Figure 163: Illustration of the above example of a semi-infinite superconductor in a homogeneous
magnetic field in vacuum.
Equivalently, we can combine Eqs. (278) and (282) in order to obtain
∇^2 js−1
λ^2 L
js= 0. (284)We regard a semi-infinite superconductor (z > 0 ) in a magnetic field which is homogeneous in vacuum
(z < 0 ), see Fig. 163. In case thatB= Bxex we obtain from Eq. (281) thatjs is of the form
js=jsyey. We can calculate the magnetic field and the current density in the superconductor from
Eqs. (283) and (284):
Bx(z) =Bx^0 exp(
−
z
λL)
, (285)and
jsy(z) =j^0 syexp(
−
z
λL). (286)
This means that the magnetic field as well as the current decay exponentially with distance into the
superconductor. Here,λLis referred to as theLondonpenetration depth. For a typical supercon-
ductor such as Sn, its value is approximately 26 nm. Hence, theLondonequations describe the
Meissner - Ochsenfeldeffect particularly well.
16.3.3 Ginzburg - LandauEquations
In order to obtain theGinzburg - Landauequations one introduces a complex valued order pa-
rameterφwhere|φ|^2 =nsis the density of superconducting electrons. Based onLandau’s theory