非均匀等离子体中的低杂漂移波的研究
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摘要
在电流片中能够激发各种微观不稳定性,这些微观不稳定性可能导致的反常电阻在无碰撞等离子体的磁重联初始发生阶段起着重要的作用。特别是低杂漂移波不稳定性被广泛的认为是最有可能产生反常电阻的源。另外实验上也测量到了磁重联时低杂漂移波的存在,并发现它对磁重联有重要影响。然而关于低杂漂移波对磁场重联贡献的整个物理内涵的理解仍然不是很清楚。
本文主要运用动理学理论研究含有多种离子成份等离子体电流片中的线性低杂漂移波不稳定性以及利用双流体理论研究非均匀等离子体中的非线性低杂漂移波,讨论电流片位形以及多种粒子成分对低杂漂移波的影响,主要有以下六个方面的内容：
1、概述电流片中微观不稳定性的重要性、研究进展以及近期研究热点,重点介绍了低杂漂移波不稳定性的理论和实验研究进展。
2、在局域近似下利用动理学理论去研究三粒子成份Harris电流片中的低杂漂移不稳定性。首先由0阶Vlasov方程和安培方程得到三成分粒子的Harris电流片位形；然后在局域近似下得到含负离子的Harris电流片中的线性低杂漂移模的色散关系,对其数值求解发现发现随着负离子密度的增加,增长率增加,实频减小,另外这支波只能在很小的kz范围内会不稳定,即几乎垂直磁场传播。
3、针对空间观测表明磁重联、磁层亚爆发生时电流片中O+含量很大甚至能占主导地位这一事实,利用非局域动理学理论研究含O+电流片中的低杂漂移模,发现最快增长的低杂漂移模的增长率随O+密度和温度的变化都是非单调的,增长率随O+密度和温度的增加会出现一个最小值。
4、利用动理学理论对Kappa分布电流片中的中间波段(ky(?)～1)的线性低杂漂移波不稳定性进行研究。从线性的Vlasov-Maxwell方程组得到含微积分的本征值方程,并利用本征函数的有限元展开去求解,结果表明Kappa分布电流片中心区的不稳定的低杂漂移波模具有对称性和电磁扰动,同时热离子的引入(即κ值的减小)减小了最快增长的低杂漂移模的增长率并修正这支模的结构。
5、运用动理学理论研究含引导场等离子体中的线性低杂漂移模,发现引导场By的存在导致了本征模(本征函数)和扰动磁场原本存在的奇偶对称性被破坏。另外,引导场的存在增加了增长率、本征模幅度尤其是Az分量幅度和低杂漂移模的电磁分量。
6、利用双流体理论研究非均匀等离子中的非线性低杂漂移孤立波,采用漂移近似得到电子速度,并结合准中性条件得到描述非线性低杂漂移孤立波的Kdv方程,结果表明随着电子温度(密度)越来越不均匀,孤子的幅度和宽度减小,并且幅度最后趋于一个渐近值。
A variety of micro-instability can be excited in the current sheet, these micro-instability may lead to anomalous resistivity which plays an important role in initial stages of magnetic reconnection in the collisionless plasma. In particular, the lower-hybrid drift instability (LHDI) has often been considered as a possible candidate for producing anomalous resistivity. In addition, the LHDI is measured in related experiment when the Magnetic reconnection occurs and it is found that the LHDI has an important effect on magnetic reconnection. However, there is not still a thorough understanding with regard to the fundamental physics of the contribution of the LHDI to magnetic reconnection.
In this dissertation, we study the linear LHDI in current sheet including multi-species ions by using kinetic theory and the nonlinear lower hybrid wave in an inhomogeneous plasma by using two fluid theory. We discuss the effects of the steady state of the current sheet and multi-species on LHDI. There are mainly six aspects in our work as follows:
In the first chapter of the dissertation, some basic concepts are introduced and some recent research developments for micro-instability in current sheet are reviewed. In particularly, the theoretical and experimental research development of the LHDI are shown.
In the second chapter, the LHDI in the Harris current sheet with three species of particles is investigated using kinetic theory under the local approximation. Firstly, the Harris current sheet in a three-species plasma is obtained from zero order Vlasov Equation and Ampere equation; then the dispersion relation of linear LHDI in the Harris sheet in the presence of negative ions could be obtained, and the numerical results show that the negative ion enhances the growth rate and reduces the real frequency of the LHDI. In addition, such LHD wave is unstable in a finite kz value range and propagates almost perpendicularly to the magnetic field.
In the third chapter, for space observations that O+ions are often present and even dominate the plasma sheet, we consider the effect of O+ions on the LHDI using the nonlocal kinetic theory. It is found that the fastest growing mode is not monotonic with O+content and temperature, and there exists a minimum in the growth rate with the increase in O+contend and temperature.
We study the LHDI in a current sheet consisting of particles with theκvelocity distribution in the intermediate wavelength regime ky(?)～1 using kinetic theory. From the linearized Vlasov-Maxwell system, we obtain the corresponding eigenvalue equation, which is solved using a finite-element representation of the eigenfunction, the numerical results show that this unstable mode has even-and odd-parities and an important electromagnetic component, the addition of hot particles (decreasingκ) can decrease the growth rate and modify the mode structure of the most unstable LHD waves.
Using the kinetic theory, the linear LHDI in the plasmas with a weak guide field By is investigated, the results shows that the symmetry property of the mode structure and of the perturbed field is destroyed. The presence of Bv increases the growth rate, the amplitude, especially in the component Az and the electromagnetic component of the eigenmode.
We study the nonlinear lower hybrid drift wave in the inhomogeneity plasma using two fluid theory, electron velocity can be obtained by drift approximation and the nonlinear lower hybrid drift wave can be described by the Kdv equation using the charge quasi-neutral condition, the results show both amplitude and width of the corresponding soliton solution decrease as the inhomogeneity of the electron temperature and density increases, and the amplitude approaches an asymptotic value.
本文主要运用动理学理论研究含有多种离子成份等离子体电流片中的线性低杂漂移波不稳定性以及利用双流体理论研究非均匀等离子体中的非线性低杂漂移波,讨论电流片位形以及多种粒子成分对低杂漂移波的影响,主要有以下六个方面的内容：
1、概述电流片中微观不稳定性的重要性、研究进展以及近期研究热点,重点介绍了低杂漂移波不稳定性的理论和实验研究进展。
2、在局域近似下利用动理学理论去研究三粒子成份Harris电流片中的低杂漂移不稳定性。首先由0阶Vlasov方程和安培方程得到三成分粒子的Harris电流片位形；然后在局域近似下得到含负离子的Harris电流片中的线性低杂漂移模的色散关系,对其数值求解发现发现随着负离子密度的增加,增长率增加,实频减小,另外这支波只能在很小的kz范围内会不稳定,即几乎垂直磁场传播。
3、针对空间观测表明磁重联、磁层亚爆发生时电流片中O+含量很大甚至能占主导地位这一事实,利用非局域动理学理论研究含O+电流片中的低杂漂移模,发现最快增长的低杂漂移模的增长率随O+密度和温度的变化都是非单调的,增长率随O+密度和温度的增加会出现一个最小值。
4、利用动理学理论对Kappa分布电流片中的中间波段(ky(?)～1)的线性低杂漂移波不稳定性进行研究。从线性的Vlasov-Maxwell方程组得到含微积分的本征值方程,并利用本征函数的有限元展开去求解,结果表明Kappa分布电流片中心区的不稳定的低杂漂移波模具有对称性和电磁扰动,同时热离子的引入(即κ值的减小)减小了最快增长的低杂漂移模的增长率并修正这支模的结构。
5、运用动理学理论研究含引导场等离子体中的线性低杂漂移模,发现引导场By的存在导致了本征模(本征函数)和扰动磁场原本存在的奇偶对称性被破坏。另外,引导场的存在增加了增长率、本征模幅度尤其是Az分量幅度和低杂漂移模的电磁分量。
6、利用双流体理论研究非均匀等离子中的非线性低杂漂移孤立波,采用漂移近似得到电子速度,并结合准中性条件得到描述非线性低杂漂移孤立波的Kdv方程,结果表明随着电子温度(密度)越来越不均匀,孤子的幅度和宽度减小,并且幅度最后趋于一个渐近值。
A variety of micro-instability can be excited in the current sheet, these micro-instability may lead to anomalous resistivity which plays an important role in initial stages of magnetic reconnection in the collisionless plasma. In particular, the lower-hybrid drift instability (LHDI) has often been considered as a possible candidate for producing anomalous resistivity. In addition, the LHDI is measured in related experiment when the Magnetic reconnection occurs and it is found that the LHDI has an important effect on magnetic reconnection. However, there is not still a thorough understanding with regard to the fundamental physics of the contribution of the LHDI to magnetic reconnection.
In this dissertation, we study the linear LHDI in current sheet including multi-species ions by using kinetic theory and the nonlinear lower hybrid wave in an inhomogeneous plasma by using two fluid theory. We discuss the effects of the steady state of the current sheet and multi-species on LHDI. There are mainly six aspects in our work as follows:
In the first chapter of the dissertation, some basic concepts are introduced and some recent research developments for micro-instability in current sheet are reviewed. In particularly, the theoretical and experimental research development of the LHDI are shown.
In the second chapter, the LHDI in the Harris current sheet with three species of particles is investigated using kinetic theory under the local approximation. Firstly, the Harris current sheet in a three-species plasma is obtained from zero order Vlasov Equation and Ampere equation; then the dispersion relation of linear LHDI in the Harris sheet in the presence of negative ions could be obtained, and the numerical results show that the negative ion enhances the growth rate and reduces the real frequency of the LHDI. In addition, such LHD wave is unstable in a finite kz value range and propagates almost perpendicularly to the magnetic field.
In the third chapter, for space observations that O+ions are often present and even dominate the plasma sheet, we consider the effect of O+ions on the LHDI using the nonlocal kinetic theory. It is found that the fastest growing mode is not monotonic with O+content and temperature, and there exists a minimum in the growth rate with the increase in O+contend and temperature.
We study the LHDI in a current sheet consisting of particles with theκvelocity distribution in the intermediate wavelength regime ky(?)～1 using kinetic theory. From the linearized Vlasov-Maxwell system, we obtain the corresponding eigenvalue equation, which is solved using a finite-element representation of the eigenfunction, the numerical results show that this unstable mode has even-and odd-parities and an important electromagnetic component, the addition of hot particles (decreasingκ) can decrease the growth rate and modify the mode structure of the most unstable LHD waves.
Using the kinetic theory, the linear LHDI in the plasmas with a weak guide field By is investigated, the results shows that the symmetry property of the mode structure and of the perturbed field is destroyed. The presence of Bv increases the growth rate, the amplitude, especially in the component Az and the electromagnetic component of the eigenmode.
We study the nonlinear lower hybrid drift wave in the inhomogeneity plasma using two fluid theory, electron velocity can be obtained by drift approximation and the nonlinear lower hybrid drift wave can be described by the Kdv equation using the charge quasi-neutral condition, the results show both amplitude and width of the corresponding soliton solution decrease as the inhomogeneity of the electron temperature and density increases, and the amplitude approaches an asymptotic value.
引文
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