Hasegawa-Wakatani方程解的非线性分析
Nonlinear Analysis of the Solutions of the Hasegawa-Wakatani Equations
摘要：
长谷川-若谷模型用于研究外加磁场对热等离子体的约束。长谷川-若谷模型中的非线性项使系统的分析复杂化，因为它们将局部变化传播到整个系统。中心流形分析使我们能够向下投影到更容易分析的更小的系统上。关于简化系统的行为的定性信息，例如它是稳定的还是不稳定的，可以用来预测原始完整系统的行为。我们展示了如何简单的结构的线性部分的长谷川若谷方程可以用来定义这些投影算子。中心流形分析将用于几个例子，以突出长谷川若谷模型的某些属性。
英文摘要：
The Hasegawa-Wakatani models are used in the study of confinement of hot plasmas with externally imposed magnetic fields. The nonlinear terms in the Hasegawa-Wakatani models complicate the analysis of the system as they propagate local changes across the entire system. Centre manifold analysis allows us to project down onto much smaller systems that are more easily analysed. Qualitative information about the behaviour of the reduced system, such as whether it is stable or unstable, can be used to predict the behaviour of the original full system. We show how the simple structure of the linear part of the Hasegawa-Wakatani equations can be used to define these projection operators. The centre manifold analysis will be used on a few examples to highlight certain properties of the Hasegawa-Wakatani models.
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