Beam blowup due to synchro-beta resonance with/without beam-beam effects

A blowup of vertical emittance has been observed in particle tracking simulations with beam-beam and lattice misalignments. It was somewhat unexpected, since estimation without lattice errors did not predict such a blowup unless a residual vertical dispersion at the interaction point (IP) is larger than a certain amount. Later such a blowup has been seen in a tracking of lattices without beam-beam effect. A possible explanation of the blowup is given by a Vlasov model for an equilibrium of quadratic transverse moments in the synchrotron phase space. This model predicts such a blowup as a synchro-beta resonance mainly near the first synchrotron sideband of the main x-y coupling resonance line.Comment: Presented at the 62nd ICFA Advanced Beam Dynamics Workshop on High Luminosity Circular e+e- Colliders\\(eeFACT 2018), Hong Kong, Sep. 2018, WEXBA0

On blowup formulae for the S-duality conjecture of Vafa and Witten

This is the first part of two papers. In this part, we prove the blowup formulae for virtual Hodge polynomials of Gieseker moduli spaces of rank-2 stable sheaves and Uhlenbeck compactification spaces over algebraic surfaces. In particular, we verify the blowup formulae for the S-duality conjecture of Vafa-Witten, i.e. the blowup formulae for the Euler numbers of instanton moduli spaces over algebraic surfaces.Comment: 24 page