Body
https://phys.org/news/2017-10-hidden-mechanics-magnetic-field-reconnection.html
On 1/9/2019 8:14 AM, Norman Wootan wrote:
>
> 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