  In this paper, we describe the vortex dynamics under high-amplitude microwave
drive and its effect on the surface resistance of superconductors. The vortex
surface resistance is calculated with a Montecarlo approach, where the vortex
motion equation is solved for a collection of vortex flux lines each
oscillating within a random pinning landscape. This approach is capable of
providing a detailed description of the microscopic vortex dynamics and in turn
important insights into the microwave field amplitude dependence of the vortex
surface resistance. The numerical simulations are compared against experimental
data of vortex surface resistance at high microwave amplitude measured by means
of bulk niobium superconducting-radio frequency cavities operating at 1.3 GHz.
The good qualitative agreement of simulations and experiments suggests that the
non-linear dependence of the trapped flux surface resistance with the microwave
field amplitude is generated by progressive microwave depinning and vortex
jumps.
