Nonlinear Density Waves in the Single-Wave Model

Details Nonlinear Density Waves in the Single-Wave Model Nonlinear Density Waves in the Single-Wave Model

2010-11-14

arxiv.org/abs/1011.3263v4

Phys. Plasmas 18, 032305 (2011)

Physics

Plasma Physics

7 pages, To appear in the Physics of Plasmas, Volume 18, Issue 3

Scientific paper

10.1063/1.3562878

The single-wave model equations are transformed to an exact hydrodynamic closure by using a class of solutions to the Vlasov equation corresponding to the waterbag model. The warm fluid dynamic equations are then manipulated by means of the renormalization group method. As a result, amplitude equations for the slowly varying wave amplitudes are derived. Since the characteristic equation for waves has in general three roots, two cases are examined. If all three roots of the characteristic equation are real, the amplitude equations for the eigenmodes represent a system of three coupled nonlinear equations. In the case, where the dispersion equation possesses one real and two complex conjugate roots, the amplitude equations take the form of two coupled equations with complex coefficients. The analytical results are then compared to the exact system dynamics obtained by solving the hydrodynamic equations numerically.

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