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1938 Phys. Plasmas, Vol. 8, No. 5, May 2001 Egedal et al.
shown in Fig. 6D are obtained by evaluating the density
along the poloidal location indicated by the dashed red line
in Fig. 5D. The data used in creating the diagram in Fig.
6D corresponds to data samples obtained at constant time
interval t0.5 ms after the rf heating pulses.
Similarly, the data used in creating the diagrams in Figs.
7 was obtained with t0.3, 0.5 ms. The value of l 0
B /B cusp for the magnetic configuration of Fig. 6 and
Figs. 7A and 7B is 0.3 m, whereas l 0 0.5 m for the
magnetic configurations forming the basis for the data shown
in Figs. 7C and 7D. In the diagram of Fig. 6D and the
four diagrams in Fig. 7 the locations of the plasma boundaries
are well defined and coincide with the location of the
black dashed lines. These lines obtained through (t)
tRE (t) represent the theoretical location of the plasma
boundary assuming that the plasma is frozen into the poloidal
magnetic flux. Hence, we find experimentally that the
plasma is frozen into the poloidal magnetic flux. Due to the
absence of a detectable toroidal current and an associate diffusion
region, the poloidal magnetic field reconnect unhindered
and arbitrarily fast. The rate of reconnection in the
VTF experiment is solely determined by the operator by imposing
a given value of the induced toroidal electric field.
The poloidal drift speed, expressed in terms of the flux
variable, d/dtRE , translates into a drift speed in real
space given by v d E /B cusp , independent of the toroidal
magnetic field. In the presence of a toroidal magnetic field,
this drift speed is much larger than usual EB drift speed
given by E /B inferred on the basis of the induced electric
field where B is the total magnetic field.
FIG. 4. Loop voltage induced by the ohmic pulse on a copper wire at the
center of the vessel.
V. INTERPRETATION OF EXPERIMENTAL RESULTS
ON THE BASIS OF SINGLE PARTICLE ORBITS
The mean free path between collisions for the electrons
in VTF is in the order of 5 m. The thermal speed of the
electrons is typically 110 6 m/s, so during a particle confinement
time, p 0.2 ms, the electrons execute hundreds of
complete particle bounce orbits in the poloidal cross sections.
It is therefore natural to seek the explanation for the
observed plasma behavior in the properties of the particle
orbits.
The particle confinement in the VTF device is analyzed
in Ref. 12, based upon the guiding center approximation. In
Ref. 13 an analysis was given for the particle orbits in a
linear magnetic cusp including and electric field along the
direction of the X line, summarized here below.
The crucial mechanism for confining the particles in a
magnetic cusp is the adiabatic invariance of the magnetic
moment mv 2 /(2B), where v is the particle velocity
perpendicular to the magnetic field. We assume that a sufficient
magnetic guide field in the direction of the X line is
present, such that the magnetic moment is conserved at all
locations throughout the cross section. In the absence of an
electric field the particles gyrate around specific field lines
and are confined to regions of the magnetic configuration
where BE k . Here E k is the particle kinetic energy, which,
FIG. 5. Color Density contours measured before, during
and after an ohmic pulse. The ohmic pulse induces
EB-flows, the directions of which are illustrated by
the red arrows in B and C, which perturb the shape
of the density profile. The red dashed lines in D indicate
the locations along which the plasma density is
evaluated in Figs. 6 and 7 as a function of time and the
magnetic flux variable .
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