Non-spherical source-surface model of the heliosphere: a scalar formulation
Non-spherical source-surface model of the heliosphere: a scalar formulation
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日光层的非球形源面模型：标量公式
DOI：
10.1007/s00585-997-1379-1
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发表时间：
1997
影响因子：
1.9
通讯作者：
M. Schulz
中科院分区：
文献类型：
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作者：
M. Schulz
源面法为日球层的全MHD模拟提供了一种替代方法。它需要指定一个表面，从那里太阳风通常沿直线向外流动。与MHD结果的兼容性要求这个（源）表面通常是非球形的，并且在轴对称的原型情况下是长形的（与太阳偶极子轴对齐）。因此，源表面的中纬度特征映射到日球层中明显较低的纬度。该模型通常是通过从以球面谐波形式展开的标量势中推导出B场（在源表面周围的区域）来实现的，所选择的系数使B在该表面上的均方切向分量最小。在简化（标量）版本中，最小化的量是源表面上标量势的方差。标量公式大大减少了计算所需矩阵元素所需的时间，同时施加了与矢量公式基本相同的物理边界条件（即，日冕磁场尽可能与源表面垂直，以便与日球层保持连续性）。实际应用的源面为常数$$\tilde{F}\equiv r^{-k}\tilde{B}$$，其中r为日心距离，B为太阳内部电流产生的B场的标量量级。与MHD模拟的比较表明，k≈1.4是可调指数的较好选择。在卡灵顿自转1869年（1993年5月至6月）期间，这个值被用来绘制源表面上的中性线，在尤利西斯的磁力计观测中，扇形结构消失的那个月，这个纬度范围正好掠过尤利西斯的位置。
The source-surface method offers an alternative to full MHD simulation of the heliosphere. It entails specification of a surface from which the solar wind flows normally outward along straight lines. Compatibility with MHD results requires this (source) surface to be non-spherical in general and prolate (aligned with the solar dipole axis) in prototypical axisymmetric cases. Mid-latitude features on the source surface thus map to significantly lower latitudes in the heliosphere. The model is usually implemented by deriving the B field (in the region surrounded by the source surface) from a scalar potential formally expanded in spherical harmonics, with coefficients chosen so as to minimize the mean-square tangential component of B over this surface. In the simplified (scalar) version the quantity minimized is instead the variance of the scalar potential over the source surface. The scalar formulation greatly reduces the time required to compute required matrix elements, while imposing essentially the same physical boundary condition as the vector formulation (viz., that the coronal magnetic field be, as nearly as possible, normal to the source surface for continuity with the heliosphere). The source surface proposed for actual application is a surface of constant $$\tilde{F}\equiv r^{-k}\tilde{B}$$, where r is the heliocentric distance and B is the scalar magnitude of the B field produced by currents inside the Sun. Comparison with MHD simulations suggests that k ≈ 1.4 is a good choice for the adjustable exponent. This value has been shown to map the neutral line on the source surface during Carrington Rotation 1869 (May–June 1993) to a range of latitudes that would have just grazed the position of Ulysses during that month in which sector structure disappeared from Ulysses’ magnetometer observations.