J. Plasma Physics (2006), vol. 72, part 6, pp. 1015–1018. c  2006 Cambridge University Press doi:10.1017/S0022377806005137 Printed in the United Kingdom 1015 Charging of a spherical dust particle on a plasma-facing wall YUKIHIRO TOMITA 1 , R. SMIRNOV 2 , T. TAKIZUKA 3 and D. T S K H A K A Y A 4 1 National Institute for Fusion Science, 322-6 Oroshi-cho, Toki 509-5292, Japan 2 The Graduate University for Advanced Studies (Soken-dai), 322-6 Oroshi-cho, Toki 509-5292, Japan 3 Naka Fusion Research Establishment, Japan Atomic Energy Research Institute, Naka, Ibaraki 311-0193, Japan 4 Association Euratom- ¨ OAW, Institute of Theoretical Physics, University of Innsbruck, Technikerstrasse 25/II, Innsbruck A-6020, Austria (Received 15 August 2005 and accepted 2 December 2005) Abstract. The induced charge of a spherical conducting dust particle on a plasma- facing wall is studied analytically. An external non-uniform electric field is ap- proximated by the polynomial of the axial coordinate and the bipolar coordinate is introduced in order to employ the boundary condition. The result is applied to the dust in the non-uniform electric field in the Debye sheath in front of the conducting wall. The results are useful for analyzing the shielding effects of the plasma surrounding a dust particle. 1. Introduction Dust in plasmas is an interesting topic with a developing science community connec- ted to astrophysical, space, laboratory, and processing plasma applications as well as nuclear fusion. The dust in fusion plasmas is important because it may influence the plasma as a source of impurities or other confinement limitations, and presents safety and operational challenges for a nuclear fusion facility, such as ITER, due to absorption of radioactive tritium [1]. In this study, we investigate analytically the charge formation of a spherical conducting dust particle on a plasma-facing wall. The two-dimensional structure of the sheath around the spherical dust is formed. The non-uniform electric field induces the charge on the surface of the dust particle. The plasma shields the induced charge. We study analytically the induced charge on the spherical dust immersed in the non-uniform electric field, which is formed in the Debye sheath in front of the plasma-facing wall. 2. Electrostatic potential A spherical conducting dust particle with a radius R d is attached on an infinitely extended conducting plane wall. The potential φ in due to the induced charge on the dust satisfies the Laplace equation  ∂ ∂α  α α 2 + β 2 ∂ ∂α  + ∂ ∂β  α α 2 + β 2 ∂ ∂β  φ in =0 (2.1)