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 (omega(p)t(mix)) as a function of amplitude of the wave packet (delta) and width of the spectrum (Delta k/k) has been derived. It is found that the phase mixing time crucially depends on the relative magnitude of amplitude "delta" and the spectral width "Delta k/k". For Delta k/k <= 2 omega(2)(p)delta(2)/c(2)k(2), omega(p)t(mix) scales with delta as similar to 1/delta(5), whereas for Delta k/k > 2 omega(2)(p)delta(2)/c(2)k(2), omega(p)t(mix) scales with delta as similar to 1/delta(3), where omega(p) 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. Published by AIP Publishing.