We describe the evolution of a plasma equilibrium having a toroidal topology in the presence of constant electric resistivity. After outlining the main analytical properties of the solution, we illustrate its physical implications by reproducing the essential features of a scenario for the upcoming Italian experiment Divertor Tokamak Test Facility, with a good degree of accuracy. Although we find the resistive diffusion time scale to be of the order of $10^4$ s, we observe a macroscopic change in the plasma volume on a time scale of $10^2$ s, comparable to the foreseen duration of the plasma discharge by design. In the final part of the work, we compare our self-consistent solution to the more common Solov'ev one, and to a family of nonlinear configurations.

中文翻译：

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环形等离子体的 Grad-Shafranov 方程的扩散时间演化

我们描述了在电阻率恒定的情况下具有环形拓扑的等离子体平衡的演变。在概述了解决方案的主要分析特性之后，我们通过为即将到来的意大利实验 Divertor Tokamak 测试设施重现场景的基本特征来说明其物理意义，并且具有很高的准确性。虽然我们发现电阻扩散时间尺度是 $10^4$ s，我们观察到血浆体积在时间尺度上的宏观变化 $10^2$ s，与设计预期的等离子体放电持续时间相当。在工作的最后一部分，我们将我们的自洽解决方案与更常见的 Solov'ev 解决方案以及一系列非线性配置进行比较。