Force on a Charged Test Particle in a Collisional Flowing Plasma A.V. Ivlev, S. A. Khrapak, S. K. Zhdanov, and G. E. Morfill Centre for Interdisciplinary Plasma Science, Max-Planck-Institut fu ¨r Extraterrestrische Physik, D-85741 Garching, Germany G. Joyce Plasma Physics Division, Naval Research Laboratory, Washington, D.C. 20375-5346, USA (Received 28 October 2003; revised manuscript received 27 January 2004; published 21 May 2004) The force on a charged test particle embedded in a flowing (electron-ion) plasma is calculated using the linear dielectric response formalism. This approach allows us to take into account ion-neutral collisions self-consistently. The effect of collisions on the ion drag force is analyzed. It is shown that collisions can play a major role and can enhance the force substantially. DOI: 10.1103/PhysRevLett.92.205007 PACS numbers: 52.27.Lw, 52.20.Hv The main forces acting on a charged particle embedded in a weakly anisotropic (unmagnetized) plasma have an electrostatic nature. They are usually exerted due to self- consistent large-scale electric fields and the plasma fluxes induced by these fields. The combination of the momen- tum transfer due to the relative plasma flow (‘‘drag force’’) and the electrostatic force determines equilibrium plasma configurations. Knowledge of the drag force is especially important in complex (dusty) plasmas, when equilibrium states as well as dynamics of charged micro- particles are considered. In this Letter, we calculate the force on a charged test particle embedded in a flowing (electron-ion) plasma using the linear dielectric response formalism. This approach allows us to take into account ion-neutral collisions self-consistently and also to re- trieve the potential distribution around the particle. We analyze how the collisions change the flow-induced force on the particle and apply the obtained results to evaluate the ion drag force on charged microparticles in complex plasmas. We start by calculating the potential around a pointlike test particle. The plasma flows with very small relative velocity u (much smaller than the ion thermal velocity v T i   T i =m i p , e.g., ambipolar drift in bulk plasmas). The equivalent problem is to calculate a potential around the particle moving through the plasma with the velocity u. The potential is [1] ’R Z 4eZe ikR k 2 "ku;k dk 2 3 ; (1) where R is the coordinate with respect to the particle center and Z is the particle charge number (positive or negative). The plasma permittivity is "  1   e   i , with the electron susceptibility  e ’k De  2 . The ion suscepti- bility is [2]  i !;k 1 k Di  2  1  F  1  i !i F   ;   !  i  2 p kv T i : (2) Here  De;i   T e;i =4e 2 n q is the electron or ion Debye length with n the unperturbed (electron or ion) density, and  is the effective frequency of the ion-neutral colli- sions. The power series for the dispersion function is F ’2 2  i   p  (for jj 1), and the asymptotic series is F ’1  1 2  2 (for jj 1) [3].We assume the flow is along the z axis. Introducing the ion mean-free path ‘  v T i = and the thermal Mach number M T  u=v T i , we substitute ! k z u in Eq. (2) and expand it into a series over small M T . Then the first two expansion terms for the plasma permittivity are "k’ 1  1 k 2  8 > < > :  1  iM T k z k 2 ‘  ;M T  k‘  1;  1  iM T   2 p k z k  ; k‘  1: (3) Here "k "k z u;k and  is the linearized Debye length,  1    2 Di   2 De q , which is assumed to be very close to the ion Debye length (since T e is usually much larger than T i ). In the hydrodynamic limit (k‘  1), the plasma polarization along the flow is due to the ion collisions with neutrals. In the opposite weakly colli- sional limit (k‘  1) it is because of the ion Landau damping. Note that for k‘  M T the permittivity scales as /M T k z  1 , or even / k 2 (depending on k). One can divide the potential in Eq. (1) into the ‘‘screened’’ and the ‘‘wake’’ parts: ’  ’ 0  ’ w . The isotropic screened potential ’ 0 ReZ=R expR= is determined by "0;k " 0 k’ 1 k 2 , so that the distortion due to the plasma flow is ’ w R eZ 2 2 Z  1 "k  1 " 0 k  e ikR k 2 dk: (4) Let us consider the potential profile along the z axis. We normalize the wave number and coordinate by the screen- ing length, k ! k and z= ! z, and, substituting Eq. (3) in Eq. (4), finally obtain for the wake potential: PHYSICAL REVIEW LETTERS week ending 21 MAY 2004 VOLUME 92, NUMBER 20 205007-1 0031-9007= 04=92(20)=205007(4)$22.50  2004 The American Physical Society 205007-1