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首页> 外文期刊>Physica Scripta: An International Journal for Experimental and Theoretical Physics >Nonlinear Landau damping in a relativistic electron-ion plasma-non-local nonlinear Schrodinger-equation and Krylov Bogoliubov Mitropolsky method
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Nonlinear Landau damping in a relativistic electron-ion plasma-non-local nonlinear Schrodinger-equation and Krylov Bogoliubov Mitropolsky method

机译：非线性Landau在相对论电子离子等离子体中阻尼 - 非局部非线性Schrodinger等式和Krylov Bogoliubov Mitropolsky方法

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A nonlinear theory of amplitude modulation of electrostatic envelopes in an electron-ion plasma is developed taking care of relativistic effect, using the Vlasov-Poisson equation. By using the multiple scale reductive perturbation, it is shown that such evolution is characterized by the non-local, nonlinear Schrodinger equation. This non-local term is known to take care of the resonant particles having group velocity = partial derivative omega/partial derivative kappa on a finite amplitude plasma wave. On the other hand it is well-known that waves in plasmas can undergo collision-less damping when they resonantly interact with trapped/free particles. Such collision-less damping was termed Landau damping. Our intention in this analysis is to analyze the effect of relativistic electron motion on such collision-less damping in detail. But since the corresponding effect of phase velocity resonance in this classical case is not so prominent, we have not attempted to treat it here and, as assumed, the amplitude is not very large. This gives rise to some new estimates of the frequency shift and energy transfer rate, in both relativistic and non-relativistic cases. In the next phase, we have analyzed the condition of a modulational instability in the non-local, nonlinear Schrodinger equation. Then, the Bogoliubov-Mitropolsky approach is used to study the change in the solitary wave profile due to the presence of non-local nonlinearity in the equation, which is being treated as a perturbation. Last but not the least, the magnitude of the Landau damping is also computed. In the concluding remarks we have compared the kinetic and the usual reductive perturbation approach to the nonlinear Schrodinger equation.
机译：使用Vlasov-Poisson方程，开发了电子离子等离子体中静电包络振幅调节的非线性理论。通过使用多级还原性扰动，示出这种进化的特征在于非局部非线性薛定兆式方程。已知该非局长术语是在有限幅度等离子体波上处理具有组速度=部分衍生ω/部分衍生kappa的共振颗粒。另一方面，众所周知，当它们谐振与捕获/自由粒子相互作用时，等离子体中的波浪可以经历冲突的阻尼。这种冲突的阻尼被称为Landau Damping。我们在该分析中的目的是分析相对论电子运动对这种冲突的抑制的影响。但是，由于该古典案例中相速度共振的相应效果并不是那么突出，因此我们没有尝试在这里对待它，并且如假设，幅度不是很大。这引起了相对论和非相对论的频移和能量转移率的一些新估计。在下一阶段，我们已经分析了非本地非线性薛定林方程中的调制不稳定条件。然后，通过在等式中存在非局部非线性的存在，将Bogoliubov-Mitropolsky方法研究孤立波形曲线的变化，其被视为扰动。最后但并非最不重要的是，也计算了Landau阻尼的大小。在结束语中，我们将动力学和通常的还原扰动方法与非线性薛定林方程进行了比较。

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