AI 中文总结
该研究提出正交多项式分解框架，用于分解太阳风速度分布函数，可应用于多航天器实测数据，实现降噪、重构及结构诊断，搭建实测分布与动力学等离子体物理的桥梁。
AI 中文摘要
我们提出了一种使用正交多项式基分解太阳风速度分布函数（VDFs）的框架，旨在建立将多项式分解应用于原位航天器VDF的实用流程，并阐明所得的展开系数功率谱如何用于降噪、VDF重构及速度空间结构诊断。该方法用厄米-厄米（Hermite-Hermite）和厄米-拉盖尔（Hermite-Laguerre）展开表示实测VDF结构，提供对麦克斯韦分布偏离情况的非参数描述，如各向异性、偏度、束流和超热尾。将实测分布插值到多项式节点后，通过高斯加权求积估计展开系数。我们展示了多项式分解在太阳轨道器（Solar Orbiter）、帕克太阳探测器（Parker Solar Probe）及磁层多尺度1（Magnetospheric Multiscale 1）测量中的若干应用，包括通过高阶谱平坦化识别噪声、降噪VDF重构，以及表征不同等离子体条件（如湍流太阳风流和激波）下的VDF结构变化。例如，降噪重构的VDF可提供更平滑的不同离子种群及VDF梯度估计。来自太阳风流和无碰撞激波穿越的实例进一步表明，所得谱对平行和垂直VDF结构的变化有响应，说明其在不同等离子体条件下比较动力学修正的潜力。总体而言，正交多项式分解通过将复杂的VDF形态转换为定量速度空间谱，搭建了实测粒子分布与动力学等离子体物理之间的桥梁。
英文摘要
We present a framework for decomposing solar-wind velocity distribution functions (VDFs) using orthogonal polynomial bases. We aim to establish a practical procedure for applying polynomial decompositions to in-situ spacecraft VDFs and to clarify how the resulting spectra of expansion-coefficient power can be used for noise reduction, VDF reconstruction, and diagnostics of velocity-space structure. The method represents measured VDF structure with Hermite-Hermite and Hermite-Laguerre expansions, providing a nonparametric description of departures from Maxwellians, such as anisotropy, skewness, beams, and suprathermal tails. Expansion coefficients are estimated by Gaussian-weighted quadrature after interpolation of measured distributions onto polynomial nodes. We demonstrate several applications of polynomial decomposition to Solar Orbiter, Parker Solar Probe, and Magnetospheric Multiscale 1 measurements, including noise identification through high-order spectral flattening, noise-reduced VDF reconstruction, and characterization of VDF-structure variations under different plasma conditions, e.g., turbulent solar-wind streams and shocks. For instance, noise-reduced reconstructed VDFs can provide smoother estimates of distinct ion populations and VDF gradients. Examples from solar-wind streams and collisionless-shock crossings further show that the resulting spectra respond to changes in parallel and perpendicular VDF structure, illustrating their potential for comparing kinetic modifications under different plasma conditions. Overall, orthogonal-polynomial decomposition provides a bridge between measured particle distributions and kinetic plasma physics by converting complex VDF morphology into quantitative velocity-space spectra.
