  We address production of massive axion-like particles by two electromagnetic
modes inside a superconducting radio-frequency (SRF) cylindrical cavity. We
discuss in detail the choice of pump modes and cavity design. We numerically
compute time-averaged energy density of produced axion field for various cavity
modes and wide range of axion masses. This allows us to estimate optimal
conditions for axion production within a cavity. In addition, we consider
photon regeneration process initiated by produced axion field in a screened
radio-frequency cavity and derive constraints in parameter space
$(g_{a\gamma\gamma},\ m_a)$ for different choice of pump modes.
