Body
http://young.caltech.edu/Collisionless_Magnetic_Reconnection.html
On 1/9/2019 8:21 AM, Norman Wootan wrote:
>
> 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