A geometric theory of waves and its applications to plasma physics
A geometric theory of waves and its applications to plasma physics
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波的几何理论及其在等离子体物理学中的应用
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发表时间：
2017
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通讯作者：
D. E. Ruiz
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作者：
D. E. Ruiz
波在等离子体科学的许多方面发挥着重要作用，例如等离子体操纵和诊断。由于控制方程的复杂性，通常需要近似模型来描述波浪动力学。在本论文中，波被视为变分理论的几何对象，而不是特定偏微分方程的形式解。这种方法简化了计算，突出了潜在的波浪对称性，并改进了波浪动力学的建模。本论文介绍了波浪一般理论所取得的两项突破。第一个主要贡献是几何光学（GO）的扩展和重新表述，作为第一原理拉格朗日理论，它正确地描述了偏振效应，例如偏振进动和偏振驱动的光线轨迹弯曲，它们表现为 GO 的前阶校正。该理论被应用于多个感兴趣的系统，例如相对论自旋 1/2 粒子和磁化等离子体中的射频波。本论文的第二个主要贡献是开发了一种相空间方法来研究非线性波-波相互作用的基本性质。具体来说，我证明了在调制介质（经典介质和量子介质）中传播的波可以经历由波射线上的有效质动力引起的时间平均折射。这种现象类似于带电粒子在高频电磁场中遇到的有质动力效应。我还表明，相空间方法可用于研究波湍流领域的问题，例如高频波与大型结构的非线性相互作用。总的来说，所获得的结果可以作为未来研究更复杂的非线性波-波相互作用的基础，例如一般波系综或波湍流中的调制不稳定性。
Waves play an essential role in many aspects of plasma science, such as plasma manipulation and diagnostics. Due to the complexity of the governing equations, approximate models are often necessary to describe wave dynamics. In this dissertation, waves are treated as geometric objects of a variational theory rather than formal solutions of specific PDEs. This approach simplifies calculations, highlights the underlying wave symmetries, and leads to improved modeling of wave dynamics. This thesis presents two breakthroughs that were obtained in the general theory of waves. The first main contribution is an extension and reformulation of geometrical optics (GO) as a first-principle Lagrangian theory that correctly describes polarization effects, such as polarization precession and the polarization-driven bending of ray trajectories, which appear as leading-order corrections to GO. The theory was applied to several systems of interest, such as relativistic spin-1/2 particles and radio-frequency waves in magnetized plasma. The second main contribution of this thesis is the development of a phase-space method to study basic properties of nonlinear wave--wave interactions. Specifically, I show that waves propagating in modulated media, both classical and quantum, can experience time-averaged refraction caused by effective ponderomotive forces on wave rays. This phenomenon is analogous to the ponderomotive effect encountered by charged particles in high-frequency electromagnetic fields. I also show that phase-space methods can be useful to study problems in the field of wave turbulence, such as the nonlinear interaction of high-frequency waves with large-scale structures. Overall, the results obtained can serve as a basis for future studies on more complex nonlinear wave--wave interactions, such as modulational instabilities in general wave ensembles or wave turbulence.