A traveling wave nuclear fission reactor, fuel assembly, and a method of controlling burnup therein. In a traveling wave nuclear fission reactor, a nuclear fission reactor fuel assembly comprises a plurality of nuclear fission fuel rods that are exposed to a deflagration wave burnfront that, in turn, travels through the fuel rods. The excess reactivity is controlled by a plurality of movable neutron absorber structures that are selectively inserted into and withdrawn from the fuel assembly in order to control the excess reactivity and thus the location, speed and shape of the burnfront. Controlling location, speed and shape of the burnfront manages neutron fluence seen by fuel assembly structural materials in order to reduce risk of temperature and irradiation damage to the structural materials.
