A simple zero-dimensional model for a tokamak disruption is used to evaluate the effect of radial runaway losses on the avalanche multiplication of a runaway primary seed during the current quench phase of a fast disruptive event as well as during its termination phase. Analytical expressions for the resulting runaway current, the energy of the runaway beam, and the runaway energy distribution function are obtained. It is found that the formation of the runaway current takes place under an effective critical electric field for runaway current generation due to the radial losses larger than the avalanche threshold associated with the energy losses only. As a result, the amount of runaway current generated by avalanche decreases due to the radial losses, but because of the lower amount of runaway current during the formation phase, the electric field increases, which can lead to a noticeable energy deposition on the runaway population, most of it ultimately deposited onto the plasma facing components, unless the radial losses are sufficiently large. The decay of the current after the formation phase follows a marginal stability scenario, during which the electric field remains close (but below) to the effective critical field for the runaway current, which, as the critical field is larger than the avalanche threshold due to the energy losses only, can result in a substantial conversion of magnetic into runaway kinetic energy during slow current terminations.

中文翻译：

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托卡马克中断造成的径向失控损失

用于托卡马克中断的简单零维模型用于评估在快速中断事件的当前猝灭阶段及其终止阶段，径向失控损失对失控初生种子雪崩繁殖的影响。获得了所产生的失控电流，失控束的能量以及失控能量分布函数的解析表达式。已经发现，由于径向损耗大于仅与能量损耗相关的雪崩阈值，所以在产生失控电流的有效临界电场下发生了失控电流的形成。结果，雪崩产生的失控电流量由于径向损耗而减少，但是由于在形成阶段中失控电流量较小，电场增加，这会导致明显的能量沉积在失控的总体上，除非径向损耗足够大，否则大部分最终会沉积到面向等离子的部件上。形成阶段之后电流的衰减遵循边际稳定性方案，在此方案中，电场保持接近（但低于）电场对失控电流的有效临界场，因为临界场大于雪崩阈值，这是由于仅能量损失会导致在慢速电流终止期间将磁能大量转换为失控的动能。