Pellet injection in tokamaks has been simulated in an MHD model. The pellet is assumed to rapidly ablate and ionize, forming a dense plasma cloud. The cloud's formation is adiabatic, with no energy imparted to the plasma. The flux surface average of the pressure is the same, before and after pellet injection. The model advances the temperature so that it tends to be constant along the magnetic field. The density of the cloud is initially highly nonuniform on flux surfaces.
The simulations show that the plasma evolves through 3D states, ultimately tending towards a 2D equilibrium in which the density and temperature are flux functions. In the initial stages of this evolution, the cloud moves in the direction of increasing major radius. For pellets injected on the outboard side of the plasma, this means that the pellet cloud moves outwards, toward the wall enclosing the plasma. If a wall interaction model were included, part of the cloud's mass would have been lost to the wall. This is consistent with experiments, in which a significant fraction of the pellet mass is lost.
On the other hand, injection on the inboard side causes the cloud to move toward the magnetic axis. The pellet cloud is better confined then with outboard injection. This effect has also been seen in a recent experiment. We showed that if the pellet pressure perturbation is large enough, the effect is sufficient to carry the pellet all the way to the plasma center, an important result for fuelling or quenching of large tokamaks.
Moreover, magnetic reconnection driven by the pellet in this case gives rise to a negative central shear profile, which can be highly favorable for transport. Pellet injection might offer a way to maintain reversed central shear in large long pulse tokamaks.
Injection at the top (or bottom) causes relatively less pellet motion. This might be acceptable for experimental purposes, and would certainly be more accessible than inboard injection.
Finally, we showed that the numerical data is consistent with a simple model, in which the pellet displacement is proportional to the pressure enhancement of the pellet, and to the cosine of the angle between the outward normal to a flux surface at the pellet and the major radius direction. Within our parameter range, the data fit the model quite well. In the future, we plan to incorporate a more realistic ablation model, in higher resolution computations with smaller, denser, pellets, to see whether the model continues to hold. We also plan longer time simulations to track the approach to a two dimensional steady state.