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We report numerical calculations of a dynamic pairbreaking current density$J_d$ and a critical superfluid velocity $v_d$ in a nonequilibriumsuperconductor carrying a uniform, large-amplitude ac current density$J(t)=J_a\sin\Omega t$ with $\Omega$ well below the gap frequency $\Omega\ll\Delta_0/\hbar$. The dependencies $J_d(\Omega,T)$ and $v_d(\Omega,T)$ near thecritical temperature $T_c$ were calculated from either the full time-dependentnonequilibrium equations for a dirty s-wave superconductor and thetime-dependent Ginzburg-Landau (TDGL) equations for a gapped superconductor,taking into account the GL relaxation time of the order parameter $\tau_{GL}$and the inelastic electron-phonon relaxation time of quasiparticles $\tau_E$.We show that both approaches give similar frequency dependencies of$J_d(\Omega)$ and $v_d(\Omega)$ which gradually increase from their staticpairbreaking GL values $J_c$ and $v_c$ at $\Omega\tau_E\ll 1$ to $\sqrt{2}J_c$and $\sqrt{2}v_c$ at $\Omega\tau_E\gg 1$. Here $J_d$, $v_d$ and a dynamicsuperheating field at which the Meissner state becomes unstable were calculatedin two different regimes of a fixed ac current and a fixed ac superfluidvelocity induced by the applied ac magnetic field $H=H_a\sin\Omega t$ in a thinsuperconducting filament or a type-II superconductor with a large GL parameter.We also calculated a nonlinear electromagnetic response of a nonequilibriumsuperconducting state, particularly a dynamic kinetic inductance and adissipative quasiparticle conductivity, taking into account the oscillatorydynamics of superconducting condensate and the kinetics of quasiparticlesdriven by a strong ac current. It is shown that an ac current density producesmultiple harmonics of the electric field, the amplitudes of the higher-orderharmonics diminishing as $\tau_E$ increases.

Dynamic pair-breaking current, critical superfluid velocity and nonlinear electromagnetic response of nonequilibrium superconductors