Nonlinear electron oscillations in a viscous and resistive plasma.
Nonlinear, spatially periodic, long-wavelength electrostatic modes of an electron fluid oscillating against a motionless ion fluid (Langmuir waves) are given, with viscous and resistive effects included. The cold plasma approximation is adopted, which requires the wavelength to be sufficiently large. The pertinent requirement valid for large amplitude waves is determined. The general nonlinear solution of the continuity and momentum transfer equations for the electron fluid along with Poisson's equation is obtained in simple parametric form. It is shown that in all typical hydrogen plasmas, the influence of plasma resistivity on the modes in question is negligible. Within the limitations of the solution found, the nonlinear time evolution of any (periodic) initial electron number density profile ne(x,t=0) can be determined (examples). For the modes in question, an idealized model of a strictly cold and collisionless plasma is shown to be applicable to any real plasma, provided that the wavelength λ>>λmin(n(0),Te) , where n(0)=const and Te are the equilibrium values of the electron number density and electron temperature. Within this idealized model, the minimum of the initial electron density n(e)(xmin,t=0) must be larger than half its equilibrium value, n(0)/2 . Otherwise, the corresponding maximum n(e)(xmax,t=τ(p)/2) , obtained after half a period of the plasma oscillation blows up. Relaxation of this restriction on n(e)(x,t=0) as one decreases λ , due to the increase of the electron viscosity effects, is examined in detail. Strong plasma viscosity is shown to change considerably the density profile during the time evolution, e.g., by splitting the largest maximum in two.
Skorupski
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Department of Theoretical Physics, Soltan Institute for Nuclear Studies, Hoza 69, 00-681 Warsaw, Poland. askor@fuw.edu.pl
Infeld
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