The Hydrogen Bomb: The Basics
A fission bomb, called the primary, produces a flood of radiation including a large number of neutrons. This radiation impinges on the thermonuclear portion of the bomb, known as the secondary. The secondary consists largely of lithium deuteride. The neutrons react with the lithium in this chemical compound, producing tritium and helium.
This reaction produces the tritium on the spot, so there is no need to include tritium in the bomb itself. In the extreme heat which exists in the bomb, the tritium fuses with the deuterium in the lithium deuteride.