IEEE TRANSACTIONS ON PLASMA SCIENCE, VOL. 32, NO. 2, APRIL 2004 555 Scattering in the Attractive Yukawa Potential: Application to the Ion-Drag Force in Complex Plasmas S. A. Khrapak, A. V. Ivlev, G. E. Morfill, S. K. Zhdanov, and H. M. Thomas Abstract—Scattering in the attractive screened Coulomb (Yukawa) potential is investigated. The momentum-transfer cross section is numerically calculated and analytical approximations are presented. The results are applied to estimate the ion-drag force acting on an isolated micron-sized grain in low-pressure bulk plasmas. Index Terms—Complex (dusty) plasmas, ion-drag force, ion-grain collision. I. INTRODUCTION T HE SCREENED Coulomb (Debye–Hückel or Yukawa) potential is widely used in physics, being a good ap- proximation to describe interaction between charged particles in (dusty/complex) plasmas, colloidal suspensions, etc. The momentum transfer in pair collisions of particles interacting via the Yukawa potential is well investigated in the limit when the interaction is “weak” in the sense that its range (distance at which the interaction energy is equal to the kinetic energy) is much shorter than the plasma screening length. This limit is known as the theory of Coulomb scattering and is extensively used to describe collisions in usual electron–ion plasma [1]–[3]. At the same time, we are not aware of any systematic classical calculation of the momentum-transfer cross section in the opposite limit of “strong” interaction (range of interaction exceeds the screening length). The latter situation is of interest when (at least) one of the particles is highly charged and/or their relative velocity is small. For example, it is quite common for ion-grain collisions in complex plasmas with (sub)thermal ion drifts. In this paper, we report an analytical approach (based on our numerical calculations) to obtain the momentum-transfer cross section for pair collisions of particles interacting via the attrac- tive Yukawa potential. Most attention is paid to the limit when the interaction is strong. We apply the obtained results to de- scribe ion-grain collisions and estimate the ion drag force acting on a negatively charged grain in a bulk plasma. The area of ap- plicability of the estimates (which assume “collisionless” ions and “isolated” grain) is defined in terms of neutral gas pressure and grain concentration. Manuscript received August 13, 2003; revised October 22, 2003. The authors are with the Centre for Interdisciplinary Plasma Science, Max-Planck-Institut für Extraterrestrische Physik, D-85741 Garching, Ger- many (e-mail: skhrapak@mpe.mpg.de). Digital Object Identifier 10.1109/TPS.2004.826073 II. FORMULATION OF THE PROBLEM Let us consider collision between two particles of masses and interacting via isotropic potential . This problem is equivalent to the scattering of a single particle of reduced mass, , in a field (whose center is at the center of masses). First, we study the case of pointlike particles; the role of finite sizes is addressed later. Introducing the relative velocity and the impact parameter , we get the deflection angle , where [4] (1) Here is the effective potential energy (normalized by the kinetic energy ) (2) The scattering momentum-transfer cross section is given by (3) Integration in (1) is performed from the distance of the closest approach, —the largest root of the following: (4) Using (1)–(4), the momentum-transfer cross section can be generally calculated for arbitrary potential . For the Yukawa potential (where is the screening length and is positive for attraction), the following important parameter can be introduced: (5) which is the ratio of the Coulomb radius to the screening length . First, we note that this parameter characterizes the strength of interaction. The interaction can be called “weak” if the Coulomb radius is much shorter than the screening length . In the opposite limit, the interaction can be called “strong.” Second, normalizing and by the screening length, we get that is the only parameter the function depends on. The same applies for the deflection angle [see (1)]. Therefore, we conclude from (3) that depends only on and, hence, (5) defines a unique parameter which describes scattering for Yukawa interaction. In Section III, the dependence is investigated in a wide range of . 0093-3813/04$20.00 © 2004 IEEE