3D MHD Coronal Oscillations about a Magnetic Null Point: Application of WKB Theory
3D MHD Coronal Oscillations about a Magnetic Null Point: Application of WKB Theory
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关于磁零点的 3D MHD 日冕振荡：WKB 理论的应用
DOI：
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发表时间：
2007
期刊：
影响因子：
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通讯作者：
A. Hood
中科院分区：
文献类型：
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作者：
James McLaughlin;J. Ferguson;A. Hood
本文是一个示范的WKB近似可以用来帮助解决线性化的三维MHD方程。利用Charpit方法和Runge-Kutta数值格式，我们对一个潜在的三维磁零点B=[x，εy，−（ε+1）z]证明了这种方法。在我们的冷等离子体假设下，我们考虑了两种类型的波传播：快磁声波和阿尔文波。我们发现，快速磁声波的经验折射向磁零点，这种折射的效果取决于阿尔文速度分布。波和波能在零点处积累。我们已经发现，电流建立是指数的，并且指数取决于ε。因此，对于快波，在零点处存在优先加热。对于阿尔文波，我们发现波是沿着场线沿着传播的。对于沿沿着扇形面生成的阿尔文波，波沿脊沿着累积。对于在脊柱上生成的阿尔文波，ε的值决定了波累积将发生的位置：扇形面（ε=1），沿着x轴（01）。我们已经分析表明，电流呈指数增长，导致这些地区的优先加热。这里所描述的工作突出了了解日冕磁场的磁拓扑结构对波加热位置的重要性。
This paper is a demonstration of how the WKB approximation can be used to help solve the linearised 3D MHD equations. Using Charpit’s method and a Runge – Kutta numerical scheme, we have demonstrated this technique for a potential 3D magnetic null point, B=[x,εy,−(ε+1)z]. Under our cold-plasma assumption, we have considered two types of wave propagation: fast magnetoacoustic and Alfvén waves. We find that the fast magnetoacoustic wave experiences refraction towards the magnetic null point and that the effect of this refraction depends upon the Alfvén speed profile. The wave and thus the wave energy accumulate at the null point. We have found that current buildup is exponential and the exponent is dependent upon ε. Thus, for the fast wave there is preferential heating at the null point. For the Alfvén wave, we find that the wave propagates along the field lines. For an Alfvén wave generated along the fan plane, the wave accumulates along the spine. For an Alfvén wave generated across the spine, the value of ε determines where the wave accumulation will occur: fan plane (ε=1), along the x-axis (01). We have shown analytically that currents build up exponentially, leading to preferential heating in these areas. The work described here highlights the importance of understanding the magnetic topology of the coronal magnetic field for the location of wave heating.