Bogomyagkov, A.V. Glukhov, S.A. Levichev, E.B. Sinyatkin, S.V. JACoW Publishing Geneva, Switzerland 978-3-95450-216-5 10.18429/JACoW-eeFACT2018-TUOAB01 English 46-56 TUOAB01 synchrotron radiation quadrupole betatron resonance Contribution to a conference proceedings 2019 2019-04 https://doi.org/10.18429/JACoW-eeFACT2018-TUOAB01 http://jacow.org/eefact2018/papers/tuoab01.pdf In a lepton storage ring of very high energy (e.g. in the e⁺e⁻ Higgs factory) synchrotron radiation from quadrupoles constraints transverse dynamic aperture even in the absence of any magnetic nonlinearities. This was observed in LEP and the Future Circular e⁺e⁻ Collider (FCC-ee). Synchrotron radiation in the quadrupoles modulates the particle energy at the double betatron frequency. Energy modulation varies transverse focusing strength at the same frequency and creates a parametric resonance of the betatron oscillations. Starting from 6d equations of motion we derive and solve the relevant differential equation describing the resonance, and show good agreement between analytical results and numerical simulation.