Body
https://gss.pppl.gov/talks/reconnection%20lecture%201.pdf
On 1/9/2019 8:09 AM, Norman Wootan wrote:
>
> 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