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.