Fundamentals of Plasma Physics

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.

1. 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).