High-Temperature Superconductor Coatings for Beam Impedance Reduction in Particle Colliders: Nonlinear Effects

Coating of surfaces facing particle beams with high-temperature superconductors (HTS) for reducing the beam coupling impedance is being considered for the next generation of hadron colliders, such as the FCC-hh at CERN, where HTS would be exposed to the high-frequency wakefields generated by the particle bunches and to the strong field of the steering magnets. In this frame, we present a simple model for the calculation of the microwave response of HTS exposed to a strong external magnetic field, which takes into account the nonlinearity of the pinning potential of the vortex lattice. The equation of motion of the vortex lattice is solved in first-order approximation, and we calculate the amplitude of the third-harmonic components in the electric field produced by vortex oscillation. We deduce the time-dependent surface impedance, which could serve as a boundary condition in the simulation codes for the calculation of beam-stability phenomena in particle accelerators. Finally, time-integration of the surface impedance allows exploring the dependence of the surface impedance on surface currents, useful for analyzing the experimental results obtained using simple resonators in terms of our model.