Electron Inertia and Magnetic Reconnection

The finite electron mass can cause magnetic reconnection even in the absence of any other non-ideal effect. It will be shown that when electron inertia is the only non-ideal effect in the evolution of a magnetic field B⃗, there is a related field that evolves ideally. This field is B⃗ ≡ B⃗ + ∇⃗× ( (c/ωₚₑ)²μ₀j⃗ ) with ωₚₑ the plasma frequency and j⃗ the current density. In three dimensional space, the practical importance of the ideal evolution of B⃗ on its reconnection appears limited. When the evolution velocity of modified field is chaotic, B⃗ will reconnect on a timescale that depends only logarithmically on any non-ideal effect that is diffusive, such as resistivity, with a current density enhancement that is also proportional to the logarithm. In near ideal magnetic fields, this logarithm is typically of order ten, and it is difficult to conceive of a physically realistic situation in which it larger than a hundred.