Particle-in-cell (PIC) simulations on plasma–sheath boundary in collision-free plasmas with warm-ion sources

Abstract

In this work we investigate how fluid plasma parameters are related to the kinetic plasma properties for plasmas with warm-ion sources and finite Debye lengths. This is an important issue in applying fluid codes to experimental, laboratory, technological and fusion plasmas. Namely, fluid codes for scrape-off layer (SOL) region in fusion devices are applicable only up to the plasma–sheath boundary (also called plasma edge or sheath entrance) and cannot be extended to the material boundaries themselves, because the sheath region is far from thermodynamic equilibrium and hence near the wall plasma can be correctly described only in terms of some kinetic model. Since, accordingly, the boundary conditions for plasma modeled in the fluid description should be defined at the plasma–sheath boundary (rather than at the physical surfaces), this boundary needs to be appropriately identified. However, identifying such a boundary and calculating the hydrodynamic parameters there is a demanding task which up to now has been solved only approximately and for a limited number of plasma discharges (i.e., only for some particular particle and energy production and loss balance scenarios). In available PIC codes the ion source strength profile is usually hard-coded into program and does not change during the simulation (see e.g., Berkeley codes or BIT1). On the contrary, we have built very flexible PIC procedure enabling one to use different source strength profiles in each simulation step. In the present work we present the results obtained with the ion source strength profiles proportional to potential— S i ( x ) ≈ e α Φ ( x ) . We run simulation for cases with α = 0 and α = 1 and compare results of simulation with “classic” numerical results of Scheuer and Emmert (1988) [Scheuer, J.T., Emmert, G.A., 1988. Sheath and presheath in a collisionless plasma with a Maxwellian source. Phys. Fluids 31, 3645] and recently reported results of Kos et al. (2009) [Kos, L., Jelic, N., Kuhn, S., Duhovnik, J., 2009. Extension of the Bissel–Johnson plasma–sheath model for application to fusion-relevant and general plasmas. PhysPlasmas 16 (9)]. We determine the plasma boundary as the point of equality of ion directional velocity and ion-sound velocity calculated with local ion polytropic coefficient as defined by Kuhn et al. (2006) [Kuhn et al., 2006. Link between fluid and kinetic parameters near the plasma boundary. Phys. Plasmas 13, 013503].