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arXiv 0910.5709physics.plasm-ph
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粘性电阻等离子体中的非线性电子振荡

Nonlinear Electron Oscillations in a Viscous and Resistive Plasma

A. A. Skorupski, E. Infeld

摘要:

给出了电子流体与静止离子流体振荡的新的非线性、空间周期性、长波长静电模式(朗缪尔波),其中包括粘性和电阻效应。采用冷等离子体近似,这要求波长足够大。确定了适用于大振幅波的相关要求。电子流体的连续性方程和动量传递方程以及泊松方程的一般非线性解以简单的参数形式得到。结果表明,在所有典型的氢等离子体中,等离子体电阻率对所讨论的模式的影响可以忽略不计。在所得到的解的限制范围内,可以确定任意(周期性)初始电子数密度分布n_e(x,t = 0)的非线性时间演化(实例)。对于所讨论的模式,只要波长λ>> lambda_{min}(n_0,T_e),严格冷无碰撞等离子体的理想化模型适用于任何实际等离子体,其中n_0 =常数,T_e为电子数密度和电子温度的平衡值。在这个理想化的模型中,初始电子密度n_e(x_{min},t = 0)的最小值必须大于其平衡值n_0/2的一半。否则,在等离子体振荡半个周期后得到的相应最大n_e(x_{max},t = τ_p/2)将爆破。放松这个限制n_e(x,t = 0)作为一个减少λ,由于电子粘度效应的增加,详细检查。强的等离子体粘度被证明在时间演化过程中会显著改变密度分布,例如,将最大值一分为二

英文摘要:

New non-linear, 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 non-linear 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 non-linear time evolution of any (periodic) initial electron number density profile n_e(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 lambda >> lambda_{min}(n_0,T_e), where n_0 = const and T_e 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(x_{min}, t=0) must be larger than half its equilibrium value, n_0/2. Otherwise, the corresponding maximum n_e(x_{max},t=tau_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 lambda, 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.

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