### Theory Weekly Highlights for February 2001

##### February 16, 2001

In the conventional spherically symmetric steady-state solution of pellet ablation, the solid phase and the gas/plasma phase are treated as distinct domains, imposing certain boundary conditions at the solid-gas interface where the density gradient is extremely sharp. For a time-dependent numerical simulation, a better method is needed the handle the interface. A relatively new method CIP (Cubic-Interpolated Pseudo-particle) can treat the entire domain simultaneously and handles the sharp density gradients by time-splitting the advection part followed by a non-advection part, which avoids numerical diffusion. The real advantage of the CIP method is that it ensures the continuity of acceleration at the interface without the need to introduce special boundary conditions. In pellet ablation, the surface pressure is low enough to treat the solid pellet phase as an essentially incompressible material, and the gas phase as an ideal gas. The CIP method was applied in this idealized framework, and after 3 sec the pellet ablation rate approached a steady state value which is in agreement with the conventional model’s result to high accuracy (< 2%). This is a significant improvement over the results reported at APS 2000 (Ishizaki & Parks). The 2-D version of the code is now operating which will allow us to model the interaction of the ablation flow with the magnetic field.

##### February 09, 2001

The Hall-driven toroidal magnetic field was found to be an important factor in preventing FRC confinement disruption. It stabilizes kink formation by increasing the magnetic field energy without destabilizing curvature-driven plasma motion. For the first time FLAME code simulation runs were long enough to demonstrate nonlinear saturation of the tilt instability and plasma relaxation to a quasi-steady kinetic state. During this transition the FRC was shown to dissipate a substantial amount of initially trapped flux and plasma energy. These effects agree remarkably well with available experimental data.

A paper by Y. Omelchenko, M. Schaffer and P. Parks “Nonlinear Stability of Field-Reversed Configurations witSelf-Generated Toroidal Field” passed internal review and was submitted to Phys. Plasmas.

##### February 02, 2001

A real geometry version of the GKS gyro-kinetic stability code has been ported from the Cray to a local Linux workstation. Comparisons of the linear growth rates from the GLF23 transport model, which was derived for circular geometry, are being compared against the GKS code. The goal is to assess how well the model fits the real geometry growth rates over a range of parameters and explore possible extensions of the model to capture any geometrical effects.

**Disclaimer**

These highlights are reports of research work in progress and are accordingly subject to change or modification