In 1940 upon completion of his PhD with Douglas Hartree, Buneman joined Hartree's magnetron research group assisting the development of radar during World War II. They discovered the Buneman–Hartree criterion for the voltage threshold of a magnetron operation. After the war, Buneman developed theories and simulations of collision-less dissipation of currents called the Buneman instability. This is an example of anomalous resistivity or absorption. It is anomalous because the phenomenon does not depend on collisions. Buneman advanced elliptic equation solver methods and their associated applications (as well as for the fast Fourier transforms).