A low-energy positron beam is a unique probe of Fermi surfaces, defects, surfaces and interfaces. In high-energy electron and positron storage rings (E > 6 GeV) it is possible to generate intense synchrotron radiation with 1-3 MeV photons by installing a high-field superconducting wiggler. The strength of the wiggler should be ~8-12 T. High-energy photons are emitted from the wiggler and converted to low-energy positrons by using a suitable target-moderator system. For an 8 GeV electron storage ring at a beam current of 100 mA, final yields are estimated to be ~10(10)-10(12) (slow-e(+) s(-1)) with the size of positron source ~10(2)-10(3) cm(2). The possibility of increasing the brightness of the low-energy positron beam is discussed. Advantages of using synchrotron radiation for producing positrons are pointed out. The effect of a superconducting wiggler on the stored electron beam is also discussed.