Parametric instabilities of commensurable and incommensurable nonlinear plasma waves

Astronomy and Astrophysics – Astrophysics

Scientific paper

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Cold Plasmas, Crab Nebula, Magnetohydrodynamic Stability, Plasma Waves, Relativistic Plasmas, Stability Tests, Circular Polarization, Density Distribution, Ion Distribution, Low Frequencies, Nonlinear Systems, Polarization (Waves), Relativistic Electron Beams, Two Dimensional Flow

Scientific paper

The behavior of two-dimensional nonlinear waves with an 'ellipticity' ranging from linearly to circularly polarized in a cold relativistic plasma is examined. The stability of commensurable and incommensurable waves is studied using a numerical technique based on Floquet's theorem for periodic systems, an approach which yields a fully self-consistent stability analysis without approximation beyond that of linearization. Plane wave solutions which are strong enough to make the electrons relativistic (assuming the ions to be stationary) are derived, and conditions for obtaining commensurable waves are examined. Relatively low-strength nonlinear waves with a maximum period of about 1 and number density of the background ion distribution of about 0.00001/cu cm were found to be unstable on a time scale of order the wave period. It is suggested that the process of parametric instabilities could be effective in randomizing the energy of the Crab nebula's low frequency wave.

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