Physica 105A (1981) 337-346 O North-Holland Publishing Co. DYNAMICS OF A BROWNIAN PARTICLE IN A PLASMA IN THE LONG-TIME LIMIT R. DICKMANt and R.L. VARLEY Hunter College C.U.N.Y., Department of Physics and Astronomy, New York, New York 10021, USA Received 23 July 1980 The velocity autocorrelation function (VAF) of a Brownian particle in a plasma is calculated in the long-time limit. The Brownian particle VAF exhibits the same qualitative behavior as the electron VAF in a one-component plasma: oscillations at the plasma frequency and decay -t 3/2. 1. Introduction The velocity autocorrelation function (VAF), CD(t), is defined as CD(t) = <V(0)v(t)), where v(t) is the velocity of a particle along the x-axis at time t and (...) indicates an ensemble average. Interest in the long-time behavior of the VAF was stimulated by the molecular dynamics simulations of Alder and Wain- wright'), which showed that after about 10 collision times the VAF decays non-exponentially, and is governed instead by a power law CD-- t -~/2 (d is the dimensionality of the system). A survey of the theory of the Alder-Wain- wright effect may be found in the review of Pomeau and Resibois2). The molecular dynamics results also led to a re-examination of the motion of a macroscopic (Brownian) particle through a fluid. Alder and Wainwright suggested the long-time tail could be understood qualitatively by analogy with the vortex flow pattern due to a small disturbance in an initially stationary fluid. The molecular velocity field and the flow obtained by solving the Navier-Stokes equation show a striking similarity in the long-time limit. The hydrodynamic theory has been confirmed by Kim 3) and his co-workers, who have demonstrated long-time non-exponential decay of the velocity of small (2-3 gm) spheres. If the VAF of an ensemble of Brownian particles is calculated using the Langevin equation, with the force (i.e. the non-stochastic component) on the t Present address: The University of Texas at Austin, Department of Physics, Austin, Texas 78712, USA. 337