Relative Magnetic Helicity Based on a Periodic Potential Field
Relative Magnetic Helicity Based on a Periodic Potential Field
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DOI：
10.3847/1538-4357/ab8810
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发表时间：
2020-04
期刊：
影响因子：
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通讯作者：
Kai E. Yang;M. Wheatland;S. Gilchrist
中科院分区：
文献类型：
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作者：
Kai E. Yang;M. Wheatland;S. Gilchrist
磁螺旋度在理想磁流体力学下是守恒的，即使在电阻过程下也是准守恒的。磁螺旋度的标准定义不能直接应用于体积中的开放磁场，因为它是规范依赖的。相反，相对磁螺旋度被广泛使用。我们发现，在一个矩形域周期性的横向边界条件的潜在磁场的能量小于一个固定的正常分量的字段在所有六个边界。为了利用这种较低能量的势场来分析相对磁螺旋度，我们引入了一种新的磁场磁螺旋度的定义，它包含了周期势场。我们将此定义应用到一系列的解析解和数值模拟。结果表明，我们的新规范不变螺旋度非常接近于原始磁场的相对磁螺旋度的载流部分。我们还发现，载流螺旋度和相对磁螺旋度的原始和我们定义的相对螺旋度之间的比率表现出不同的行为。新的螺旋度似乎对由于体积中的电流而引起的场的分量更敏感，这是不稳定性和太阳爆发现象的来源。
Magnetic helicity is conserved under ideal magnetohydrodynamics and quasi-conserved even under a resistive process. The standard definition for magnetic helicity cannot be applied directly to an open magnetic field in a volume, because it is gauge-dependent. Instead, the relative magnetic helicity is widely used. We find that the energy of a potential magnetic field in a rectangular domain with periodic lateral boundary conditions is less than that of the field with a fixed normal component on all six boundaries. To make use of this lower energy potential field in the analysis of relative magnetic helicity, we introduce a new definition for magnetic helicity for the magnetic field, which involves the periodic potential field. We apply this definition to a sequence of analytic solutions and a numerical simulation. The results show that our new gauge-invariant helicity is very close to the current-carrying part of the relative magnetic helicity of the original magnetic field. We find also that the ratio between the current-carrying helicity and the relative magnetic helicity for the original and our defined relative helicity show different behavior. It seems that the new helicity is more sensitive to the component of the field due to the electric current in the volume, which is the source for instabilities and solar eruptive phenomena.