Let me begin by telling you what transmutation is and how its proponents say it will solve the problem of nuclear waste management.
Transmutation simply means transforming one element or isotope into another.
Some early transmutation proposals even suggested that a deep geologic repository could be avoided altogether. Transmutation is also supposed to solve the problem of proliferation by using the weapons-usable materials, particularly the plutonium contained in the spent fuel from current nuclear reactors. However, even if all of the technologies deemed necessary by its proponents are developed, this scheme cannot be realized. Even proponents of the scheme now acknowledge that a geologic repository would still be needed for much of the residual long-lived waste, including elements like plutonium and neptunium, as well as fission and activation products. In fact, only two of the dozen or so long-lived fission and activation products can be effectively transmuted.