Collisionless Magnetic Reconnection:
       The Origin of Electrical Resistivity

"A dissipation process proceeds without dissipation."

This had been a paradox of magnetic reconnection
beginning in 1950s when H.Alfven created magneto-
I first solved (demonstrated) this
numerically using the macro(meso)scale
particle simulation code
. The whole story was
simpler than expected.

Why is it a Paradox?

Almost all our universe (99.99%)is made of gaseous charged object called
which was named by Langmuir in analogy to biological plasmas as
collective sticky objects. The current flowing in it generates magnetic field which
in turn confines the plasma particles inside. However, magnetohydrodynamic
equations derived from Maxwell equations and the Navier-Stokes (fluid) equations
indicate that the two separate plasmas of different origins with their own magnetic
fields never merge in the absence of dissipation.
 In reality, however, magnetic reconnection occurs in the space surrounding our
earth, the magnetosphere. Such a phenomenon - a substorm, takes place and ends
typically within one hour, resulting in
radio communication disturbances and aurora
in arctic regions.
 These things were observed and confirmed by ground-based and
satellite observations. On the other hand, the characteristic time of dissipation in
this environment is about a week, which is much longer than one hour. This is
the reason why I called
the discrepancy as a paradox.

 Many researchers thought of magnetic reconnection in the context of
hydrodynamics (MHD).
and that theory required a dissipation term for occurrence
of the phenomenon, which is termed as
electrical resistivity. Without resistivity,
magnetic reconnection was confirmed not to occur by laboratory experiments and
computer simulations using MHD equations.

What is the Origin of Resistivity?

The answer to the paradox turned out to be much simpler than one expected.
Magnetic reconnection takes place in the conditions where the MHD theory breaks
down - no extension of the theory should be made. 
Namely, in the dissipationless
condition that I used in my macro-particle simulations magnetic reconnection did
take place.  More specifically, magnetic reconnection occurs in a small region
an X-point where magnetic field lines merge and annihilate. There, electrons
move along the magnetic filed line, and protons move both along and perpendicularly
to the field line due to large gyroradii. Except that region, two components of the
plasma - electrons and protons - move together, which is
a basic assumption of
the MHD theory.
 Thus, the MHD theory and its notion as fluid dynamics must be
abandoned for studying the fundamental process of magnetic reconnection.

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