密度分层和膨胀太阳波导中的纵向振荡
Longitudinal oscillations in density stratified and expanding solar waveguides
摘要：
波和振荡可以提供关于它们在其中传播的波导的内部结构的重要信息。在这里，我们分析调查的线性纵向磁流体动力学（MHD）波的密度和磁分层的影响。本文的重点是研究这些振荡的本征模。我们的具体目标是了解在具有非恒定（例如，膨胀或磁性瓶）的横截面积和密度变化。导出了纵模的控制方程，并进行了解析和数值求解。特别是，薄通量管近似的限制进行检查。本文给出了描述等密度磁通磁通量管中慢纵向MHD波的一般解，并分析了等磁场密度分层回路中的纵向MHD波。从解析解出发，研究了分层波导中第一泛音与基模的频率比。对于小的膨胀，频率比和膨胀因子之间存在线性关系，数值计算发现频率比强烈地依赖于所选择的密度分布，数值结果与解析结果基本一致。太阳磁震学的这些结果的相关性进行了讨论。
英文摘要：
Waves and oscillations can provide vital information about the internal structure of waveguides they propagate in. Here, we analytically investigate the effects of density and magnetic stratification on linear longitudinal magnetohydrodynamic (MHD) waves. The focus of this paper is to study the eigenmodes of these oscillations. It is our specific aim is to understand what happens to these MHD waves generated in flux tubes with non-constant (e.g., expanding or magnetic bottle) cross-sectional area and density variations. The governing equation of the longitudinal mode is derived and solved analytically and numerically. In particular, the limit of the thin flux tube approximation is examined. The general solution describing the slow longitudinal MHD waves in an expanding magnetic flux tube with constant density is found. Longitudinal MHD waves in density stratified loops with constant magnetic field are also analyzed. From analytical solutions, the frequency ratio of the first overtone and fundamental mode is investigated in stratified waveguides. For small expansion, a linear dependence between the frequency ratio and the expansion factor is found. From numerical calculations it was found that the frequency ratio strongly depends on the density profile chosen and, in general, the numerical results are in agreement with the analytical results. The relevance of these results for solar magneto-seismology is discussed.
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