You can also synthesize plutonium in particle accelerators without a nuclear reactor, but only in very small quantities and very slowly.
" Plutonium (specifically, plutonium-238) was first produced, isolated, and then chemically identified between December 1940 and February 1941 by Glenn T. Seaborg, Edwin McMillan, Emilio Segrè, Joseph W. Kennedy, and Arthur Wahl by deuteron bombardment of uranium in the 60-inch (150 cm) cyclotron at the Berkeley Radiation Laboratory at the University of California, Berkeley. "
https://en.wikipedia.org/wiki/Plutonium#Discovery
There are interesting designs for Subcritical reactors. A nuclear fission reactor operating without achieving criticality, but with additional neutrons from a particle accelerator.