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A self-similar solution of expanding cylindrical flux ropes for any polytropic index value

机译：任何多方指数值的圆柱状通量钢丝绳的自相似解

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We found a new class of solutions for MHD equations that satisfies the condition that cylindrical flux ropes can expand self-similarly even when the polytropic index g is larger than 1. We achieved this by including the effects of elongation along the symmetry axis as well as radial expansion and assuming that the radial expansion rate is the same as the elongation rate. In previous studies (Osherovich et al ., 1993a, 1995), a class of self-similar solutions was described for which cylindrical flux ropes expand only in the medium where g is less than 1. We compare the models including elongation and excluding elongation observationally by using the WIND key parameters. The difference in the fitting results of the magnetic field between these two models is slight. However the fitting of the velocity is improved when elongation is included and when new geometric parameters that are necessary to represent the elongation are introduced. The values of these parameters are almost the same scale as the radius of flux ropes, which is consistent with the assumption of the isotropic expansion. This new exact solution to a time-dependent two-dimensional MHD problem can also be used to test numerical codes.
机译：我们发现了一类新的MHD方程解，它满足以下条件：即使在多变指数g大于1时，圆柱通量绳索也可以自相似地膨胀。我们通过包括沿对称轴的伸长以及径向膨胀率，并假定径向膨胀率与伸长率相同。在以前的研究中（Osherovich等，1993a，1995），描述了一类自相似解，其中圆柱状通量绳仅在g小于1的介质中膨胀。我们比较了包括伸长率和不包括伸长率在内的模型通过使用WIND键参数。这两个模型之间的磁场拟合结果差异很小。但是，当包括伸长率并引入表示伸长率所需的新几何参数时，速度的拟合度会提高。这些参数的值几乎与通量绳的半径相同，这与各向同性膨胀的假设是一致的。这种对时间相关的二维MHD问题的精确解决方案也可以用于测试数字代码。

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