A microscopic model of cosmic ray small-scale anisotropies from magnetic turbulence

地球不断受到来自外太空的带电粒子流的轰击，这种粒子被称为宇宙射线。宇宙线传输的标准图像预测，在最大角度尺度(180度)下，宇宙线到达方向的波动非常小，能量在1TeV到1PeV之间，约为千分之一。然而，观测到的各向异性在小得多的角度尺度上，甚至低至几度。这些小尺度的各向异性在宇宙线传输的标准图像中没有被预测到，并且已经提出了不同的想法来解释它们。可以说，最有希望的建议是，小尺度的各向异性反映了我们银河系邻近地区磁场的动荡结构。事实上，宇宙线输运的标准图像只考虑系综平均的相空间密度，从而忽略了宇宙线对之间的关联，这导致了对小角度尺度上的各向异性水平的低估。在修正后的图像中，观测者在几个无均值路径内的湍流磁场的空间相关性决定了观测者所看到的角相关性。到目前为止，这一想法只通过通过湍流磁场对粒子进行数值跟踪来验证，或者在宏观行为的有效理论中得到验证，例如使用启发式的参数化法来确定散射率的角度相关性。因此，迫切需要一种严格的理论来将湍流磁场的空间关联映射到宇宙线到达方向的角关联。这一理论的一个令人兴奋的应用是通过观测宇宙线各向异性来研究星际介质的湍流结构(如Kolmogorov或Kraichnan，湍流的外部尺度，湍流与常规场的比率)。我们建议建立一个详细的微观模型，预测给定的湍流磁场模型的小尺度各向异性的角功率谱。其目的是描述宇宙线对之间的关联的时间演化，研究在宇宙射线流存在的情况下各向异性准稳态的形成，并计算其角功率谱。我们方法的核心是两粒子传播子的计算，它可以展开成两粒子有效相互作用强度的微扰级数。由此，我们将计算角功率谱，并与现有的观测结果进行比较，以测试各种湍流模型。这种宇宙线传输的方法，特别是相空间密度关联的计算，是一种全新的方法，据我们所知，以前从未尝试过。虽然这个项目确实雄心勃勃，但我们已经详细地列出了我们的项目计划，因此我们有信心成功的机会非常高。

The Earth is constantly bombarded by a flux of charged particles from outer space, called cosmic rays. The standard picture for cosmic ray transport predicts very small fluctuations in their arrival directions at the largest angular scales (180 degrees), of about 1 part in 1000 for energies between 1 TeV and 1 PeV. Yet, observations have shown anisotropies on much smaller angular scales, down to a few degrees. These small-scale anisotropies are not predicted in the standard picture of cosmic ray transport and various ideas have been put forward to explain them. Arguably the most promising suggestion is that the small-scale anisotropies are a reflection of the turbulent structure of the magnetic field in our Galactic neighbourhood. In fact, the standard picture of cosmic ray transport is only considering the ensemble-averaged phase-space density, thus ignoring the correlations between pairs of cosmic rays, which leads to an underestimation of the level of anisotropies on small angular scales. In the revised picture, the spatial correlations of the turbulent magnetic field within a few mean-free paths of the observer are determining the angular correlations seen by the observer.This idea has so far only been tested by numerically tracking particles through turbulent magnetic fields, or in effective theories for the macroscopic behaviour, e.g. using heuristic parametrizations for the angular dependence of scattering rates. A rigorous theory for the mapping of spatial correlations of the turbulent magnetic field to angular correlations of cosmic ray arrival directions is thus urgently needed. An exciting application of such a theory would be the investigation of the turbulence structure of the interstellar medium (e.g. Kolmogorov or Kraichnan, outer scale of turbulence, ratio of turbulent to regular field) through the observation of cosmic ray anisotropies.We propose developing a detailed microscopical model that predicts the angular power spectrum of the small-scale anisotropies for a given model of the turbulent magnetic field. The goal is to describe the time-evolution of the correlations between pairs of cosmic rays, to investigate the formation of a quasi-steady state of anisotropies in the presence of cosmic ray streaming and to compute its angular power spectrum. At the heart of our approach is the computation of the two-particle propagator which can be expanded into a perturbative series in the strength of effective interactions of two particles. From this, we will compute the angular power spectrum and compare to available observations to test various turbulence models.This approach to cosmic ray transport, in particular the computation of the correlations of phase-space densities, is completely new and to the best of our knowledge has never been attempted before. While the project is certainly ambitious, we have laid out our project plan in some detail and are therefore confident that the chances of success are very high.