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1942 Phys. Plasmas, Vol. 8, No. 5, May 2001 Egedal et al.
FIG. 11. Color Contours measured current densities
for the same conditions as in Fig 10. The dashed lines
represent contours of constant poloidal magnetic flux.
VI. MEASUREMENTS OF CURRENT SHEETS
In magnetic configurations where the toroidal magnetic
field is much stronger than the cusp field, the majority of the
particles are no longer trapped. In such configurations we do
indeed find a current sheet. In Figs. 10 and 11 snap shots in
time of the plasma density and current density at the beginning
of the formation of the current layers are shown. These
correspond to the formation of current sheets for three different
values of the ratio of toroidal field and cusp field: l 0
B /B cusp 23, 17, 12 m note that the profiles of all
the previous figures are obtained with l 0 1m. In Fig. 12
*E / j max is the ratio of the electric field and the current
density at the center of the current sheet. Here E
(R,Z)
(d/dt)/R, where (R,Z) R0,Z0 RB dl is the
poloidal flux variable, R is the major radius, Z describes the
vertical position, and the subscript denotes the poloidal
plane. is calculated on the basis of the currents applied in
the poloidal field coils and the plasma current profiles
j (R,Z). The profiles of j (R,Z) are obtained through a
singular fit to the measured magnetic field profiles.
The Spitzer resistivity s is calculated using an electron
temperature of 20 eV. It is seen that the constant Spitzer
resistivity is insufficient to account for the low values of the
current observed. Using an approach similar to that of Ref.
15, the discrete particle enhanced inertial resistivity pei was
introduced in Ref. 16 to describe the inertial resistivity based
upon the time each individual particle spends in the region of
the X line in a linear magnetic cusp. Although the values of
pei are too low by a factor of about 6 to describe the
measured values of * it is seen that pei accurately reproduces
the scaling of * as a function of l 0 . It should be
noted that pei was obtained on the basis of heuristic arguments
for a linear cusp geometry. Using the measured geometry
of the magnetic field a more accurate value of pei can
be obtained which may fully account for the observed values
of *. This work is currently underway. The current sheets
shown in Fig. 11 evolve very differently in time. For the case
where l 0 23 m, the X point evolves into an O point and the
total plasma current increases from 1 kA to 10 kA. In the
other two cases the X points are maintained throughout the
pulses and the total plasma currents do not increase.
VII. CONCLUSION
Collisionless magnetic reconnection is routinely observed
in the Versatile Toroidal Facility. In the cases where
the strength of the cusp magnetic field is in the order of or
larger than the strength of the toroidal magnetic field (l 0
1 m the following experimental observations have been
made
1 Fast collisionless magnetic reconnection occurs without
the formation of a macroscopic current sheet.
FIG. 12. Inferred resistivities. A circles; *E / j ; diamonds, pei ;
triangles, s ; B diamonds, */ pei ; triangles, */ s .
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