Optimizing X-ray mirror thermal performance using matched profile cooling

To cover a large photon energy range, the length of an X-ray mirror is often longer than the beam footprint length for much of the applicable energy range. To limit thermal deformation of such a water-cooled X-ray mirror, a technique using side cooling with a cooled length shorter than the beam footprint length is proposed. This cooling length can be optimized by using finite-element analysis. For the Kirkpatrick-Baez (KB) mirrors at LCLS-II, the thermal deformation can be reduced by a factor of up to 30, compared with full-length cooling. Furthermore, a second, alternative technique, based on a similar principle is presented: using a long, single-length cooling block on each side of the mirror and adding electric heaters between the cooling blocks and the mirror substrate. The electric heaters consist of a number of cells, located along the mirror length. The total effective length of the electric heater can then be adjusted by choosing which cells to energize, using electric power supplies. The residual height error can be minimized to 0.02 nm RMS by using optimal heater parameters (length and power density). Compared with a case without heaters, this residual height error is reduced by a factor of up to 45. The residual height error in the LCLS-II KB mirrors, due to free-electron laser beam heat load, can be reduced by a factor of similar to 11 below the requirement. The proposed techniques are also effective in reducing thermal slope errors and are, therefore, applicable to white beam mirrors in synchrotron radiation beamlines.