more dimensions of individual pieces of the biomass feedstock, e.g. by shearing, grinding, cutting, squeezing and/or compressing; and treating the biomass feedstock with one or more other pretreatment methods comprising sonication, pyrolysis or oxidation. The biomass feedstock has been sheared to an extent that its internal fibers are substantially exposed. Preferred Components: The biomass feedstock is a low molecular weight sugar, a starch (preferred), paper, paper products, paper waste, wood, particle board, sawdust, agricultural waste, sewage, silage, grasses, rice hulls, bagasse, cotton, jute, hemp, flax, bamboo, sisal, abaca, straw, corn cobs, corn stover, switchgrass, alfalfa, hay, coconut hair, synthetic celluloses, seaweed and/or algae. The biomass feedstock has internal fibers and a bulk density of less than 0.25 g/cm3. EXAMPLE - No suitable example given.