Topic/Type: 1.2 Fusion Plasmas (magnetic & inertial confinement), Poster

### SEM code for radiofrequency sheath Physics

E. Faudot1, S. Heuraux1, L. Colas2

1 IJL, Nancy Universit?, 54500 Vandoeuvre les Nancy
2 CEA, IRFM, F-13108 Saint-Paul-lez-Durance, France

The SEM (Sheath Effect Modeling) code is dedicated to compute the rectified potentials induced by radio-frequency (RF) sheaths in magnetized plasmas. The rectification of the RF sheaths at the connection points on the wall of a magnetic field line works as a diode bridge and then transforms a RF signal into a rectified RF signal with a non null DC component. The explanation of the rectification process comes from the non linear I-V characteristic of sheaths, which looks like a diode characteristic. Then the SEM code is based on the conservation of currents coupled with the momentum equation for ions. The resulting non linear equation for the potential is implemented in a 2D fluid code with a semi-implicit scheme assuming a constant potential along the magnetic field line, then the length of magnetic field becomes a parameter. Without this last assumption the code should be 3D. The finite difference algorithm is written by using the UMFPACK, a set of linear algebra routines able to solve large sparse matrix very efficiently. The main difficulty came from the second order time derivative for the potential to simulate inductive currents coupled with the non linear characteristic of sheath. For covering all the frequency range used in the heating scenarios this term has been added to validate the code for frequencies lower and higher than the ion cyclotron frequency, which is the resonant frequency for the transverse RF currents (perpendicular to the magnetic field). The low frequency scheme is stable for a wide range of parameters and can be solved analytically as a function of time in 0D. The analytic solution of the low frequency scheme is a combination of Bessel functions with a steady state, a transient and oscillatory terms. On the contrary the all frequency scheme works only in a range of parameters for which the RF potential is not too much high ($\small < 100$ Te with Te the electron temperature in eV) and not known analytic solution. Finally examples of 467 by 50 cells potential maps input in the SEM code are presented as a function of time, which permits to visualize oscillations of rectified potential structures in front of a Tokamak Ion Cyclotron RF antenna.