Collisionless Magnetic Reconnection: The Origin of
Electrical Resistivity or Something Else ?

This had been a paradox of magnetic reconnection beginning in 1950s when H.Alfven created magneto-hydrodynamics. I first solved (demonstrated) this problem 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 objectcalled plasma, 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 magneto-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 called 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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