All other things being equal, the 3D evolution depends on the
initial location of the pellet perturbation in the poloidal plane,
as well as the pellet density.
In the case of outboard injection,
the initial density 
is shown in Fig.4(a),
in the
plane 
where the density is a maximum. The pellet is
located at the outboard midplane.
The density enhancement 
where 
is the initial, uniform density, is 15.
On a rapid time scale, during
which there is approximate fast magnetosonic and shear Alfvén
equilibration, the pellet expands outwards
towards larger major radius.
Next, Fig.4(b) shows the
density in the plane at time 
where 
is the Alfvén time defined in terms of the
average toroidal magnetic field and background density.
The pellet both shifts outwards and expands along the
magnetic field.
The displacement of the pellet can be measured by calculating the
flux surface average 
as in (8), using the
toroidally averaged 2D magnetic field, its n=0 component.
This is acceptable if the initial and asymptotic states have
axisymmetric magnetic field. In fact even at intermediate
times, 
the n = 0 part of 
changes relatively little
in comparison with the changes in the average density profile.
The averaged density
is shown in Fig.5 at
times (a) t = 0, (b) t = 30, and (c) t = 96.
The maximum shift occurs at about t = 30.
The peak of the
profile moves to lower
which means that 
has moved closer to the
wall boundary at 
Afterwards,
the peak starts to bounce back towards its initial state. In principle
it should return to its initial state, if the density in each
magnetic flux tube is conserved.
However, there is some loss caused by density diffusivity D and
temperature diffusivity 
with
The three dimensional evolution of the density can be seen
in Fig.6(a,b) and Fig.7(a,b), which are isoplots
of the density surface at 
of its maximum.
Initially the density is localized near toroidal angle
In Fig.6(b)at time t = 51, the pellet has
spread more than once around the torus, which gives an idea of the
sound wave transit time for this case. In Fig.7(a),
at time t = 79, the pellet material has spread out
twice around the torus, and forms a
``snake" like structure.
The pellet material
is not resonant with the q = 2 surface, since the pellet
was injected on an initial 
surface with q ;SPMgt; 2. Hence
it smoothes out as time elapses, as seen in
Fig.7(b) at t = 96.