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Wavebreaking of longitudinal plasma oscillations

A general treatment for obtaining the maximum amplitude for nonlinear plasma oscillations is given. Both temperature and relativistic effects are included. The maximum or wavebreaking amplitude is derived for cold plasmas and nonrelativistic fluid velocities, cold plasmas and relativistic fluid velocities, warm plasmas and nonrelativistic fluid velocities and, warm plasmas and relativistic fluid velocities. The various derivations which appear in the literature are unified.