The fundamental solution of the Fokker-Planck equation for heavy (or large) ions in a fluid in a generally time-varying electric field is presented. The solution procedure makes use of a convenient transformation of the variables (position r and velocity v) which is suggested by the physics of the problem, and which reduces the solution of the complete Fokker-Planck equation to the well-known solution of this equation in the field-free case. The result obtained shows that, at any time t, the "local" ion velocity distribution f(r,v,t) (apart from the normalization factor taking into account the total number of the ions) differs from the product of the ion number density n(r,t) by the "global" ion velocity distribution Phi(v,t), for a corrective factor C(r,v,t) which is generally different from unity also in the absence of the electric field. The fundamental solution of the Fokker-Planck equation is then widely discussed, in the long-time limit, in the cases of a static-and of an alternate-electric field acting on the fluid. From this discussion, the physical meaning and the importance of C(r,v,t) emerge in a particularly evident manner. (C) 2003 American Institute of Physics.