Abstract

In this paper, we analyze the so-called Master Equation of the linear backreaction of a plasma disk in the central object magnetic field, when small scale ripples are considered. This study allows to single out two relevant physical properties of the linear disk backreaction: (i) the appearance of a vertical growth of the magnetic flux perturbations; (ii) the emergence of sequence of magnetic field O-points, crucial for the triggering of local plasma instabilities. We first analyze a general Fourier approach to the solution of the addressed linear partial differential problem. This technique allows to show how the vertical gradient of the backreaction is, in general, inverted with respect to the background one. Instead, the fundamental harmonic solution constitutes a specific exception for which the background and the perturbed profiles are both decaying. Then, we study the linear partial differential system from the point of view of a general variable separation method. The obtained profile describes the crystalline behavior of the disk. Using a simple rescaling, the governing equation is reduced to the second-order differential Whittaker equation. The zeros of the radial magnetic field are found by using the solution written in terms Kummer functions. The possible implications of the obtained morphology of the disk magnetic profile are then discussed in view of the jet formation.

GraphicAbstract

中文翻译：

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吸积盘线性晶体形态的一般特征

摘要

在本文中，当考虑到小规模的纹波时，我们分析了等离子体盘在中心物体磁场中的线性反向反应的所谓主方程。这项研究可以找出线性磁盘反向反应的两个相关物理特性：（i）磁通量扰动在垂直方向上的增长；（ii）磁场O序列的出现点，对于触发局部血浆不稳定性至关重要。我们首先分析解决该线性偏微分问题的通用傅里叶方法。这项技术可以显示出反作用的垂直梯度通常相对于背景如何反转。取而代之的是，基波谐波解决方案构成了一个特定的例外，背景和受干扰的轮廓都在衰减。然后，我们从一般变量分离方法的角度研究线性偏微分系统。所获得的轮廓描述了圆盘的结晶行为。使用简单的重新定标，控制方程式可简化为二阶微分Whittaker方程式。径向磁场的零点是使用用Kummer函数编写的解找到的。鉴于射流的形成，然后讨论了所获得的磁盘磁廓形的可能含义。

图形摘要