McAllerson's Radiation was a type of radiation.
According to the Seventh Doctor, it was discovered on Earth in 2542 by Professor Bernadette McAllerson while she was working at the New Scientific Central Trust, and was extremely harmful to living things.
How much of this was true was uncertain, as the Doctor knew his explanation was being overheard by Jason. He was trying to trick Jason into making the Force be composed of McAllerson's Radiation. His plan succeeded, since when the possessed Phil Chambers tried to kill the Doctor and his friends with a burst of that radiation, it instead caused disruption of the control systems of the Land. This allowed the Doctor, Ace and Bernice Summerfield to escape in the TARDIS. (PROSE: Conundrum)