Abstract. The description of the relationship between interplanetary plasma and geomagnetic activity requires complex models. Drastically reducing the ambition of describing this detailed complex interaction and, if we are interested only in the fractality properties of the time series of its characteristic parameters, a magnetohydrodynamic (MHD) shell model forced using solar wind data might provide a possible novel approach. In this paper we study the relation between the activity of the magnetic energy dissipation rate obtained in one such model, which may describe geomagnetic activity, and the fractal dimension of the forcing. In different shell model simulations, the forcing is provided by the solution of a Langevin equation where a white noise is implemented. This forcing, however, has been shown to be unsuitable for describing the solar wind action on the model. Thus, we propose to consider the fluctuations of the product between the velocity and the magnetic field solar wind data as the noise in the Langevin equation, the solution of which provides the forcing in the magnetic field equation. We compare the fractal dimension of the magnetic energy dissipation rate obtained, of the magnetic forcing term, and of the fluctuations of v⋅bz , with the activity of the magnetic energy dissipation rate. We examine the dependence of these fractal dimensions on the solar cycle. We show that all measures of activity have a peak near solar maximum. Moreover, both the fractal dimension computed for the fluctuations of v⋅bz time series and the fractal dimension of the magnetic forcing have a minimum near solar maximum. This suggests that the complexity of the noise term in the Langevin equation may have a strong effect on the activity of the magnetic energy dissipation rate.

中文翻译：

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太阳风波动强迫的磁流体动力壳模型分形性研究

摘要。行星际等离子体与地磁活动之间关系的描述需要复杂的模型。大大降低了描述这种详细复杂相互作用的雄心，如果我们只对其特征参数的时间序列的分形特性感兴趣，那么使用太阳风数据强制使用的磁流体动力学 (MHD) 壳模型可能会提供一种可能的新方法。在本文中，我们研究了在一个这样的模型中获得的磁能耗散率的活动与强迫的分形维数之间的关系，该模型可以描述地磁活动。在不同的壳模型模拟中，强制由朗之万方程的解提供，其中实现了白噪声。然而，这种强迫，已被证明不适合描述模型上的太阳风作用。因此，我们建议将速度和磁场太阳风数据之间乘积的波动视为朗之万方程中的噪声，其解提供磁场方程中的强迫。我们将获得的磁能耗散率、磁力项和 v⋅bz 波动的分形维数与磁能耗散率的活动进行比较。我们研究了这些分形维数对太阳周期的依赖性。我们表明，所有活动量度都有一个接近太阳活动最大值的峰值。此外，为 v⋅bz 时间序列的波动计算的分形维数和磁强迫的分形维数在太阳极大值附近都有一个最小值。