The Spallation Neutron Source at the Oak Ridge National Laboratory (USA) is the most powerful of its kind in the world. By using a proton beam to pound a mercury target with more than 300 kilowatts of energy, it is able to produce 4.8x10(^16) neutrons per second. These neutrons will eventually be focussed into beams that will allow the molecular analysis of advanced materials.
(^16) = to the power of 16.
Comments below may relate to previous holders of this record.