The performance of a cryogenically cooled monochromator for an in-vacuum undulator beamline

The channel-cut silicon monochromator on beamline ID09 at the European Synchrotron Radiation Facility is indirectly cooled from the sides by liquid nitrogen. The thermal slope error of the diffracting surface is calculated by finite-element analysis and the results are compared with experiments. The slope error is studied as a function of cooling coefficients, beam size, position of the footprint and power distribution. It is found that the slope error versus power curve can be divided into three regions: (i). The linear region: the thermal slope error is linearly proportional to the power. (ii). The transition region: the temperature of the Si crystal is close to 125 K; the thermal slope error is below the straight line extrapolated from the linear curve described above. (iii). The non-linear region: the temperature of the Si crystal is higher than 125 K and the thermal slope error increases much faster than the power. Heat-load tests were also performed and the measured rocking-curve widths are compared with those calculated by finite-element modeling. When the broadening from the intrinsic rocking-curve width and mounting strain are included, the calculated rocking-curve width versus heat load is in excellent agreement with experiment.