The W7-X plasma vessel (PV) is part of the cryostat wall and forms a vacuum and thermal barrier between the hot vessel interior and the superconducting coils. The vessel is thermally loaded from the inside and is actively cooled by numerous cooling water pipes in order to control its temperature.

However, due to the complex geometry and large number of different types of ports, the cooling pipes are distributed irregularly with varying distances in between them. So the temperature distribution of the PV becomes quite inhomogeneous even with homogeneous load density, and impermissible temperature hot spots >130 °C may arise. Particularly for the upcoming long pulse operation phase 2 (OP2), it is necessary to know the locally allowed thermal loads on the PV. Therefore, temperature distribution maps for different heat loads from 1 kW/m² to 12 kW/m² were calculated in order to determine the corresponding hot spots.

The available CAD geometry was not convenient for this extensive and complex analysis; therefore, a simplified shell-beam model was employed to get an approximate temperature distribution, and a correction formula was derived to calculate more accurate values at the positions of interest.

In some areas with large distances between cooling pipes, additional copper stripes are welded onto the PV to improve the heat transfer. For these regions local models were built to calculate the temperature distributions, and, in the course of this analysis, to judge the effect of the copper stripes.

The calculation results indicate positions to be additionally protected and will be used to determine safe operation limits.

W7-X等离子容器（PV）是低温恒温器壁的一部分，并在热容器内部和超导线圈之间形成真空和热障。该容器从内部进行热加载，并通过许多冷却水管进行主动冷却，以控制其温度。

然而，由于复杂的几何形状和大量不同类型的端口，冷却管不规则地分布，并且在它们之间具有不同的距离。因此，即使在负载密度均匀的情况下，PV的温度分布也变得非常不均匀，并且可能会出现> 130°C的不允许的温度热点。特别是对于即将到来的长脉冲操作阶段2（OP2），有必要知道PV上本地允许的热负荷。因此，为了确定相应的热点，计算了从1 kW / m ²到12 kW / m ^2的不同热负荷的温度分布图。

对于这种广泛而复杂的分析，可用的CAD几何图形并不方便。因此，采用简化的壳梁模型获得近似的温度分布，并推导了校正公式以计算感兴趣位置处的更精确值。

在一些冷却管之间距离较远的区域中，附加的铜条被焊接到PV上以改善热传递。对于这些区域，建立了本地模型来计算温度分布，并在此分析过程中判断铜带的影响。

计算结果表明需要进一步保护的位置，并将用于确定安全操作极限。