Nonlinear Flux Diffusion and ac Susceptibility of Superconductors - Exact Numerical Results
Abstract
The ac response of a slab of material with electrodynamic characteristics
E∼
j
κ+1
,
κ≥0
, is studied numerically. From the solutions of the nonlinear diffusion equation, the fundamental and higher-order components of the harmonic susceptibility are obtained. A large portion of the data for every
κ
can be scaled by a single parameter,
ξ
=
t
1/(κ+2)
⋅
H
κ/(κ+2)
0
/D
, where
t
is the period of the ac field at the surface,
H
0
is its amplitude and
D
is the slab thickness. This is, however, only an approximate scaling property: The field penetration into a nonlinear medium is a more complex phenomenon than in the linear case. In particular, the susceptibility values are not uniquely defined by a set of only two parameters, such as
κ
and
ξ
, while one parameter, i.e.
t
1/2
/D, is sufficient to describe the electrodynamic response of a linear medium.