Phase mixing of relativistically intense longitudinal wave packets in a cold plasma

Phase mixing of relativistically intense longitudinal wave packets in a cold homogeneous unmagnetized plasma has been studied analytically and numerically using the Dawson Sheet Model. A general expression for phase mixing time ( ω p t m i x ) as a function of amplitude of the wave packet (δ) and width of the spectrum ( Δ k / k ) has been derived. It is found that the phase mixing time crucially depends on the relative magnitude of amplitude “δ” and the spectral width “ Δ k / k ”. For Δ k / k ≤ 2 ω p 2 δ 2 / c 2 k 2 , ω p t m i x scales with δ as ∼ 1 / δ 5 , whereas for Δ k / k > 2 ω p 2 δ 2 / c 2 k 2 , ω p t m i x scales with δ as ∼ 1 / δ 3 , where ωp is the non-relativistic plasma frequency and c is the speed of light in vacuum. We have also verified the above theoretical scalings using numerical simulations based on the Dawson Sheet Model.