超短超强激光脉冲与高密度等离子体相互作用的粒子模拟研究
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摘要
近年来，随着超短超强激光脉冲的迅猛发展和“快点火”研究的深入，超短超强激光脉冲与高密度等离子体相互作用成为当前激光等离子体领域的一个研究热点。本文的研究目的是：利用粒子模拟方法，对超短超强激光脉冲与高密度等离子体相互作用中高能强电流的产生和输运、准静态磁场产生、高能离子产生等物理过程进行研究。
为了研究激光等离子体相互作用中复杂的非线性过程，本文研制了2D3V(空间二维，速度三维)直角坐标相对论全电磁粒子模拟程序APIC2D(Advanced Particle-in-cell 2D)。该程序的主要特点是对粒子模拟中的一些算法进行了优化，主要工作包括：
1、将等离子体粒子模拟中得到广泛应用的Borris旋转推动粒子方法进行了改进。这种改进型Borris旋转方法在模拟电子的相对论动力学行为时具有相当高的计算精度，且耗费计算量较小。
2、采用有效电流分配方法求电流密度。按这种方法求得的电流密度代入旋度方程所解得的电场，自动地满足散度方程，而无需再求电荷密度并进行Poisson修正，减少了粒子模拟的工作量。数值模拟中发现，粒子边界条件的施加破坏了有效电流分配方法对静电修正的自动满足。我们针对不同的粒子边界条件提出了解决方法，得到了较好的效果。
采用自行研制的2D3V直角坐标相对论全电磁粒子模拟程序APIC2D，对超短超强激光脉冲与高密度等离子体相互作用进行了粒子模拟研究。研究内容包括：
1、对Gauss型激光脉冲垂直辐照高密度等离子体的物理过程进行了粒子模拟研究。在垂直于激光磁场的平面(E面)上，观察到激光有质动力向两侧推动粒子产生钻孔效应。在平行于激光磁场的平面(H面)上，观察到等离子体表面的波纹化现象，并演变为等离子体空泡(Bubble)。观察到等离子体内部MG量级自生磁场的产生。
2、系统地研究了高能电流在稠密等离子体内输运的复杂的非线性过程。对高能束流和电子回流构成的双流系统，建立冷等离子体流体模型，采用简正模分析方法，分别考虑扰动波矢在平行于电流传播方向的平面(记为XY平面)上和在垂直于电流传播方向的平面(记为YZ平面)上这两种情况，推导了不稳定性的色散关系。在XY平面上对电流输运过程进行了2D3V粒子模拟，观察到电流丝的形成、聚合和磁场产生。XY平面上激发的不稳定性是纵向的静电双流不稳定性和横向的Weibel不稳定性的耦合，称为二维EMBP(Electromagnetic Beam-Plasma Instability)不稳定性。因为EMBP不稳定性所激发的波和束流电子之间的共振相互作用，束流电子不是连续地传播，而是以电流团的形式传播，传
国防科技大学研究生院学位论文
播速度接近于波的相速度。在抢平面上对电流输运过程进行了ZD3V粒子模拟。
观察到电流丝形成、聚合和磁场产生。电流丝自组织形成同轴结构，束流被强磁
场和回流鞘层包围，磁场在电流丝外迅速衰减到0。
3、研究了线偏振超短超强激光脉冲垂直辐照固体靶过程中高能离子的产生。
模拟观察到三群高能离子的产生，并对其加速机制一一进行了分析:在靶的前部，
向外喷射的高能电子在靶前形成电子云，将一部分离子拉出靶面，形成第一群高
能离子;激光驱动大量高能电子向靶内输运，这些电子牵引靶前部的离子向前加
速，形成第二群高能离子:高能电子很快穿透靶，在靶后形成电子云，加速靶后
表面处的离子，形成第三群高能离子。第三群高能离子的这种加速机制称为
TNSA加速机制，这种机制只可能在超短超强激光脉冲辐照的条件下才能起作
用。第一、二群高能离子的出射角较大;第三群高能离子的出射角小于20度，
具有很好的定向性。研究了前、后表面等离子体密度标长对高能离子产生的影响。
前、后表面等离子体具有陡峭的密度标长，更有利于高能离子的产生。
4、对线极化、圆极化超短超强激光脉冲和靶前有一段低密度预等离子体的
固体靶的相互作用进行了理论和粒子模拟研究。研究表明，通过有质动力加速过
程，预等离子体中的电子可以得到强烈的加速，并通过进入固体靶而摆脱激光脉
冲的束缚，这个加速过程比激光直接与固体靶相互作用中的电子加速过程要有效
得多。预等离子体中的离子也得到相当大的加速。总之，在超短超强激光脉冲与
固体靶的相互作用中，预等离子体相当于一个“高能电子库”，其存在有利于高
能电流的产生。
作为和PIC方法的比较，对一种无网格粒子模拟方法:三维FMM方法进行
了研究和程序实现。我们改进了FMM方法中的第三位移公式以提高计算精度。
在低维模拟中采用运动受限的球粒子模型，对三维公式进行简化，得到一维和二
维FMM方法的公式。编程实现了一维、二维、三维FMM方法，并用一维FMM
方法模拟了静电双流不稳定性。计算实例初步证实了FMM方法应用于等离子体
的静电模粒子模拟的可行性。
In recent years, laser pulses with focused intensities I ~ 1018~22 W /cm2 and pulse width r < Ips are available in many laboratories. The study of the interaction of ultra-short ultra-intense laser pulses with overdense plasmas, which is motivated primarily by the fast ignition scheme of inertial confinement fusion, has received more and more attention. This thesis is devoted to studying those issues relevant to the interaction of ultra-short ultra-intense laser pulses with overdense plasmas, including the generation and transport of relativistic electron beams, the generation of quasistatic magnetic field, the energetic ions production, and the influence of preplasma on electrons acceleration.
We developed a 2D3V(two dimensional in space and three dimensional in velocity) particle-in-cell code APIC2D. In this code, we improved some algorithms of particle simulation as following:
1. An advanced Borris rotation method is proposed to solve the relativistic Lorentz equation. The method can describe the relativistic dynamic behavior of particles accurately and is especially adaptive to simulate the dynamic behavior of particles in ultra-intense laser field.
2. A charge conserving current weighting algorithm, which is based on the current conservation equation, is used in the code. However, the application of particle boundary condition may destroy the validity of the method. We present some methods to ensure the rigorous charge conservation.
With our code APIC2D, the following physics problems are studied:
1. The interaction of ultra-short ultra-intense laser pulses with overdense plasmas are simulated. Laser hole boring effect due to the large ponderomotive force is observed on the surface which is verticle to the magnetic field. As for the phenomena on the surface which is verticle to the electric field, the plasma surface oscillations are generated, and then electron bubbles and ion bubbles are formed. Quasistatic magnetic fields are generated by the laser driven relativistic electron stream.
2. The transport of a relativistic-electron-beam(REB) in dense plasmas with a cold return electron current is examined by theory and particle simulation. Using the two-stream fluid model, the linear dispersion relation is derived assuming a two-dimensional spatial geometry. Two cases are considered, one is that the 2D spatial geometry is defined by the plane containing the two counterstreaming electron populations and the perturbation wave vector(referred as the XY plane), and the other is that the geometry is defined by the plane being vertical to the two counterstreaming electron populations(referred as the YZ plane). The transport of REB is examined by
2D3V particle simulation in the XY plane. The filamentation and coalescence of currents and related magnetic field pattern, caused by the two-dimensional electromagnetic-beam-plasma(EMBP) instability, are observed. Because of the resonant interaction between the REB electrons and the wave excitated by the EMBP instability, the REB electrons cannot transport continuously, but in form of current clumps. The transport velocity is close to the phase velocity of the wave. The transport of REB is also investigated by 2D3V particle simulation in the YZ plane. A large number of Current filaments emerge in the system. Those filaments self-organize in coaxial structures where the relativistic current in the center is surrounded by intense magnetic field and the return current sheath, and the magnetic field decreases abruptly to zero outside the relativistic current.
3. The generation of energetic ions during the interaction of a linear-polarized ultra-short ultra-intense laser pulse with solid targets are examined by particle simulation. Three energetic ion populations are observed and the acceleration mechanisms are analyzed, respectively. The first population is pulled out from the target by the electron jet in front of the target. The second population is pulled forwards by the propagating energetic electrons. The third energetic ion popu
为了研究激光等离子体相互作用中复杂的非线性过程，本文研制了2D3V(空间二维，速度三维)直角坐标相对论全电磁粒子模拟程序APIC2D(Advanced Particle-in-cell 2D)。该程序的主要特点是对粒子模拟中的一些算法进行了优化，主要工作包括：
1、将等离子体粒子模拟中得到广泛应用的Borris旋转推动粒子方法进行了改进。这种改进型Borris旋转方法在模拟电子的相对论动力学行为时具有相当高的计算精度，且耗费计算量较小。
2、采用有效电流分配方法求电流密度。按这种方法求得的电流密度代入旋度方程所解得的电场，自动地满足散度方程，而无需再求电荷密度并进行Poisson修正，减少了粒子模拟的工作量。数值模拟中发现，粒子边界条件的施加破坏了有效电流分配方法对静电修正的自动满足。我们针对不同的粒子边界条件提出了解决方法，得到了较好的效果。
采用自行研制的2D3V直角坐标相对论全电磁粒子模拟程序APIC2D，对超短超强激光脉冲与高密度等离子体相互作用进行了粒子模拟研究。研究内容包括：
1、对Gauss型激光脉冲垂直辐照高密度等离子体的物理过程进行了粒子模拟研究。在垂直于激光磁场的平面(E面)上，观察到激光有质动力向两侧推动粒子产生钻孔效应。在平行于激光磁场的平面(H面)上，观察到等离子体表面的波纹化现象，并演变为等离子体空泡(Bubble)。观察到等离子体内部MG量级自生磁场的产生。
2、系统地研究了高能电流在稠密等离子体内输运的复杂的非线性过程。对高能束流和电子回流构成的双流系统，建立冷等离子体流体模型，采用简正模分析方法，分别考虑扰动波矢在平行于电流传播方向的平面(记为XY平面)上和在垂直于电流传播方向的平面(记为YZ平面)上这两种情况，推导了不稳定性的色散关系。在XY平面上对电流输运过程进行了2D3V粒子模拟，观察到电流丝的形成、聚合和磁场产生。XY平面上激发的不稳定性是纵向的静电双流不稳定性和横向的Weibel不稳定性的耦合，称为二维EMBP(Electromagnetic Beam-Plasma Instability)不稳定性。因为EMBP不稳定性所激发的波和束流电子之间的共振相互作用，束流电子不是连续地传播，而是以电流团的形式传播，传
国防科技大学研究生院学位论文
播速度接近于波的相速度。在抢平面上对电流输运过程进行了ZD3V粒子模拟。
观察到电流丝形成、聚合和磁场产生。电流丝自组织形成同轴结构，束流被强磁
场和回流鞘层包围，磁场在电流丝外迅速衰减到0。
3、研究了线偏振超短超强激光脉冲垂直辐照固体靶过程中高能离子的产生。
模拟观察到三群高能离子的产生，并对其加速机制一一进行了分析:在靶的前部，
向外喷射的高能电子在靶前形成电子云，将一部分离子拉出靶面，形成第一群高
能离子;激光驱动大量高能电子向靶内输运，这些电子牵引靶前部的离子向前加
速，形成第二群高能离子:高能电子很快穿透靶，在靶后形成电子云，加速靶后
表面处的离子，形成第三群高能离子。第三群高能离子的这种加速机制称为
TNSA加速机制，这种机制只可能在超短超强激光脉冲辐照的条件下才能起作
用。第一、二群高能离子的出射角较大;第三群高能离子的出射角小于20度，
具有很好的定向性。研究了前、后表面等离子体密度标长对高能离子产生的影响。
前、后表面等离子体具有陡峭的密度标长，更有利于高能离子的产生。
4、对线极化、圆极化超短超强激光脉冲和靶前有一段低密度预等离子体的
固体靶的相互作用进行了理论和粒子模拟研究。研究表明，通过有质动力加速过
程，预等离子体中的电子可以得到强烈的加速，并通过进入固体靶而摆脱激光脉
冲的束缚，这个加速过程比激光直接与固体靶相互作用中的电子加速过程要有效
得多。预等离子体中的离子也得到相当大的加速。总之，在超短超强激光脉冲与
固体靶的相互作用中，预等离子体相当于一个“高能电子库”，其存在有利于高
能电流的产生。
作为和PIC方法的比较，对一种无网格粒子模拟方法:三维FMM方法进行
了研究和程序实现。我们改进了FMM方法中的第三位移公式以提高计算精度。
在低维模拟中采用运动受限的球粒子模型，对三维公式进行简化，得到一维和二
维FMM方法的公式。编程实现了一维、二维、三维FMM方法，并用一维FMM
方法模拟了静电双流不稳定性。计算实例初步证实了FMM方法应用于等离子体
的静电模粒子模拟的可行性。
In recent years, laser pulses with focused intensities I ~ 1018~22 W /cm2 and pulse width r < Ips are available in many laboratories. The study of the interaction of ultra-short ultra-intense laser pulses with overdense plasmas, which is motivated primarily by the fast ignition scheme of inertial confinement fusion, has received more and more attention. This thesis is devoted to studying those issues relevant to the interaction of ultra-short ultra-intense laser pulses with overdense plasmas, including the generation and transport of relativistic electron beams, the generation of quasistatic magnetic field, the energetic ions production, and the influence of preplasma on electrons acceleration.
We developed a 2D3V(two dimensional in space and three dimensional in velocity) particle-in-cell code APIC2D. In this code, we improved some algorithms of particle simulation as following:
1. An advanced Borris rotation method is proposed to solve the relativistic Lorentz equation. The method can describe the relativistic dynamic behavior of particles accurately and is especially adaptive to simulate the dynamic behavior of particles in ultra-intense laser field.
2. A charge conserving current weighting algorithm, which is based on the current conservation equation, is used in the code. However, the application of particle boundary condition may destroy the validity of the method. We present some methods to ensure the rigorous charge conservation.
With our code APIC2D, the following physics problems are studied:
1. The interaction of ultra-short ultra-intense laser pulses with overdense plasmas are simulated. Laser hole boring effect due to the large ponderomotive force is observed on the surface which is verticle to the magnetic field. As for the phenomena on the surface which is verticle to the electric field, the plasma surface oscillations are generated, and then electron bubbles and ion bubbles are formed. Quasistatic magnetic fields are generated by the laser driven relativistic electron stream.
2. The transport of a relativistic-electron-beam(REB) in dense plasmas with a cold return electron current is examined by theory and particle simulation. Using the two-stream fluid model, the linear dispersion relation is derived assuming a two-dimensional spatial geometry. Two cases are considered, one is that the 2D spatial geometry is defined by the plane containing the two counterstreaming electron populations and the perturbation wave vector(referred as the XY plane), and the other is that the geometry is defined by the plane being vertical to the two counterstreaming electron populations(referred as the YZ plane). The transport of REB is examined by
2D3V particle simulation in the XY plane. The filamentation and coalescence of currents and related magnetic field pattern, caused by the two-dimensional electromagnetic-beam-plasma(EMBP) instability, are observed. Because of the resonant interaction between the REB electrons and the wave excitated by the EMBP instability, the REB electrons cannot transport continuously, but in form of current clumps. The transport velocity is close to the phase velocity of the wave. The transport of REB is also investigated by 2D3V particle simulation in the YZ plane. A large number of Current filaments emerge in the system. Those filaments self-organize in coaxial structures where the relativistic current in the center is surrounded by intense magnetic field and the return current sheath, and the magnetic field decreases abruptly to zero outside the relativistic current.
3. The generation of energetic ions during the interaction of a linear-polarized ultra-short ultra-intense laser pulse with solid targets are examined by particle simulation. Three energetic ion populations are observed and the acceleration mechanisms are analyzed, respectively. The first population is pulled out from the target by the electron jet in front of the target. The second population is pulled forwards by the propagating energetic electrons. The third energetic ion popu
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