How are particle accelerators related to transmutation?
Particle accelerators are required for the controlled production of transmutation. They are used to accelerate heavy elements for high-speed impacts with other heavy elements.
They are used to accelerate heavy elements for high-speed impacts with other heavy elements with sufficient energy to fuse the nuclei and create a new, heavier element (transmutation). This also occurs naturally, as in a plutonium breeder reactor. Heavy elements usually decompose by radioactive fission quickly in nature, so they are not found naturally. They must be made by fusing different elements to form the desired element.
Nuclear fusion requires a great deal of energy. A particle accelerator uses an electric/magnetic system to accelerate elements to very high speeds. Two opposite-moving beams of accelerated particles are then collided with each other to create the energy necessary for the desired fusion to occur.
Further explanation and many diagrams and pictures may be found here: