Chapter 4. Motion of a Particle in a Field
4.4.2 Reconnection in a Vacuum.
X-type points consist a topological peculiarity of a magnetic field. They are places where where redistribution of magnetic fluxes occurs, which changes the connectivity of field lines. Let us illustrate such a process by the simplest example of 2 parallel electric currents of equal magnitude I in vacuum as shown in Figure 4.17. The magnetic field of these currents forms three different fluxes in the plane (x,y). Two of them belong to the upper and the lower currents, respectively, and are situated inside the separatrix field line A, which forms the figure of the eight-like curve with zeroth X-point. The third flux belongs to both currents and is situated outside of the separatrix.
If the currents are displaced in the direction of each other, then the following magnetic flux redistribution will take place. The currents proper fluxes will diminish by the quantity dA, while their common flux will increase by the same quantity. So the field line A2 will be the separatrix of the final state.
This process is realized as follows: Two field lines approach the X-point, merge there, forming a separatrix, and then they reconnect forming a field line which encloses both currents. Such a process us termed reconnection of field lines or magnetic reconenction. A2 is that last reconnect field line.
Magnetic reconnection is of fundamental importance for the nature of many non-stationary phenomena in cosmic plasma. We shall discuss the physics of this process more fully in chapters 16 to 22. Suffice it to say that reconnection is inevitable associated with electric field generation. The field is the inductive one, since
[equation 4.65]
where A is the vector potential of magnetic field,
[equation 4.66]
In the above example, the electric field is directed along the z axis. It is clear if that if dt is the characteristic time of the reconnection process shown in Figure 4.17 then according to (4.65)
[equation 4.67]
the last equality will be justified n Section 9.2
Reconnection in vacuum is a real physical process: magnetic field lines move to the X-type neutral point and reconnect in it as well as
| the electric field is induced and can accelerate a charge particle or
| particles in the vicinity of the neutral point.
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