用拉格朗日相干结构计算工具预测弱碰撞等离子体中的温度势垒
Prediction of temperature barriers in weakly collisional plasmas by a Lagrangian Coherent Structures computational tool
摘要：
拉格朗日相干结构分析是解释磁化等离子体中输运势垒形成的有效数学方法。这样的LCS，借用流体动力学理论，可以被认为是隐藏的骨架系统，并可以用于研究广泛的传输机制，甚至在等离子体。在本文中，我们证明了这种结构可以特别有用的潜在的隐藏路径管理的磁场线在混沌磁场的运动。为了进行这样的分析，我们开发了一个数值工具，能够检测LCS的一般动力系统。该工具是能够处理一般的坐标系，它被证明是匹配与其他技术已经用于分析混乱的磁场，例如连接长度。在描述了计算工具之后，我们重点讨论了热输运方程以及LCS的温度分布和拓扑结构之间的比较。我们提供的证据表明，数值模拟能够重现类似于RFP实验中观察到的温度分布，我们的工具成功地预测了温度梯度的位置。结果表明，在混沌区域内，场线运动是远离随机和隐藏模式的存在允许发展的高温梯度。
英文摘要：
Analysis of Lagrangian Coherent Structures (LCSs) has been showed to be a valid mathematical approach to explain the formation of transport barriers in magnetized plasmas. Such LCSs, borrowed from fluid dynamics theory, can be considered as the hidden skeleton of the system and can be used for studying a wide spectrum of transport mechanisms even in plasmas. In this paper, we demonstrate that such structures can be particularly useful for underlying the hidden paths governing the motion of magnetic field lines in chaotic magnetic fields. To perform such an analysis, we developed a numerical tool able to detect LCSs for a general dynamical system. The tool is able to deal with general coordinate systems and it is shown to match with other techniques already used to analyse chaotic magnetic fields, e.g. connection length. After the description of the computational tool, we focus on the heat transport equation and the comparison between temperature profile and topology of the LCSs. We provide evidence that numerical simulations are able to reproduce the temperature profiles similar to those observed in RFP experiments and that our tool successfully predicts the location of temperature gradients. The results suggest that, inside the chaotic region, the field-lines motion is far from stochastic and that the presence of hidden patterns allows the development of high temperature gradients.
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