pdf-file - Institut für Theoretische Physik
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available, such as for a turbulent boundary layer. If we check our ambitions<br />
with respect to resolving the turbulence in details, this layer and its turbulence<br />
enhanced magnetic diffusivity should be well accounted for by the same<br />
boundary condition.<br />
The second example is less straight forward. Here, we employ the hydrodynamic<br />
theory for a dielectric as the higher resolution description of the conductor.<br />
This sounds somewhat surprising at first and should be explained.<br />
The dielectric theory (including a finite conductivity) contains a stationary,<br />
collective mode (the sq-mode) that is given by an exponential decay of the<br />
electromagnetic field from the system’s surface [4]. Because the decay length<br />
shrinks with the conductivity, the hydrodynamic theory for conductors does<br />
not contain this mode, (though this may be amended by including higher order<br />
gradient terms). Nevertheless, the derived boundary conditions are such<br />
that the long ranged effects of the sq-mode are well accounted for, albeit on<br />
a grain size on which the sq-mode is no longer resolved. This statement is<br />
explicitly proven by comparing the dielectric with the conductor theory.<br />
5.1 The Highly Conducting Surface Layer<br />
We consider an infinitely long and conducting wire (region 1), of r0, which<br />
is located in a vacuum (region 2), and subjected to a parallel, constant and<br />
homogeneous electrical field E = E0 ez.<br />
coarse-grained theory<br />
Within the wire we have<br />
E D = const ez = E0 ez, (127)<br />
and from Eq(76)<br />
∇×H = 1<br />
βc ED , (128)<br />
in vacuum we have<br />
∇×H =0. (129)<br />
The connecting condition, Eq(126), is<br />
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