Van Kampen and Case Formalism Applied to Linear and Weakly Nonlinear Initial Value Problems in Unmagnetized Plasma

A unified account is given of the normal mode theory of homogeneous unmagnetized plasma. Electron (Langmuir), ion sound and electromagnetic waves are treated in stable and (Penrose) unstable plasma with the Van Kampen-Case formalism, using generalized functions. Simplified formulae are derived for second-order Langmuir waves, taking full account of free-streaming effects.