Dust acoustic instability driven by solar and stellar winds J. Vranjes Belgian Institute for Space Aeronomy, Ringlaan 3, 1180 Brussels, Belgium Abstract. A quantitative analysis is presented of the dust acoustic wave instability driven by the solar or stelar wind. This is a current-less kinetic instability which develops in permeating plasmas, i.e.., when one quasi-neutral electron-ion plasma propagates through another quasi-neutral plasma which contains dust, electrons and ions. The cometary dusty plasma in the solar wind appears to be practically always unstable. Keywords: Dust, acoustic, solar wind PACS: 52.27.Lw, 52.35.Fp, 96.50.Dj, 96.50.Ci INTRODUCTION In the presence of a macroscopic electron velocity relative to static singly-charged ions, a kinetic current-driven instability of the ion acoustic mode may develop. The instability may require rather high values for the electron current. A lower instability threshold may be obtained in the case of two interpenetrating (permeating) plasmas, which implies a current-less instability [1]. This will be demonstrated in the example of the solar wind propagating through the cometary dusty plasma. DERIVATIONS Using the linearized Vlasov-Boltzmann kinetic equation for the perturbed distribution function, the perturbed number density may be calculated from n j1 =  f j1 d 3  v. For the general species j this yields n j1 n j0 = − q j φ 1 κ T j [1 − Z (α j )] . (1) Here, for non-streaming species we have α j = ω /(kv T j ), and Z (α j )= α j (2π ) 1/2  d ξ exp(−ξ 2 /2)/(α j − ξ ). (2) For the streaming species (that flow with the common speed v 0 ) the derivation is similar and Eq. (1) is obtained, but instead of α j and ξ now we have β j =(ω − kv 0 )/(kv T j ) and ζ =(v z − v 0 )/v T j . The quasi-neutrality in the perturbed state n wi1 + n ci1 = n we1 + n ce1 + Z d n d1 will directly yield the dispersion equation. The indices c and w stand for the cometary and wind plasma, respectively. In Eq. (1) for dust the following expansion will be used Z (α d ) ≃ 1 + 1 α 2 d + 3 α 4 d + ... − i  π 2  1/2 α d exp(−α 2 d /2). (3) This is valid if |α d |≫ 1 and |Re(α ) d |≫|Im(α d )|. For the two electron populations we shall use Z (α ce ) ≃ −i(π /2) 1/2 α ce , Z (β we ) ≃−i(π /2) 1/2 β we , that is valid for |α ce |≡ |ω | kv T ce ≪ 1, |β we |≡ |ω − kv 0 | kv T we ≪ 1. The same will be used for the cometary ions, |α ci |≡|ω |/(kv T ci ) ≪ 1. As for the wind ions, the parameter β wi = (ω − kv 0 )/(kv Twi ) contains two terms, where for the first one we expect that ω /(kv Twi ) ≪ 1, while for the second one Dusty/Complex Plasmas: Basic and Interdisciplinary Research AIP Conf. Proc. 1397, 407-408 (2011); doi: 10.1063/1.3659866 © 2011 American Institute of Physics 978-0-7354-0967-5/$30.00 407