超临界密度等离子体中快电子束稳定性的研究
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摘要
惯性聚变中的快点火(FI)概念是与传统的惯性聚变方法不同的方案,它不需要严格的对称压缩,从而减少了点火所需要的能量并获得更高的能量增益。它把燃料的压缩和点火过程分开,其中对燃料仍采用传统的长脉冲激光进行压缩,但是用短脉冲激光束直接对靶心等离子体进行点火。但是靶芯部等离子体的密度一般已经大大超过激光传播的临界密度(对这种等离子体我们称为“dense plasmas”,即“超临界密度”等离子体)。幸运的是激光束在临界密度面会激发高能量(相对论)电子,部分激光能量会转换成用快电子能量在超临界密度等离子体中传播,用来实现压缩后燃料的点火。携带点火所需的最小能量达到靶心需要(相对论)快电子束可以在超临界密度等离子体中稳定传播。这对于实现快点火是至关重要的一步。并且,类似这种相对论电子束在等离子体中运动的物理过程,在许多高能量密度天体物理学现象中也会遇见。因此,在最近的十到十五年中,人们对这种在超临界密度等离子体中传播的相对论电子束进行了各种理论和数值模拟上的研究。然而,由于这种电子束带有极强的电流及其产生的电磁场,会带来各种发展很快的不稳定性。因此,对于这种电子束在超临界密度的等离子体中的传播过程仍然存在很多待解决的问题。
本论文采用双电子流体模型假设来研究(相对论)快电子束在超临界密度等离子体中的传播的稳定性。在宏观尺度下,相对论束流条件是束具有很高流速(即u_b-c,其中u_b和c分别表示束的流速和光速),而在微观尺度上(动理学效应尺度)非相对论的热运动(满足T_b<<(γ_b-1)m_ec~2,其中T_b代表束的温度,在KeV的量级,γ_b代表的是质量的相对论因子),我们所做的双流体模型的分析不仅研究了(相对论)快电子束的稳定性,同时也是首次揭示准静电(QES)模式的产生及其对电流“空洞(Hollowing)模的影响。得以提高对电子束流空洞结构形成的认识。
第一章,简要介绍了(相对论)快电子束及其应用,特别是惯性约束聚变的及快点火研究方面。
第二章,在双电子流体模型近似下,用初值问题的方法,研究了在超临界密度等离子体中传播的(相对论)轴对称快电子束的径向模式。通过改变束与等离子体的分布因子α=r_0/R_0(其中r_0和R_0分别代表快电子束和等离子体的半径),,研究了非相对论温度即碰撞对激发的径向模式的影响。结果发现对于不同的轴向波矢区间,各种模数的径向模式都可能被激发:在长波区主要是研究了角向模式m=0及径向模数分别为n=2和n=3的hollowing-like模式,而在短波区即更高的径向模数,研究了束与等离子体的电磁不稳定性。并发现,对于束与等离子体密度不对称的情况,在有限的温度及碰撞的影响下,不稳定性的增长率得到一定的抑制。
第三章,运用能谱分析方法,对在超临界密度等离子体中传播的相对论电子束的非线性演化进行了三维研究。分析了在三维空间存在的各种模式。研究表明,线性阶段同时具有双流(two-stream)和成丝(filamentation)模式的“斜传播”(oblique)模式首先被激发,与之前用PIC方法研究得到的结果相符。对于早期非线性阶段的能谱分析揭示了更高波数模式的激发和发展。具有静电箍缩特点的新模式在第四章中加以研究。
第四章,研究了(相对论)快电子束的不同剖面,包括均匀分布、高斯分布和前段较平的轴对称类型的分布剖面,对电子束的空洞或环的演化所带来的影响。研究发现类似空洞或环的结构只在分布函数具有很大梯度的地方发生。空洞的形成机制可以借助净电流(束和等离子体叠加在一起)和密度的演化来解释。该工作是基于能谱分析,研究高波数的模式的非线性演化,以便更好的理解(相对论)快电子束的空洞和成丝(filamentation)。
第五章,介绍了今后的工作展望:从一个考虑了热电子束的全部相对论效应的双流体模型方程出发,研究超临界密度等离子体中的相对论热电子束的理论。
最后,对全文进行了简短总结。
Fast ignition (FI) inertial fusion is a varied concept to the standard inertial confinement fusion (ICF) approach, -one which offers the relaxed symmetry conditions, reduced energy requirements and high energy gains. It involves the separation of the fuel compression and ignition phases, where the fuel compressed by using the conventional long pulse lasers is ignited by using the separate short pulse laser beams. In the later, laser beam energy is converted to the fast electrons at the critical density surface which then carry it to the ignition spot in the compressed fuel. To carry the minimum required energy to the ignition spot, stable propagation of the fast electron beam through the dense plasma fuel, ahead of the critical density surface, is a crucial step for FI concept. Furthermore, similar situations, where motion of relativistic electron beams through plasmas is involved, are also encountered in many high energy astrophysical phenomena. Therefore, in the last ten to fifteen years, various theoretical and numerical studies have been carried out to investigate the propagation properties of such relativistic electron beams through dense plasmas. However, due to the fact that such beams carry large amount of electric currents, their self-generated electromagnetic fields are very strong and that beam-plasma system involves various kinds of instabilities, their propagation through plasmas is a complex process that is still far from being well understood.
In this dissertation, applying two-electron fluid model approximations, we study the propagation stability of the fast electron beams through the dense plasmas. Under macroscopic relativistic flow conditions, those related to the large beam velocities (i.e. u_b-c, where u_b is the beam flow velocity and c the speed of light), but non-relativisticthermal (microscopic) motions (with T_b<<(γ_b-1)m_ec~2,where T_b is the beam temperature in KeV andγ_b the mass relativistic factor), our two-fluid analysis not only confirms theexisting notions about beam stability but also reveals for the first time the onset of quasi-electrostatic (QES) modes as well as an improved understanding of the beam hollowing structures.
In chapter 1, a brief introduction about fast electron beams and their applications, the basics of nuclear fusion as well as the concept of FI inertial fusion energy, is provided.
In chapter 2, axisymmetric radial modes of the fast electron beams in dense plasmas are investigated by employing an initial value approach under two-electron fluid approximations. The non-relativistic temperatures as well as collisional drag effects on the excited radial modes are studied by varying beam-plasma configurations,α=r_0/R_0,(where r_0 and R_0are the radial size of the beam and plasma respectively). It has been found that various radial modes are excited over the entire range of axial wavelengths, with long-wavelength regime dominated by hollowing-like modes characterized by azimuthal number of m=0 and radial numbers of n=2 and n=3, while short-wavelength regime dominated by higher radial mode numbers electromagnetic beam-plasma instabilities. Under asymmetric beam-plasma density conditions, finite temperatures and collisional effects are found to reduce the growth rate of the instabilities.
In chapter 3, the nonlinear mode evolution for relativistic electron beams in dense plasmas is investigated with the help of power spectrum analysis in a three-dimensional (3D) space. It is found that various modes are excited over the entire 3D space. While, linear stage analysis confirms the onset and hierarchy of the known excited modes, with oblique modes dominating the two-stream and filamentation ones, as shown in the previous particle-in-cell (PIC) studies, the power spectrum analysis of the early nonlinear stage reveals excitation and development of the higher wavenumber modes. The electrostatic pinching like characteristics of such newly explored modes are further studied in chapter 4.
In chapter 4, effect of various beam distribution profiles, those including uniform, Gaussian and flat-front cylindrical type profiles, is studied on hollowing or ring like evolution of the beam. It is found that the hollow or ring like structures occur only for that profile which has steep gradients. The hollow formation mechanism is explained with the help of net current (beam plus plasma) and density evolution. Investigations based on power spectrum analysis reveal the nonlinear development of the high wavenumber modes, which further help to understand the mechanism of beam hollowing and filamentation.
Chapter 5 contains a two-fluid model, with fully relativistic fluid equations for the hot electron beam, a plan for ongoing research, for studying the microscopic dynamics of the relativistic hot electron beams in dense plasmas. The analysis based on such a model is currently in progress.
Finally, a brief summary ends the dissertation.
本论文采用双电子流体模型假设来研究(相对论)快电子束在超临界密度等离子体中的传播的稳定性。在宏观尺度下,相对论束流条件是束具有很高流速(即u_b-c,其中u_b和c分别表示束的流速和光速),而在微观尺度上(动理学效应尺度)非相对论的热运动(满足T_b<<(γ_b-1)m_ec~2,其中T_b代表束的温度,在KeV的量级,γ_b代表的是质量的相对论因子),我们所做的双流体模型的分析不仅研究了(相对论)快电子束的稳定性,同时也是首次揭示准静电(QES)模式的产生及其对电流“空洞(Hollowing)模的影响。得以提高对电子束流空洞结构形成的认识。
第一章,简要介绍了(相对论)快电子束及其应用,特别是惯性约束聚变的及快点火研究方面。
第二章,在双电子流体模型近似下,用初值问题的方法,研究了在超临界密度等离子体中传播的(相对论)轴对称快电子束的径向模式。通过改变束与等离子体的分布因子α=r_0/R_0(其中r_0和R_0分别代表快电子束和等离子体的半径),,研究了非相对论温度即碰撞对激发的径向模式的影响。结果发现对于不同的轴向波矢区间,各种模数的径向模式都可能被激发:在长波区主要是研究了角向模式m=0及径向模数分别为n=2和n=3的hollowing-like模式,而在短波区即更高的径向模数,研究了束与等离子体的电磁不稳定性。并发现,对于束与等离子体密度不对称的情况,在有限的温度及碰撞的影响下,不稳定性的增长率得到一定的抑制。
第三章,运用能谱分析方法,对在超临界密度等离子体中传播的相对论电子束的非线性演化进行了三维研究。分析了在三维空间存在的各种模式。研究表明,线性阶段同时具有双流(two-stream)和成丝(filamentation)模式的“斜传播”(oblique)模式首先被激发,与之前用PIC方法研究得到的结果相符。对于早期非线性阶段的能谱分析揭示了更高波数模式的激发和发展。具有静电箍缩特点的新模式在第四章中加以研究。
第四章,研究了(相对论)快电子束的不同剖面,包括均匀分布、高斯分布和前段较平的轴对称类型的分布剖面,对电子束的空洞或环的演化所带来的影响。研究发现类似空洞或环的结构只在分布函数具有很大梯度的地方发生。空洞的形成机制可以借助净电流(束和等离子体叠加在一起)和密度的演化来解释。该工作是基于能谱分析,研究高波数的模式的非线性演化,以便更好的理解(相对论)快电子束的空洞和成丝(filamentation)。
第五章,介绍了今后的工作展望:从一个考虑了热电子束的全部相对论效应的双流体模型方程出发,研究超临界密度等离子体中的相对论热电子束的理论。
最后,对全文进行了简短总结。
Fast ignition (FI) inertial fusion is a varied concept to the standard inertial confinement fusion (ICF) approach, -one which offers the relaxed symmetry conditions, reduced energy requirements and high energy gains. It involves the separation of the fuel compression and ignition phases, where the fuel compressed by using the conventional long pulse lasers is ignited by using the separate short pulse laser beams. In the later, laser beam energy is converted to the fast electrons at the critical density surface which then carry it to the ignition spot in the compressed fuel. To carry the minimum required energy to the ignition spot, stable propagation of the fast electron beam through the dense plasma fuel, ahead of the critical density surface, is a crucial step for FI concept. Furthermore, similar situations, where motion of relativistic electron beams through plasmas is involved, are also encountered in many high energy astrophysical phenomena. Therefore, in the last ten to fifteen years, various theoretical and numerical studies have been carried out to investigate the propagation properties of such relativistic electron beams through dense plasmas. However, due to the fact that such beams carry large amount of electric currents, their self-generated electromagnetic fields are very strong and that beam-plasma system involves various kinds of instabilities, their propagation through plasmas is a complex process that is still far from being well understood.
In this dissertation, applying two-electron fluid model approximations, we study the propagation stability of the fast electron beams through the dense plasmas. Under macroscopic relativistic flow conditions, those related to the large beam velocities (i.e. u_b-c, where u_b is the beam flow velocity and c the speed of light), but non-relativisticthermal (microscopic) motions (with T_b<<(γ_b-1)m_ec~2,where T_b is the beam temperature in KeV andγ_b the mass relativistic factor), our two-fluid analysis not only confirms theexisting notions about beam stability but also reveals for the first time the onset of quasi-electrostatic (QES) modes as well as an improved understanding of the beam hollowing structures.
In chapter 1, a brief introduction about fast electron beams and their applications, the basics of nuclear fusion as well as the concept of FI inertial fusion energy, is provided.
In chapter 2, axisymmetric radial modes of the fast electron beams in dense plasmas are investigated by employing an initial value approach under two-electron fluid approximations. The non-relativistic temperatures as well as collisional drag effects on the excited radial modes are studied by varying beam-plasma configurations,α=r_0/R_0,(where r_0 and R_0are the radial size of the beam and plasma respectively). It has been found that various radial modes are excited over the entire range of axial wavelengths, with long-wavelength regime dominated by hollowing-like modes characterized by azimuthal number of m=0 and radial numbers of n=2 and n=3, while short-wavelength regime dominated by higher radial mode numbers electromagnetic beam-plasma instabilities. Under asymmetric beam-plasma density conditions, finite temperatures and collisional effects are found to reduce the growth rate of the instabilities.
In chapter 3, the nonlinear mode evolution for relativistic electron beams in dense plasmas is investigated with the help of power spectrum analysis in a three-dimensional (3D) space. It is found that various modes are excited over the entire 3D space. While, linear stage analysis confirms the onset and hierarchy of the known excited modes, with oblique modes dominating the two-stream and filamentation ones, as shown in the previous particle-in-cell (PIC) studies, the power spectrum analysis of the early nonlinear stage reveals excitation and development of the higher wavenumber modes. The electrostatic pinching like characteristics of such newly explored modes are further studied in chapter 4.
In chapter 4, effect of various beam distribution profiles, those including uniform, Gaussian and flat-front cylindrical type profiles, is studied on hollowing or ring like evolution of the beam. It is found that the hollow or ring like structures occur only for that profile which has steep gradients. The hollow formation mechanism is explained with the help of net current (beam plus plasma) and density evolution. Investigations based on power spectrum analysis reveal the nonlinear development of the high wavenumber modes, which further help to understand the mechanism of beam hollowing and filamentation.
Chapter 5 contains a two-fluid model, with fully relativistic fluid equations for the hot electron beam, a plan for ongoing research, for studying the microscopic dynamics of the relativistic hot electron beams in dense plasmas. The analysis based on such a model is currently in progress.
Finally, a brief summary ends the dissertation.
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