Abstract The construction of an Intense Positron Source (IPS) is suggested. The intensity of the produced positrons is to exceed that of any other existing source by orders of magnitude. The instantaneous intensity is to be 10 3 to 10 6 times higher yet. Fast positrons are to be produced in pulses of time duration ≈ 1 ns to 10 ps. Slow positron pulses of order ≲ 100 ps are expected. The phase space density of positrons at production will be in excess of what can be achieved by other methods. The IPS is to consist of 1) an undulator (usually a micropole undulator, i.e. an undulator with submillimeter period) in which gamma rays in the MeV range will be generated by electron beams circulating in a storage ring; 2) a heavy metal target, in which e + e − pairs will be produced by the generated gamma rays; 3) moderators to thermalize the produced positrons; and 4) a transport system through which the slow positrons will move. Spinoff benefits provided by the suggested device include the following: The equipment may be used to create (or destroy) nuclear isotopes in a controlled manner (i.e. without producing unwanted species); to produce (or destroy) in a controlled way chemical elements; to produce well collimated intense photon beams in the multi 100 MeV range for nuclear physics research, with intensities many orders of magnitude higher than can be achieved today; to generate intense bursts of neutrons; to supply fast positrons produced at high intensities (10 16 to 10 17 s −1 ) and within a small transverse phase space, to future high energy colliders, thereby perhaps even eliminating the need for damping rings.