Alfvén脉动的控制方程

本文由磁流体力学方程组导出了行星际空间中不可压缩小尺度脉动的控制方程组。对这一组方程的讨论表明,在小振幅极限下,脉动幅度的径向变化可由通常文献中引用的Alfvén波在缓变磁流体介质中传播的WKB解来描述。当脉动幅度与平均磁场强度之比为有限值时,在一般情况下,控制方程中的非线性项不能略去,因而不能用WKB解来描述有限振幅脉动幅度的径向变化。这一结论可以解释为什么在0.3—0.9AU实测Alfvén脉动振幅和谱的变化与WKB解不一致。在这组控制方程的基础上提出了一个定性的模式。将Alfvén脉动看作主要由许多具有不同波矢k的向外传播的有限振幅的Alfvén模式组成。它们在传播过程中将产生一级小量的波动。零级量与一级量的非线性相互作用使波能向高频区串级。零级量波动振幅的变化不仅受到太阳风慢变化的影响,而且受到这一非线性相互作用的影响。这一模式可以定性解释主要的Alfvén脉动的观测事实。 

THE GOVERNING EQUATIONS OF THE VARIATION OF ALFVENIC FLUCTUATIONS

A group of equations governing the incompresible small time scale fluctuations in interplanetary magnetic field are derived from the MHD equations.The discusion of the governing equations show that the radial variation of the amplitude of the fluctuation can be discribed by the Alfven wave WKB model only at the small amplitude limite.When the amplitude of the fluctuation is finite with respect to the average magnetic field intensity,the nonlinear terms in the garvening equations can not be droped and the WKB aproxima-tion fails.That is the reason why the radial variation of the amplitude of the Alfvenic fluctuations from 0.3 AUto 1 AU observed by Heios does not agree with the WKBwaves model.According to the properties of the governing equations,a qualytative model for the propegation of Alfvenic fluctuations is presented.Alfvenic fluctuations can be considered to be in zeroth-order conpoused of many waves with different wave numbers propogating from the Sun towards away,but some wave modes in first-order will be generated,the nonlinear interactions between the zeroth order waves and the first order waves cause an energy cascading to high frequency range.The amplitude of the zeroth-order wave will be modified not only by the large scale variation of the solar wind but also by the cascading process.This model can explain some properties of Alfvenic fluctuations qualitatively.