Phase mixing of relativistically intense waves in a cold homogeneous plasma

Abstract

We report on spatiotemporal evolution of relativistically intense longitudinal electron plasma waves in a cold homogeneous plasma, using the physically appealing Dawson sheet model. Calculations presented here in the weakly relativistic limit clearly show that under very general initial conditions, a relativistic wave will always phase mix and eventually break at arbitrarily low amplitudes, in a time scale omegapetaumix approximately {3/64(omegape2delta3/c2k2)|Deltak/k|(|1+Deltak/k|)](1+1|1+Deltak/k|)}(-1). We have verified this scaling with respect to amplitude of perturbation delta and width of the spectrum (Deltakk) using numerical simulations. This result may be of relevance to ultrashort, ultraintense laser pulse-plasma interaction experiments where relativistically intense waves are excited.

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

“…In a typical laser/beam plasma interaction experiment, a spectrum of relativistically intense plasma waves with an arbitrary spread in ∆k(and hence in v ph ) is excited because of group velocity dispersion and nonlinear distortion of light pulse near the critical layer [19,20]. Such a wave packet exhibits phase mixing and breaks at arbitrarily small amplitudes [19]. By studying the space-time evolution of two relativistically intense waves having wave numbers separated by an amount ∆k, authors in ref.…”

“…Therefore a thorough understanding of the phase mixing process and estimation of phase mixing time (wave breaking time) of relativistically intense plasma waves is relevant for these experiments. In a typical laser/beam plasma interaction experiment, a spectrum of relativistically intense plasma waves with an arbitrary spread in ∆k(and hence in v ph ) is excited because of group velocity dispersion and nonlinear distortion of light pulse near the critical layer [19,20]. Such a wave packet exhibits phase mixing and breaks at arbitrarily small amplitudes [19].…”

“…For example study of nonlinear plasma waves is important from the point of view of wakefield acceleration where the wake wave is excited either by passing laser pulses or bunches of relativistic electron beams through a plasma chamber [1,9,16,17,18]. Amplitude of these relativistically intense space charge waves is limited by the phenomenon of wave breaking, which occurs via a well known process called phase mixing [19,20,21,22]. Phase mixing results in crossing of neighbouring electron orbits which is caused by temporal dependence of phase difference between oscillating electrons constituting the oscillation/wave [20].…”

“…By studying the space-time evolution of two relativistically intense waves having wave numbers separated by an amount ∆k, authors in ref. [19] showed that, in general a wave packet having amplitude δ and spectral width ∆k will phase mix and break in a time scale given by ω p t mix ∼ . This expression shows that in the limit ∆k/k → 0, ω p t mix → ∞ i.e a sinusoidal wave will not undergo phase mixing.…”

“…Phase mixing results in crossing of neighbouring electron orbits which is caused by temporal dependence of phase difference between oscillating electrons constituting the oscillation/wave [20]. This temporal dependence of phase difference between neighbouring oscillating electrons arises because of background density inhomogeneities (either fixed [23,24] or self-generated [25]) and/or because of relativistic mass variation effects [19,21,22,26]. The process of phase mixing leading to wave breaking not only limits the maximum achievable electric field in laser/beam driven wakefield experiments, but also is applicable to some electron injection schemes [27,28,29], where the wake wave moves along a density gradient and traps electrons by breaking.…”