Analytic model of the cathodic region of a Micro Hollow Cathode Discharge: comparison to PIC simulations.

A model of the cathodic region of a Micro Hollow Cathode Discharge (MHCD) is presented. The key feature of the model is to correctly calculate the ionization profile resulting from energetic electrons generated in the sheath and entering the plasma region with significant energy. To simplify the problem, a pure argon discharge in a 1D planar geometry is first considered. The model is decomposed into two separated regions: (i) the quasi-neutral region in the center (the so-called plasma bulk region) and (ii) the cathode sheath region near the surface. The two models are coupled at the plasma-sheath interface, where the electric fields and the discharge current must be continuous. To validate the model and guide the theoretical analysis, we use Particle-In-Cell (PIC) simulations for a base case (pure Ar at 100 Torr). Once the physics of this simplified geometry is understood and validated, a second symmetrical sheath is added to mimic the MHCD configuration. This complete model is then compared to experimental findings on the electron density and sheath thickness variations. The discharge expansion on the cathode back side and the role of the secondary electron emission coefficient are also discussed.