  We suggest a program to establish theoretical performance limits of srf
cavities using modern theories of nonequilibrium superconductivity under a
strong electromagnetic field. These theories will be used to calculate the main
parameter of merit of srf cavities: the quality factor Q and its dependencies
on the field amplitude, temperature and frequency, which would allow us to
understand how far the srf cavity performance could be pushed from the current
state of the art. Given that the quality factor is determined by multiple
mechanisms operating on very different length scales, we will address the
interconnected problems of a nonlinear surface resistance, rf losses of
vortices trapped in the cavity, the effect of materials defects and surface
topography, and the opportunities to boost the srf performance by surface
nano-structuring, impurity management and multilayers. We suggest the following
directions of theoretical srf research to address the goals of boosting the
performance of the next generation particle accelerators: 1. Establishing the Q
limit, mechanisms of nonlinear surface resistance and the residual resistance
in a nonequilibrium superconductor under a strong RF field. 2. Establishing the
srf breakdown field limit, dynamic superheating field and its dependencies on
frequency, temperature and concentration of impurities. 3. Losses due to
trapped vortices and extreme dynamics of ultrafast vortices driven by strong rf
Meissner currents in srf cavities. 4. Optimization of srf performance due to
surface nanostructuring of the cavity surface, multilayers and impurity
management.
