Collisional damping of Langmuir waves in the collisionless limit

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Abstract
Linear Langmuir wave damping by collisions is studied in the limit of collision frequency ν approaching zero. In this limit, collisions are negligible, except in a region in velocity space, the boundary layer, centered about the phase velocity. If κ, the ratio of the collisional equilibration time in the boundary layer to the Landau damping time, is small, the boundary layer width scales as ν1/3, and the perturbed distribution function scales as ν−1/3. The damping rate is thus independent of ν, although essentially all the damping occurs in the collision‐dominated boundary layer. Solution of the Fokker–Planck equation shows that the damping rate is precisely the Landau (collisionless) rate. The damping rate is independent of κ, although the boundary layer thickness is not.

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