378 Chapter 12. Magnetic reconnection
12.7 Assignments
(a) (b)
(c)
z
z
poloidal
flux surface
current
loop
(^12)
(^34)
5
(^123)
4 5
Ui n
Ui n
Uo u t Uo u t
current sheet
L
X-point X-point
Figure 12.6: (a) Two identical coaxial current loops;(b) current loops approaching each
other; (c) detail of X-point region of (b) showing inflows/outflows and current-sheet
(shaded region) having nominal lengthLand thicknessδ.
- Sweet-Parker type reconnection(Sweet 1958, Parker 1957): Consider the two identical
flux-conserving current loops shown in Fig. 12.6(a). Becausethe system is axisym-
metric, the magnetic field can be expressed as
B=
1
2 π
∇ψ×∇φ.
(a) Explain why there is an attractive force between the current loops (hint: consider
the force between parallel currents or between north and south poles of two
magnets).