Nonlinear Electron Oscillations in a Cold Plasma

Investigations of nonlinear electron oscillations in a cold plasma where the thermal motions may be neglected indicate that except for the simplest one-dimensional situation such oscillations will destroy themselves through the development of multistream flow. It is found possible to give an exact analysis of oscillations with plane, cylindrical, and spherical symmetry. Plane oscillations in a uniform plasma are found to be stable below a critical amplitude. For larger amplitudes it is found that multistream flow or fine-scale mixing sets in on the first oscillation. Oscillations with spherical or cylindrical symmetry develop multistream flow almost always, independent of the amplitude. The time required for mixing to start is inversely proportional to the square of the amplitude. Plane oscillations in a nonuniform plasma are also found to exhibit this type of behavior. Some considerations are also given to more general oscillations and a calculation is presented which indicates that multistream flow will usually set in.