In 1935, F. and H. London modified an essential equation of electrodynamics
(i.e. Ohm's Law) in such a way as to obtain the Meissner effect, without
altering Maxwell's equations themselves. In doing so, they incorporated the
two-fluid model of Gorter and Casimir [12]. The two-fluid model
separates the electron system into a *superconducting* component with an
electron density *n*_{s}, and a *normal* component with an electron density
*n*_{n}. They assumed the total electron density
behaved such that
as
,
and
when *T* > *T*_{c}.
Emerging from their phenomenological model
is the so-called
*London penetration depth*
[13]:

where

The physical significance of
pertains to the failure of the
Meissner effect to occur abruptly at the surface of a superconductor;
rather the magnetic field penetrates slightly into the bulk of the
superconducting material
on a length scale given by
.
Consider a semi-infinite superconductor with the boundary between
normal and superconducting regions at *x*=0. In the presence of an
external magnetic field applied perpendicular to the surface,
London theory predicts
that the magnetic flux decays exponentially
into the bulk of the superconductor according to
[13,16]:

where (0) is the magnetic field at the surface of the superconductor, and

2001-09-28