Scaling Law for AC Susceptibility of a Superconducting Strip with a Power-Law Dependence of Electric Field on a Magnetic-Field-Dependent Sheet Current Density

The perpendicular ac susceptibility
$\chi=\chi^{\prime}-j\chi^{\prime\prime}$
of a superconducting thin strip of width
$2a$
obeying a power-law dependence of electric field on sheet current density
$E/E_c=(K/K_c)\vert K/K_c\vert^{n-1}$
with a Kim-model
$K_c(H)=K_0[1+p_K^2\vert H\vert/(K_0/\pi)]^{-1}$
and average critical sheet current density
$K_{c,\mathrm{av}}$
is calculated as a function of the field amplitude
$H_m$
and frequency
$\omega$
. A scaling law is deduced which states that if
$\omega$
and
$H_m$
are normalized as
$\theta\equiv \mu_0 \omega a K_{c,\mathrm{av}}/2E_c$
and
$h_m\equiv H_m\pi/K_{c,\mathrm{av}}$
, then for the
$h_m$
at which
$\chi^{\prime\prime}$
takes its maximum,
$h_m(\chi_m^{\prime\prime},\theta)=h_m(\chi_m^{\prime\prime},1)\theta^{1/(n-1)-\beta}$
occurs with
$\chi_m^{\prime\prime}(\theta)=\chi_m^{\prime\prime}(1)\theta^\alpha$
, positive numbers
$\alpha$
and
$\beta$
being functions of
$n$
and
$p_K$
only.