  Ultimate storage rings (USRs), with electron emittance smaller than 100
pm.rad and on the scale of the diffraction limit for hard X-rays in both
transverse planes, have the potential to deliver photons with much higher
brightness and higher transverse coherence than that projected for the rings
currently operational or under construction. Worldwide efforts have been made
to design and to build light sources based on USRs. How to obtain a round beam,
i.e. beam with equivalent transverse emittances, is an important topic in USR
studies. In this paper, we show that a locally-round beam can be achieved by
using a pair of solenoid and anti-solenoid with a circularly polarized
undulator located in between. Theoretical analysis and application of this
novel method, particularly to one of the Beijing Advanced Photon Source storage
ring design having natural emittance of 75 pm.rad, are presented.
