  After the discovery of the Higgs boson at the Large Hadron Collider in 2012,
several possible future circular colliders -- Higgs factories are proposed,
such as FCC-ee and CEPC. At these highest-energy $e^+e^-$ colliders,
beamstrahlung, namely the synchrotron radiation emitted in the field of the
opposing beam, can greatly affect the equilibrium bunch length and energy
spread. If the dispersion function at the collision point is not zero,
beamstrahlung will also increase the transverse emittances. In this letter, we
first show that, for circular Higgs factories, a classical description of the
beamstrahlung is adequate. We then derive analytical formulae describing the
equilibrium beam parameters, taking into account the variation of the
electromagnetic field during the collision. We illustrate the importance of
beamstrahlung, including the increase of bunch length and the implied tolerance
on the spurious dispersion function at the collision point, by considering a
few examples.
