电流片中的不稳定性的研究
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摘要
电流片是自然界中一种基本的等离子体结构,广泛存在于地球磁尾,磁层顶,弦激波,太阳圈(Heliosphere)中。电流片是一个强非均匀性的过渡层,其间发生各种能量的输运与转化过程,其中最重要的是磁场重联过程。磁场重联是等离子体中的一种基本的能量输运和转化机制,它使得电流片中的反向磁场结构发生拓扑变化,并伴随着磁能向等离子体动能和热能的转化,空间中发生的很多爆发现象,如日珥,日冕物质抛射,磁层亚暴,以及托卡马克中的锯齿破裂,都与电流片中的重联过程密切相关。电流片位形中的不稳定本征模,对磁场重联的触发和发展有重要作用,其中撕裂模不稳定性本身是一种自发重联过程,它对大规模磁场重联的触发有直接作用。各种沿平衡电流方向传播的漂移不稳定性本身不重联磁场,它们通过引发反常电阻或激发二次不稳定性从而影响重联模(撕裂模)的发展。本文的工作是用无碰撞动理学理论(Vlasov-Maxwell方程组)研究这些不稳定的线性本征模,计算它们的增长率,模结构和参数依赖。我们研究了三种本征模:撕裂模,漂移扭曲模和低杂漂移模。
在对线性化Vlasov方程的处理中,本文采用的方法是传统的沿特征线(未扰轨道)积分方法。与大部分文献不同的是,我们不对未扰轨道作任何解析近似,而是用直接的数值方法求解初值问题从而给出未扰轨道,进而利用轨道的周期性计算出轨道积分。在对扰动场的处理中,我们用标势和矢势描述电磁场,扰动场的静电和电磁部分都被保留,对未知的扰动场空间分布,我们采用基函数展开的方法(谱方法),从而将关于扰动场的积分微分方程的本征值问题化为矩阵问题,最终计算出不稳定性的增长率和扰动场的空间分布。
Kappa分布能很好的描述空间等离子体中的超热分布。我们研究了具有Kappa分布的电流片中的撕裂模和漂移扭曲模,并把结果和Harris电流片的对应模式比较。我们发现具有这种超热分布的电流片中的撕裂模和漂移扭曲模的增长率要小于Harris电流片中的对应模式,且增长率随着谱指数κ的降低而降低。
我们研究了分布函数各向异性对撕裂模的影响。研究了温度各向异性性的Harris电流片中的撕裂模。结果表明,电子的温度各向异性会显著影响撕裂模的增长率,当电子垂直磁场方向上的温度高于平行磁场方向上的温度Te⊥＞Te‖时,撕裂模的增长率远大于温度各向同性时的情况,且最大增长率所对应的波长位置随着Te⊥/Te‖的增加而向短波方向移动。反之,当Te⊥＜Te‖,撕裂模受到抑止,其增长率小于温度各向同性时的情况。
离子的温度各向异性对撕裂模的影响与电子类似,但在同样的温度各向异性程度下,其影响远小于电子。
我们构造了一种分布函数各向异性的电流片,我们称之为Kappa-Maxwell电流片。这种电流片在平行磁场方向上的速度分布是Maxwell分布,而在垂直磁场上是Kappa分布。这种电流片具有内在的各向异性特点,且可以通过改变谱指数κ的值来改变各向异性程度,我们用这种电流片模型来描述实际模拟中观测到的电子分布函数的各向异性。我们计算了这种电流片中的撕裂模的增长率,结果表明,这种电流片中的撕裂模的增长率远大于各向同性情况,且增长率随着谱指数的降低而增加。而撕裂模的最大增长率所对应的波长位置随着谱指数的降低而趋于短波。
各章的主要内容如下:
第一章给出了构造等离子体电流片平衡位形的方法,并给出了Harris电流片,Kappa电流片模型的构造过程,进而我们提出了一种混合电流片模型:Kappa-Maxwell电流片模型。
第二章给出了处理电流片线性本征模的基本方法,其中包括:未扰动轨道的周期性,未扰轨道积分的计算,扰动场的基函数展开,积分微分方程的本征值问题的处理。
第三章研究了电流片中的无碰撞撕裂模不稳性,计算了不稳定性的色散关系,模结构和参数依赖。首先研究了温度各向同性的Harris电流片中的撕裂模,并把结果和文献中的结果比较。然后我们研究了温度各向异性对撕裂模的影响。结果表明,电子的温度各向异性在Te⊥＞Te‖时,对撕裂模是解稳作用,而在Te⊥＜Te‖时,对撕裂模是致稳作用。离子的温度各向异性对撕裂模的影响与电子类似,但在同样的温度各向异性程度下,离子的影响远小于电子。我们研究了具有超热分布(Kappa分布)的电流片中的撕裂模,我们发现具有这种超热分布的电流片中的撕裂模的增长率要小于Harris电流片中的对应模式,且增长率随着谱指数κ的降低而降低。对Kappa-Maxwell电流片,我们发现撕裂模的增长率远大于各向同性情况,且随着谱指数κ的减小而增加。其原因是此时谱指数κ控制垂直磁场方向上的等效温度,在κ为有限值情况下的垂直等效温度大于平行等效温度,而这种T⊥＞T‖的温度各向异性对撕裂模起促进作用。
第四章研究了Kappa电流片中的漂移扭曲模,计算了模式的增长率,模结构,和参数依赖。结果表明,此种情况下的漂移扭曲模的性质和Harris电流片中的对应模式性质相似,但增长率小于Harris电流片中的对应模式,这一点和上一章中关于撕裂模的结果相同。
在第五章中,我们在局域理论的框架下,研究了电流片中的背景等离子体对低杂漂移不稳定性的影响,结果表明,背景等离子体抑制低杂漂移模的增长,并使其实频降低。这一章中所用的方法与前两章不同:在处理中忽略了扰动场的空间分布,且对电子和离子的未扰轨道使用了近似的解析表达式。得到的结果仅对远离电流片中心的边缘区域有意义。
第六章是总结和展望。
Current sheets are basic plasma structures in nature,which have been observed in the magnetotail,magnetopause,bow shock and Heliosphere.Current sheets are strongly inhomogeneous narrow transition layers between two regions of oppositely directed magnetic fields,Important transport process are known to happen in this narrow layer,most notably is the process of magnetic reconnection,during which magnetic energy is converted to plasma kinetic and thermal energy.Magnetic reconnection is believed to play a central role in many violent plasma phenomena such as solar flares, coronal mass ejections,magnetospheric substorms,and sawtooth crashes in tokamaks. The collisionless instabilities in current sheet are crucial for determining the onset conditions and time scales of magnetic reconnection.Tearing mode in itself is a process of magnetic reconnection.Various drift instabilities do not reconnect the magnetic,however, can influence the magnetic reconnection onset through anomalous resistivity or through their effects on tearing mode.
In this paper,by using a formally exact method to solve the linear Vlasov-Maxwell system,tearing mode and drift kink mode are investigated.The orbit integrals are treated numerically using the exact unperturbed particle orbits,and the resulting eigenvalue problem of the integro-differential equations is solved using the spectral method.
It is found that tearing mode and drift kink mode in the current sheet with a superthermal velocity distribution(kappa-distribution) have smaller growth rate than their counterparts in the current sheet with an Maxwellian distribution.
The effects of distribution function anisotropy on tearing mode are investigated. For Harris sheets,the electron temperature anisotropy has important influence on tear-ing mode:electron temperature anisotropy is strongly destabilizing when Te⊥＞Te‖and strongly stabilizing when Te⊥＜Te‖.
The ion temerature anisotropy has the same destabilizing/stabilizing effect as electrons on tearing mode.However,compared with electron temperature anisotropy,the ion temerature anisotropy has much less influence on tearing mode.
We proposed a new current sheet model,namely Kappa-Maxwell sheet,which has a Maxwellian velocity distribution in the direction parallel to the magnetic field and a Kappa velocity distribution in the direction perpendicular to the magnetic field. This kind of current sheet mode can well represent the velocity distribution observed in the numerical simulation of lower-hybrid drift instability.We found that the tearing mode in Kappa-Maxwell sheet has much larger growth rate than its counterpart in isotropic Harris sheet.The explanation is that the perpendicular effective temperature is greater than parallel temperature in Kappa-Maxwell sheets and this kind of temperature anisotropy is known to be able to enhance the tearing mode growth rate.
In chapter 5,in the framework of local theory,we investigated the effect of background population in current sheet on the lower-hybrid drift instability.The results indicate that the background population has a stabilizing effect on lower-hybrid drift instability and reduces the phase velocity of the mode.
在对线性化Vlasov方程的处理中,本文采用的方法是传统的沿特征线(未扰轨道)积分方法。与大部分文献不同的是,我们不对未扰轨道作任何解析近似,而是用直接的数值方法求解初值问题从而给出未扰轨道,进而利用轨道的周期性计算出轨道积分。在对扰动场的处理中,我们用标势和矢势描述电磁场,扰动场的静电和电磁部分都被保留,对未知的扰动场空间分布,我们采用基函数展开的方法(谱方法),从而将关于扰动场的积分微分方程的本征值问题化为矩阵问题,最终计算出不稳定性的增长率和扰动场的空间分布。
Kappa分布能很好的描述空间等离子体中的超热分布。我们研究了具有Kappa分布的电流片中的撕裂模和漂移扭曲模,并把结果和Harris电流片的对应模式比较。我们发现具有这种超热分布的电流片中的撕裂模和漂移扭曲模的增长率要小于Harris电流片中的对应模式,且增长率随着谱指数κ的降低而降低。
我们研究了分布函数各向异性对撕裂模的影响。研究了温度各向异性性的Harris电流片中的撕裂模。结果表明,电子的温度各向异性会显著影响撕裂模的增长率,当电子垂直磁场方向上的温度高于平行磁场方向上的温度Te⊥＞Te‖时,撕裂模的增长率远大于温度各向同性时的情况,且最大增长率所对应的波长位置随着Te⊥/Te‖的增加而向短波方向移动。反之,当Te⊥＜Te‖,撕裂模受到抑止,其增长率小于温度各向同性时的情况。
离子的温度各向异性对撕裂模的影响与电子类似,但在同样的温度各向异性程度下,其影响远小于电子。
我们构造了一种分布函数各向异性的电流片,我们称之为Kappa-Maxwell电流片。这种电流片在平行磁场方向上的速度分布是Maxwell分布,而在垂直磁场上是Kappa分布。这种电流片具有内在的各向异性特点,且可以通过改变谱指数κ的值来改变各向异性程度,我们用这种电流片模型来描述实际模拟中观测到的电子分布函数的各向异性。我们计算了这种电流片中的撕裂模的增长率,结果表明,这种电流片中的撕裂模的增长率远大于各向同性情况,且增长率随着谱指数的降低而增加。而撕裂模的最大增长率所对应的波长位置随着谱指数的降低而趋于短波。
各章的主要内容如下:
第一章给出了构造等离子体电流片平衡位形的方法,并给出了Harris电流片,Kappa电流片模型的构造过程,进而我们提出了一种混合电流片模型:Kappa-Maxwell电流片模型。
第二章给出了处理电流片线性本征模的基本方法,其中包括:未扰动轨道的周期性,未扰轨道积分的计算,扰动场的基函数展开,积分微分方程的本征值问题的处理。
第三章研究了电流片中的无碰撞撕裂模不稳性,计算了不稳定性的色散关系,模结构和参数依赖。首先研究了温度各向同性的Harris电流片中的撕裂模,并把结果和文献中的结果比较。然后我们研究了温度各向异性对撕裂模的影响。结果表明,电子的温度各向异性在Te⊥＞Te‖时,对撕裂模是解稳作用,而在Te⊥＜Te‖时,对撕裂模是致稳作用。离子的温度各向异性对撕裂模的影响与电子类似,但在同样的温度各向异性程度下,离子的影响远小于电子。我们研究了具有超热分布(Kappa分布)的电流片中的撕裂模,我们发现具有这种超热分布的电流片中的撕裂模的增长率要小于Harris电流片中的对应模式,且增长率随着谱指数κ的降低而降低。对Kappa-Maxwell电流片,我们发现撕裂模的增长率远大于各向同性情况,且随着谱指数κ的减小而增加。其原因是此时谱指数κ控制垂直磁场方向上的等效温度,在κ为有限值情况下的垂直等效温度大于平行等效温度,而这种T⊥＞T‖的温度各向异性对撕裂模起促进作用。
第四章研究了Kappa电流片中的漂移扭曲模,计算了模式的增长率,模结构,和参数依赖。结果表明,此种情况下的漂移扭曲模的性质和Harris电流片中的对应模式性质相似,但增长率小于Harris电流片中的对应模式,这一点和上一章中关于撕裂模的结果相同。
在第五章中,我们在局域理论的框架下,研究了电流片中的背景等离子体对低杂漂移不稳定性的影响,结果表明,背景等离子体抑制低杂漂移模的增长,并使其实频降低。这一章中所用的方法与前两章不同:在处理中忽略了扰动场的空间分布,且对电子和离子的未扰轨道使用了近似的解析表达式。得到的结果仅对远离电流片中心的边缘区域有意义。
第六章是总结和展望。
Current sheets are basic plasma structures in nature,which have been observed in the magnetotail,magnetopause,bow shock and Heliosphere.Current sheets are strongly inhomogeneous narrow transition layers between two regions of oppositely directed magnetic fields,Important transport process are known to happen in this narrow layer,most notably is the process of magnetic reconnection,during which magnetic energy is converted to plasma kinetic and thermal energy.Magnetic reconnection is believed to play a central role in many violent plasma phenomena such as solar flares, coronal mass ejections,magnetospheric substorms,and sawtooth crashes in tokamaks. The collisionless instabilities in current sheet are crucial for determining the onset conditions and time scales of magnetic reconnection.Tearing mode in itself is a process of magnetic reconnection.Various drift instabilities do not reconnect the magnetic,however, can influence the magnetic reconnection onset through anomalous resistivity or through their effects on tearing mode.
In this paper,by using a formally exact method to solve the linear Vlasov-Maxwell system,tearing mode and drift kink mode are investigated.The orbit integrals are treated numerically using the exact unperturbed particle orbits,and the resulting eigenvalue problem of the integro-differential equations is solved using the spectral method.
It is found that tearing mode and drift kink mode in the current sheet with a superthermal velocity distribution(kappa-distribution) have smaller growth rate than their counterparts in the current sheet with an Maxwellian distribution.
The effects of distribution function anisotropy on tearing mode are investigated. For Harris sheets,the electron temperature anisotropy has important influence on tear-ing mode:electron temperature anisotropy is strongly destabilizing when Te⊥＞Te‖and strongly stabilizing when Te⊥＜Te‖.
The ion temerature anisotropy has the same destabilizing/stabilizing effect as electrons on tearing mode.However,compared with electron temperature anisotropy,the ion temerature anisotropy has much less influence on tearing mode.
We proposed a new current sheet model,namely Kappa-Maxwell sheet,which has a Maxwellian velocity distribution in the direction parallel to the magnetic field and a Kappa velocity distribution in the direction perpendicular to the magnetic field. This kind of current sheet mode can well represent the velocity distribution observed in the numerical simulation of lower-hybrid drift instability.We found that the tearing mode in Kappa-Maxwell sheet has much larger growth rate than its counterpart in isotropic Harris sheet.The explanation is that the perpendicular effective temperature is greater than parallel temperature in Kappa-Maxwell sheets and this kind of temperature anisotropy is known to be able to enhance the tearing mode growth rate.
In chapter 5,in the framework of local theory,we investigated the effect of background population in current sheet on the lower-hybrid drift instability.The results indicate that the background population has a stabilizing effect on lower-hybrid drift instability and reduces the phase velocity of the mode.
引文
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