Body
https://link.springer.com/chapter/10.1007%2F978-94-009-0545-0_14
Recent
Developments
in
the
Theory
of
Magnetic
Reconnection
Dieter
Biskamp
Max-Planck-Institut
fiir
Plasmaphysik
8046
Garching
bei
Miinchen,
Federal
Republic
of
Germany
Abstract
The
talk
briefly
reviews
previous
stationary
models,
mainly
configurations
of
the
Petschek
type,
pointing
out
their
shortcomings
and
basic
failure
in
accounting
for
fast
magnetic
reconnection
in
the
limit
of
large
magnetic
Reynolds
number.
It
is
shown
that
in
this
limit
no
relevant
stationary
states
exist.
Instead
strong
small-scale
MHD
turbulence
develops
even
in
2D
geometry,
giving
rise
to
energy
dissipation
and
reconnection
rates
independent
of
the
value
of
the
collisional
re-
sistivity.
I
Introduction
In
the
last
decade
it
has
been realized
that
the
presence
of
magnetic
fields
is
a
ubiquitous
phenomenon
in
cosmic
systems.
On
the
one
hand,
magnetic
fields
serve
as
a large
energy
reservoir
which
may
be
tapped
in
a fast
dynamic
process
leading
to
various
kinds
of
explosive
events
such
as
flares.
On
the
other
hand,
magnetic
fields
tend
to
be
compressed
in
processes
such
as
protostar
formation
and
are
computed
to
dominate
the
dynamics
in
the
later
phases
in
a nonrealistic
way
if
not
dissipated
sufficiently
fast.
To
account
for
such
processes of
fast
magnetic
field
annihilation
is
the
main
objective
of
the
theory
of
magnetic
reconnect
ion.
The
term
magnetic
reconnect
ion
refers
to
the
picture
of
magnetic
field
lines.
These
have
a well-defined
meaning
in
a highly
conducting
fluid,
viz.
thin
magnetic
flux
tubes
which
are
carried
along
with
the
fluid,
maintaining
their
individuality,
though
they
may
be
wound
in
a very
complex
manner.
Only
owing
to
finite
electrical
resistivity
or
some
equivalent
process
may
two
field
lines
coming
close
together
lose
their
identities
by
being
cut
and
reconnected
in
a different
way.
Though
this
is
a local
process,
it
leads
to
a change
of
field
topology
permitting
new
types
of
large-scale
plasma
motions
that
would
otherwise
be
inhibited.
The
255
w.
BrinbMnn
et
al.
(eds.J,
Physical
Processes
in
Hot
Cosmic
PlIlsmas,
255-269.
e
1990
Kluwer
Academic
Publishers.
256
change
of
the
magnetic
field
is described
by
Faraday's
law:
oB
(
...
)
2'"
7it=VX
iixB
+
'IV
B.
(1)
Here
the
ratio
of
the
diffusion
term
and
the
convection
term
(2)
is
a convenient
dimensionless
measure
of
the
resistivity,
Rm
being
the
magnetic
Reynolds
number.
In
practically
all
astrophysical
plasmas
Rm
is large,
essentially
because
of
the
large
scales
L.
Hence
magnetic
diffusion
is
in
general
a very
weak
process.
Magnetic
processes
such
as
solar
flares,
however,
seem
to
require
fast
reconnection
with
time
scales
practically
independent
of
Rm.
The
main
theoretical
problem
therefore
is
to
find
models
allowing
sufficiently
high
reconnect
ion
rates.
Fast
reconnection
is
not
a diffuse
process,
but
is
strongly
localized
in
current
sheets.
Such
current
sheets
may
arise
at
any
point
with
non-vanishing
magnetic
shear
and
a velocity
gradient
along
the
direction
of
the
shear
perpendicular
to
the
field,
i.e.
virtually
everywhere
in
the
plasma,
as
visualized
in
Fig.
1.
The
simplest
models
are
quasi-stationary
configurations
with
one
current
sheet
at
a well
defined
location
determined
by
the
overall
geometry,
which
have
been
investigated
in
the
conventional
theory
of
magnetic
reconnection.
The
basic
assumption
in
these
theoretical
approaches is
the
existence
of
a two-dimensional
subsystem
around
an
X-type
magnetic
neutral
point
which
is
small
compared
with
the
global
magnetic
configuration
but
large
compared
with
the
so-called
diffusion
region
around
the
neutral
point,
where
the
diffusion
term
in
(1)
is
important.
In
this
subsystem
conditions
would
rapidly
adjust
to
changes
in
the
global
configuration,
so
that
the
evolution
of
the
latter
would
correspond
to
a sequence
of
stationary
states
in
the
former
which
are
steady-state
solutions
with
the
boundary
conditions
determined
by
the
global
system.
This
is
the
idea
of
stationary
forced
reconnection.
The
prototype
of
such
configurations
is Petschek's
reconnection
model
1),
which
is given
schematically
in
Fig.
2.
In
fact,
much
of
the
theoretical
work
on
magnetic
reconnection
2
),3)
consists
of
modifications
and
refinements
of
this
model.
The
theory
is based
on
the
effect
that
the
motion
of
a plasma
may
be
supersonic
at
arbitrarily
low
speed
with
respect
to
the
slow
mode
. Hence,
by
analogy
with
a system
of
two
supersonic
gas
jets