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Here, in order to reduce tangential slope errors along the centreline of a first mirror's surface, a side-cooling scheme is proposed. The length of the contact area between the mirror and cooling blocks should be smaller than the beam footprint along the mirror. By optimizing the length and the height of the contact area, reduced slope errors can be obtained. Using this scheme the maximum temperature is not located at the centre of the footprint but shifts to both sides, which fundamentally changes the temperature distribution and enhances the cooling effect compared with the traditional method. This paper presents a `design of experiment' analysis for four kinds of cooling schemes. The structure of the mechanical clamps is also described.

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