In the present work a simple analytical approach is presented in order to clarify the physics behind the edge current density behaviour of a hot plasma entering in contact with a resistive conductor. When a plasma enters in contact with a highly resistive wall, large current densities appear at the edge of the plasma. The model shows that this edge current originates from the plasma response, which attempts to conserve the poloidal magnetic flux ($\Psi$) when the outer current is being lost. The loss of outer current is caused by the high resistance of the outer current path compared to the plasma core resistance. The resistance of the outer path may be given by plasma contact with a very resistive structure or by a sudden decrease of the outer plasma temperature (e.g. due to a partial thermal quench or due to a cold front penetration caused by massive gas injection). For general plasma geometries and current density profiles the model shows that given a small change of minor radius ($\delta a$) the plasma current is conserved to first order ($\delta I_p = 0 + \mathcal{O}(\delta a^2)$). This conservation comes from the fact that total inductance remains constant ($\delta L = 0$) due to an exact compensation of the change of external inductance with the change of internal inductance ($\delta L_\text{ext}+\delta L_\text{int} = 0$). As the total current is conserved and the plasma volume is reduced, the edge safety factor drops according to $q_a \propto a^2/I_p$. Finally the consistency of the resulting analytical predictions is checked with the help of free-boundary MHD simulations.

中文翻译：

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了解热 VDE 和快速边缘冷却事件期间边缘安全系数的降低

在目前的工作中，提出了一种简单的分析方法，以阐明与电阻导体接触的热等离子体的边缘电流密度行为背后的物理原理。当等离子体与高电阻壁接触时，等离子体边缘会出现大电流密度。该模型显示该边缘电流源自等离子体响应，当外部电流丢失时，等离子体响应试图守恒极向磁通量 ($\Psi$)。与等离子体核心电阻相比，外部电流路径的高电阻会导致外部电流的损失。外部路径的电阻可以通过等离子体与电阻很大的结构接触或外部等离子体温度的突然降低（例如 由于部分热淬火或由于大量气体注入引起的冷锋穿透）。对于一般等离子体几何形状和电流密度分布，该模型表明，给定小半径 ($\delta a$) 的小变化，等离子体电流守恒为一阶 ($\delta I_p = 0 + \mathcal{O}(\delta a^2)$)。这种守恒来自这样一个事实，即总电感保持恒定（$\delta L = 0$），这是由于外部电感的变化与内部电感的变化（$\delta L_\text{ext}+\delta L_\text{int} = 0$)。随着总电流守恒和等离子体体积减小，边缘安全系数根据 $q_a \propto a^2/I_p$ 下降。最后，在自由边界 MHD 模拟的帮助下检查所得分析预测的一致性。对于一般等离子体几何形状和电流密度分布，该模型表明，给定小半径 ($\delta a$) 的小变化，等离子体电流守恒为一阶 ($\delta I_p = 0 + \mathcal{O}(\delta a^2)$)。这种守恒来自这样一个事实，即总电感保持恒定（$\delta L = 0$），这是由于外部电感的变化与内部电感的变化（$\delta L_\text{ext}+\delta L_\text{int} = 0$)。随着总电流守恒和等离子体体积减小，边缘安全系数根据 $q_a \propto a^2/I_p$ 下降。最后，在自由边界 MHD 模拟的帮助下检查所得分析预测的一致性。对于一般等离子体几何形状和电流密度分布，该模型表明，给定小半径 ($\delta a$) 的小变化，等离子体电流守恒为一阶 ($\delta I_p = 0 + \mathcal{O}(\delta a^2)$)。这种守恒来自这样一个事实，即总电感保持恒定（$\delta L = 0$），这是由于外部电感的变化与内部电感的变化（$\delta L_\text{ext}+\delta L_\text{int} = 0$)。随着总电流守恒和等离子体体积减小，边缘安全系数根据 $q_a \propto a^2/I_p$ 下降。最后，在自由边界 MHD 模拟的帮助下检查所得分析预测的一致性。