Linearized potential of an ion moving through plasma

The solution of the linearized Vlasov-Poisson equations describing a projectile ion moving through a classical isotropic electron plasma is investigated analytically and numerically for a wide range of projectile velocities v_p Extending the range of earlier computations considerably, our calculations were performed for velocities up to v_p = 15v_th, showing the wake field behind the ion for distances 0 ≤ d ≤ 200λ_D, where v_th is the thermal electron velocity and λ_D the Debye length of the plasma. As a new feature, we demonstrate that the amplitude of the wake field in the region v_p/v_th ≤ d/λ_D ≤/23(v_p/v_th)³ is almost undamped, and only for larger distances from the ion does it take the 1/d behaviour shown in other work. Thus the wake field of a single ion persists for much longer than previously thought. The question of whether this effect could have practical consequences, for example, for ion-beam cooling, is briefly addressed.