Shi Yuan, Qin Hong, Fisch Nathaniel J
Department of Astrophysical Sciences, Princeton University, Princeton, New Jersey 08544, USA.
Princeton Plasma Physics Laboratory, Princeton University, Princeton, New Jersey 08543, USA.
Phys Rev E. 2017 Aug;96(2-1):023204. doi: 10.1103/PhysRevE.96.023204. Epub 2017 Aug 14.
Large amplitude waves in magnetized plasmas, generated either by external pumps or internal instabilities, can scatter via three-wave interactions. While three-wave scattering is well known in collimated geometry, what happens when waves propagate at angles with one another in magnetized plasmas remains largely unknown, mainly due to the analytical difficulty of this problem. In this paper, we overcome this analytical difficulty and find a convenient formula for three-wave coupling coefficient in cold, uniform, magnetized, and collisionless plasmas in the most general geometry. This is achieved by systematically solving the fluid-Maxwell model to second order using a multiscale perturbative expansion. The general formula for the coupling coefficient becomes transparent when we reformulate it as the scattering matrix element of a quantized Lagrangian. Using the quantized Lagrangian, it is possible to bypass the perturbative solution and directly obtain the nonlinear coupling coefficient from the linear response of the plasma. To illustrate how to evaluate the cold coupling coefficient, we give a set of examples where the participating waves are either quasitransverse or quasilongitudinal. In these examples, we determine the angular dependence of three-wave scattering, and demonstrate that backscattering is not necessarily the strongest scattering channel in magnetized plasmas, in contrast to what happens in unmagnetized plasmas. Our approach gives a more complete picture, beyond the simple collimated geometry, of how injected waves can decay in magnetic confinement devices, as well as how lasers can be scattered in magnetized plasma targets.
由外部泵浦或内部不稳定性产生的磁化等离子体中的大振幅波，可以通过三波相互作用发生散射。虽然三波散射在准直几何结构中是众所周知的，但当波在磁化等离子体中以相互成角度的方式传播时会发生什么，在很大程度上仍然未知，主要是由于这个问题的分析难度。在本文中，我们克服了这一分析难题，找到了在最一般几何结构下冷的、均匀的、磁化的和无碰撞等离子体中三波耦合系数的一个便捷公式。这是通过使用多尺度微扰展开将流体 - 麦克斯韦模型系统地求解到二阶来实现的。当我们将耦合系数的一般公式重新表述为一个量子化拉格朗日量的散射矩阵元时，它就变得清晰明了。使用量子化拉格朗日量，可以绕过微扰解，直接从等离子体的线性响应中获得非线性耦合系数。为了说明如何评估冷耦合系数，我们给出了一组示例，其中参与的波要么是准横向的，要么是准纵向的。在这些示例中，我们确定了三波散射的角度依赖性，并证明与未磁化等离子体中的情况相反，反向散射在磁化等离子体中不一定是最强的散射通道。我们的方法给出了一个比简单准直几何结构更完整的图景，展示了注入波在磁约束装置中如何衰减，以及激光在磁化等离子体靶中如何散射。
