[论文解读] The density number of filaments in the state of the weak and optical turbulence

A. D. Bulygin|arXiv (Cornell University)|Aug 20, 2012

Laser-Matter Interactions and Applications参考文献 2被引用 3

一句话总结

本文研究了在弱湍流和光学湍流下，激光束经历多丝化时丝状密度的统计动力学，重点分析反射边界和耗散如何稳定系统。研究发现，丝状密度非单调演化，经历从线性到立方增长的转变，非线性阶段熵和有效温度线性上升，而热力学函数与丝状密度成比例增长，表明系统已过渡至充分发展的湍流。

ABSTRACT

We consider the statistics of density number of filaments for the propagation of a laser beam subjected to multiple filamentation in a closed area with reflecting boundaries. Dissipation arrests the catastrophic collapse of filaments, causing their disintegration into almost linear waves.These waves form a nearly gaussian random field that seeds new filaments. The evolution of the energy distribution function of the angular spectrum and accordingly law of the dynamics of formation of the thermodynamic characteristics of the light field such as the effective temperature and entropy was found. It is established that the growth rate of the thermodynamic functions and the Hamiltonian of the system grows in proportion to the number density of filaments. Also found that depending on the level of the average (background) intensity of the light field can move in two steady state. The first mode is realized for the steady state level of the background intensity does not exceed the value, and is characterized by typical classical (linear) of a closed thermodynamic system, a constant level of entropy and temperature, while the number density of the filaments is equal to zero. In a strongly nonlinear regime, steady state when the number density of filaments goes to a constant level, depending on a cubic, but the entropy and the effective temperature rise in a linear fashion from the distance of propagation. Patterns of development of the number density of filaments with access to a steady state, are nonmonotonic and significantly determined by the initial angular spectral energy distribution of the light field. The average value of filament density depends on the intensity of the complex way the linear growth stage is replaced with the output of the nonlinear saturation, nonlinear growth, corresponding to the transition to the regime of developed turbulence with growth rate in the third degree.

研究动机与目标

• 理解在具有反射边界条件的封闭腔体内，受多丝化影响的激光束中丝状密度的统计行为。
• 研究耗散如何防止灾难性塌缩，并促使丝状结构分解为近似线性波。
• 建立角谱能量分布演化及其对有效温度和熵等热力学性质影响的模型。
• 识别光场的稳态区域及其对背景强度水平的依赖性。
• 确定弱湍流与充分发展湍流区域中丝状密度与热力学函数之间的关系。

提出的方法

• 在具有反射边界的封闭区域内建模激光束传播，以模拟受限的多丝化现象。
• 采用统计方法分析角谱能量分布及其随传播距离的演化。
• 应用热力学框架，从能量分布函数推导有效温度和熵。
• 引入哈密顿形式体系描述系统动力学及其与丝状密度的标度关系。
• 利用初始角谱能量分布作为关键输入，分析丝状密度从线性到非线性增长阶段的转变。
• 推导熵和有效温度随传播距离与丝状密度变化的标度律。

实验结果

研究问题

• RQ1 初始角谱能量分布如何影响丝状密度的非单调发展？
• RQ2 在传播过程中，有效温度和熵的标度律如何与丝状密度相关？
• RQ3 系统如何从弱湍流过渡至充分发展湍流？稳态丝状密度由什么决定？
• RQ4 背景强度在决定是否存在两种不同稳态区域中起什么作用？
• RQ5 耗散如何影响丝状结构的灾难性塌缩，并导致近似线性波结构的形成？

主要发现

• 丝状密度表现出非单调演化，经历从线性增长阶段到非线性饱和阶段，随后在充分发展湍流区域进入立方增长。
• 在强非线性阶段，熵和有效温度等热力学函数的增长率随传播距离线性增加。
• 哈密顿量和热力学函数与丝状密度成比例增长，表明丝状数量与系统能量分布之间存在直接关联。
• 存在两种稳态区域：一种为低背景强度下的零丝状密度、熵和温度恒定；另一种为高强下的恒定丝状密度与上升的熵和温度。
• 平均丝状密度以复杂非线性方式依赖于背景强度，从线性到立方增长的转变由初始角谱能量分布决定。
• 耗散导致丝状结构分解为近似线性波，形成近似高斯随机场，从而为新的丝状化事件提供种子。