Contrib. Plasma Phys. 46, No. 7-9, 649 – 654 (2006) / DOI 10.1002/ctpp.200610058 Formulation of Boundary Conditions for the Unmagnetized Multi-Ion-Component Plasma Sheath D. Tskhakaya *1,3 , S. Kuhn 1 , and Y. Tomita 2 1 Association Euratom- ¨ OAW, Department of Theoretical Physics, University of Innsbruck, A-6020 Innsbruck, Austria 2 National Institute for Fusion Science, 322-6 Oroshi-cho, Toki 509-5292, Japan 3 Permanent address: Institute of Physics, Georgian Academy of Sciences, 380076 Tbilisi, Georgia Received 19 October 2005, accepted 9 February 2006 Published online 22 August 2006 Key words Plasma sheath, PIC simulations PACS 52.40.Kh, 52.40.Hf, 52.25.Xz, 52.65.Rr Boundary conditions are derived for the unmagnetized electrostatic multi-ion-component plasma sheath. Ana- lytic results are supported by high-resolution numerical kinetic (particle-in-cell) simulations. c  2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim 1 Introduction The formulation of boundary conditions is an interesting and important task for plasma edge studies, in which one is guided by the following reasons [1], [2]: (i) these conditions are used for estimating particle and heat fluxes at the wall, and (ii) they are used as boundary conditions in fluid, gyro-kinetic and gyro-fluid codes simulating the plasma edge. Starting from [3], a huge number of contributions has been devoted to this topic. Quite surprisingly, how- ever, just a few of them deal with multi-ion-component (MIC) plasmas, which are the usual case in reality. (In this paper, the term “ion component” is used synonymously with “ion species”) Probably the first paper where boundary conditions for the MIC plasma have been studied was [4]. The author considered two extreme cases: (i) highly Coulomb-collisional plasma, where due to collisional coupling all ions have the same velocity, and (ii) the case with collisionless ions. A more general approach has been used in [5]- [7]. These authors generalized the definition of the sheath edge (SE) for the MIC plasma. This condition represents just one condition for the N ion-component plasma and cannot be used as a closed set of boundary conditions, for which N conditions are needed (one per ion component). A complete set of boundary conditions for the MIC plasma has been formulated in our previous papers [8], [9], where we derived a set of algebraic equations the solution of which yielded the corresponding boundary conditions. The aim of the present work is to re-derive the boundary conditions for MIC plasmas in a much simpler form. The conditions obtained allow for convenient general analysis of the boundary conditions and can easily be used for different applications. In the next section we derive our boundary conditions analytically, and in Sec. III these results are cross-checked via kinetic simulations. Our conclusions are drawn in Sec. IV. 2 Theory The formulation of general boundary conditions is an extremely complicated task even for a single-ion plasma (e.g. see [10], [11]). In order to simplify the analysis, it is usually assumed that λ D ≪ ρ ≪ l, (1) ∗ Corresponding author: e-mail: david.tskhakaya@uibk.ac.at, Phone: +43 512 507 6225, Fax: +43 512 507 2919 c  2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim