Pellet Ablation in Tokamak Refueling Process
 R. Samulyak and T. Lu

The purpose of this research is to develop novel mathematical models, numerical algorithms based on explicit tracking of interfaces, and computational software, and to perform large scale numerical simulations of complex physics processes associated with the injection of frozen deuterium-tritium fuel pellets in tokamaks. This research is being performed in collaboration with General Atomics and Princeton Plasma Physics Laboratory (PPPL).

Figure 1. Mach number distribution of the pellet ablation flow demonstrating double transonic layers.

We have developed a 2D axisymmetric model for the pellet ablation in tokamaks based on the front tracking MHD code [1]. Since the method of front tracking allows the study of multiphysics phenomena in multiphase systems characterized by strong discontinuities in physical properties of the system components, it is ideally suitable to the pellet ablation problem. In our computational model, explicit interfaces separate the solid pellet from the ablated gas, and the cold, dense, and weakly ionized ablation cloud from the highly conducting fusion plasma. Realistic equations of state are employed in different geometrical regions corresponding to different states of matter. The code is capable of simulating the transition of deuterium in the pellet from solid to liquid state under high ablation pressures. A surface ablation model is used for on pellet surface. An electronic heat flux model for the calculation of the thermal energy deposition in the ablation cloud and on the pellet surface uses approximate analytical solutions of kinetic equations. Atomic physics processes in the ablation cloud such as dissociation, recombination, and ionization are taken into account by a plasma equation of state. Using the developed model, we have performed studies of the pellet ablation physics, pellet ablation rate and the lifetime in the magnetic field, and compared with analytical predictions and previous numerical simulations. The 1D version of the model is in excellent agreement with the scaling laws and ablation rate predicted by the theoretical neutral gas shielding model. The 2D axisymmetric simulations agree with previously published numerical results. Our work goes beyond these studies and calculates properties of the ablation channel in magnetic fields and the reduction of the ablation rate.
 

Figure 2. Ablation rate (left) and radius of the ablation channel (right) in tokamak magnetic fields varying from 2 to 6 Tesla at different background electron plasma density ne and warm-up time tw. Solid line: tw = 10, ne = 1.0e14 cm-1 , dashed line: tw = 10, ne = 1.6e13 cm-1 , dotted line: tw = 5, ne = 10e14 cm-1.

We showed that a common expectation of the nuclear fusion community regarding the role of the anisotropic heating and magnetic field on the pellet ablation rate was incorrect. The study of striation instabilities, impossible without resolving the detailed physics in the ablation cloud, will be the focus of our future research. These instabilities are not well understood and have a significant impact on the pellet-plasma interaction that will occur in the fueling of burning plasmas in ITER. In the future, we will work with PPPL scientists on the coupling of the M3D code with FronTier-MHD as a subgrid model for detailed pellet ablation physics, and performing simulations on the BlueGene.
 

Reference

• [1] Samulyak, R., Lu, T., and Parks, P. A magnetohydrodynamic simulation of pellet ablation in the electrostatic approximation. Nucl. Fusion. Accepted, 2006.

Last Modified: January 31, 2008
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