## Section: New Results

### Quasi-neutrality equation in a polar mesh

Participants : Michel Mehrenberger, Philippe Helluy, Guillaume Latu, Nicolas Crouseilles, Christophe Steiner.

In the quasi-neutrality equation in GYSELA, we are now able to treat correctly the inner radius thanks to a simple trick by taking the inner radius $\frac{\Delta r}{2}$. We also continue working on the gyro-average approximation. The new Padé method depends on a parameter $\epsilon $. When setting $\epsilon $ to a large value, the solution is very similar to the classical Padé one, while taking small value for $\epsilon $ leads to a solution very near to the one obtained using the interpolation method (which approximates better the exact operator, but which can however lead to unstable results as it does not damp high modes). We can then prevent the scheme from instability, by setting large $\epsilon $, but not too large in order to be more accurate than the classical Padé approximation. Further study in GYSELA is under discussion.