Transit-time damping and the arrest of wave collapse

Power dissipation by transit-time damping is investigated analytically and numerically using a perturbation expansion and a test-particle code, respectively. Excellent agreement between the two methods is found for both one-dimensional and multidimensional systems. It is shown that the local power dissipation can take on positive or negative values depending on position, implying that particles not only carry off energy from localized fields, but redistribute it within them. The results are applied to estimate the arrest scales of the collapsing wave packets found in strongly turbulent plasmas. Arrest scales in the ranges (14--23)λD and (16--26)λD are found for two- and three-dimensional wave collapse, respectively. These estimates are consistent with results from particle-in-cell simulations, which yielded arrest scales of ∼14λD in 2D and ∼20λD in 3D, and with experimental results that implied arrest at scales of (17--30)λD in 3D. The previously problematical outcome that 3-D collapse is arrested at a longer scale than in 2D, despite its stronger nature, results because the larger fraction of high-velocity particles in the 3-D plasma velocity distribution leads to stronger transit-time damping than in the corresponding 2-D system. It is argued that transit-time dissipation will arrest the collapse of particularly intense wave packets at even longer scales due to the increase in the local Debye length caused by localized heating near the center of these wave packets and due to the formation of high-velocity tails by transit-time acceleration