| We obtain longitudinal Akhiezer-Polovin (AP) solution from exact nontrivial space and time dependent solution for a relativistic Langmuir wave, for a particular choice of initial conditions. Though breaking amplitude of AP waves is very high, it is found that they break through phase mixing at arbitrary low amplitude when subjected to small longitudinal perturbation. Results from the simulation show a good agreement with theoretical expectation for the scaling of phase mixing time. We show direct application of these results in recent particle acceleration experiments and simulation. |
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