Self-consistent numerical method to study nonlinearity in high-T_c superconductors using complex conductivity

The determination of the origin of the nonlinear response in high-T_c superconductors is yet to be well understood. The microwave surface impedance and current density mutually depend on one another. For this reason, we developed a self-consistent numerical method to determine the RF magnetic field, which is related to the microwave input power. To take the nonlinearity into consideration, we added quadratic nonlinear terms to the real and imaginary parts of the complex conductivity. The surface current density distribution, derived from the critical state model, along the width of the studied microstrip line resonator has been used in our calculations. This numerical method has been validated through three different reported experimental data. Then, the corresponding physical quantities like surface impedance, resonance frequency and critical current density as function of power have been calculated. Subsequently, the averages of the surface resistance (R_Sur) as well as that of the surface reactance (X_Sur) as function of the microwave input power are calculated. Moreover, two geometrical factors g and g₁/I² are shown to be dependent of input power rather than considered constant as used to be reported in literature.