The evolution of the magnetic field in a resistive-MHD plasma is
governed by the following well-known equation:

The relative magnitude of the two terms on the right-hand side of Eq. (849)
is conventionally measured in terms of *magnetic Reynolds number*, or *Lundquist
number*:

(850) |

It turns out that in the solar system very large -values are virtually guaranteed by the the extremely large scale-lengths of solar system plasmas. For instance, for solar flares, whilst is appropriate for the solar wind and the Earth's magnetosphere. Of course, in calculating these values we have identified the scale-length with the overall size of the plasma under investigation.

On the basis of the above discussion, it seems reasonable to neglect diffusive
processes altogether in solar system plasmas. Of course, this leads to
very strong constraints on the behaviour of such plasmas, since all
cross-field mixing of plasma elements is suppressed in this limit. Particles
may freely mix along field-lines (within limitations imposed by magnetic
mirroring, *etc.*), but are completely ordered perpendicular to the field,
since they always remain tied to the same field-lines as they convect in the
plasma flow.

Let us consider what happens when two initially separate plasma regions
come into contact with one another, as occurs, for example, in the
interaction between the solar wind and the Earth's magnetic field.
Assuming that each plasma is frozen to its own magnetic field, and that cross-field
diffusion is absent, we conclude that the two plasmas
will not mix, but, instead, that a thin *boundary layer* will form
between them, separating the two plasmas and their respective magnetic fields.
In equilibrium, the location of the boundary layer will be determined
by pressure balance. Since, in general, the frozen fields on either side of
the boundary will have differing strengths, and orientations tangential
to the boundary, the layer must also constitute a *current sheet*.
Thus, flux freezing leads inevitably to the prediction that in plasma
systems space becomes divided into separate cells, wholly containing the
plasma and magnetic field from individual sources, and separated from
each other by thin current sheets.

The ``separate cell'' picture constitutes an excellent zeroth-order approximation to
the interaction of solar system plasmas, as witnessed, for example, by
the well defined planetary magnetospheres. It must be noted, however, that
the large -values upon which the applicability of the frozen flux constraint
was justified were derived using the *large* overall spatial scales of the
systems involved. However, strict application of this constraint to the
problem of the interaction of separate plasma systems leads to the
inevitable conclusion
that structures will form having *small* spatial scales, at least in
one dimension: *i.e.*, the thin current sheets constituting the cell
boundaries. It is certainly not guaranteed, from the above discussion, that
the effects of diffusion can be neglected in
these boundary layers. In fact, we shall demonstrate that
the localized breakdown of the flux freezing constraint in the boundary
regions, due to diffusion, not only has an impact on the
properties of the boundary regions themselves, but can also have a decisive
impact on the large length-scale plasma regions where the flux freezing
constraint remains valid. This observation illustrates both the subtlety and the
significance of the magnetic reconnection process.