Linear theory of plasma wakes

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Abstract
A test particle immersed in a plasma produces a wake when at least one plasma species is drifting. The present work presents a new approach to the study of plasma wakes. The solution to the problem is found in terms of a spherical harmonics expansion. The solution is studied for conditions typical in dusty plasma experiments: the ions stream relative to the test particle, while the electrons have zero average velocity. The results confirm previous findings obtained with theories based on the Fourier transform method. The present method is characterized by two new aspects. First, the wake field is studied as a function of the ion to electron temperature ratio. Second, the present theory is developed fully in the real space, without introducing the Fourier transform, and can be more naturally extended to include nonlinear effects and to include the collisions between dust particles and plasma species.