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Figure captions

Figure 1.
 Magnetic
field lines of the magnetic bottle as described by
(32) with .
The full 3dimensional picture is obtained by rotation about the
axis.

Figure 2.
 Typical
dynamics in the magnetic bottle at the energy .
The dotted lines show the boundary of the accessible region of
the configuration space, defined by the condition
.

Figure 3.
 Poincaré
plots of the magnetic bottle at the energy as
described in the text. The boundary of the surface of section,
defined by
, shows up as horizontal lines.
(a) . (b) . (c) .

Figure 4.
 The quasiintegral
of the magnetic bottle
(33) plotted as a function of time
for several different values of .
(a) ,
.
(b) ,
.

Figure 5.
 Convergence plot for the magnetic bottle at the energy .
The same Poincaré surface is shown as in figure
3b. On a
grid the
convergence function
has been calculated and the
points with
have been marked with black.

Figure 6.
 A typical graph of
.
A region of pseudoconvergence and a divergent region are
separated by
.
The parameters for this picture are ,
.

Figure 7.

plots for the magnetic bottle at the same energies
as in figure 3. Again the Poincaré surface
is shown as a
grid of points which are shaded,
this time according to their respective values of
,
as shown in the key.
(a) . (b) . (c) .

Figure 8.
 Normalized standard deviations
(marked by ) and their approximants
(solid lines) for the magnetic
bottle. The parameters
and
have been computed using the
data for .
(a) ;
.
(b) ;
.
(c) ;
.

Figure 9.

plot for the magnetic bottle at the energy
. The
grid points are shaded according
to their respective values of
. The calculation
of these values is based on
for
.
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