To gain some understanding of the effect of the thermal load from the white beam on the monochromator a series of measurements were made following the course of the electron current decay, that is as a function of thermal load on to the monochromator.
A platinum resistance thermometer () was positioned on the upper side of the lower fin of the crystal and held lightly in place again with a small leaf spring. The temperature of the crystal at this position, the ring current and the number of counts per second from were measured as a function of time over one fill of the storage ring. The experiment was carried out with DORIS III running at in single bunch mode with the monochromator set to select out X-rays (calibrated approximately using metal foils). During the measurements the storage ring current decayed steadily from to .
The variation of the monochromator temperature over this period is shown in Fig. . After the beam shutter was opened at it took for the temperature to reach its maximum of after which it decreased steadily until , at which point the temperature had dropped to and the shutter was closed.
Figure: Graph showing the variation of the monochromator temperature, measured as a function of time over one fill of the storage ring using a PT100 positioned on the lower of the two inside faces of the strain relief groove.
Figure: Plot showing the change in the ionisation chamber reading (fed through a Voltage to Frequency converter) against time over one fill of the storage ring. The rapid loss of flux within the first few minutes after the main beam shutter opening is due to thermal detuning of the two reflecting surfaces of the monochromator since only the first face takes the whole load of the white beam. As the whole crystal begins to warm up there is some recovery in the flux through the ionisation chamber.
Fig. shows the corresponding curve for the signal from . At the chamber reads but within the reading drops to after which time it begin to rise again until it peaks at . For the signal decays steadily until the run end.
The initial rapid loss of intensity observed in can be accounted for by an increase in the temperature difference between the two reflecting surfaces of the monochromator due to the fact that when the crystal is first illuminated, the first reflecting face receives the full thermal load of the white beam whereas the second face receives only that of the already monochromatic beam. The monochromator is thus effectively detuned because of the mismatch in the - spacings implied by this temperature difference.
The change in temperature of the monochromator crystal also implies a change in the reflected monochromatic beam energy for a constant Bragg angle.
Given Bragg's law,
and the equation of thermal expansion,
we may calculate the energy shift for a given temperature change in the following way.
If we now differentiate Eq.( ) with respect to the lattice spacing and divide the result by the original expression we obtain the following relationship.
Now from Eq. we have
By equating with and with , and using we obtain the result
where the coefficient of thermal expansion for silicon () is taken as .
Given the large changes in temperature, it was estimated that shifts in the monochromatic beam energy equivalent to were likely during the normal decay of the electron current. Such variations are significant in the context of optimised data collection at the white lines at absorption edges and it was therefore concluded that the energy stability of the beam line was not sufficient for optimised MAD experiments.
Figure: Ten X-ray energy scans over the calibrator (573) reflection as a function of energy . The shift in position of the reflection along the pseudo energy axis is indicative of changes in the lattice spacing of the monochromator crystal. As the ring current drops the reflections are shifted to the left, corresponding to a decrease in the -spacing. The total shift observed was ().
These thoughts were verified by further measurements carried out at a later date using the Si(311) monochromator in conjunction with the energy calibrator while DORIS III was operating at with five electron bunches. The monochromator was repeatedly scanned across the calibrators (573) reflection while the electron current decayed over a fill from to . The (573) line was excited at near the Iridium absorption edge. The signal in the calibrator was recorded as a function of the monochromators motor position which was then converted to an approximate energy scale (). The results of ten scans taken at minute intervals over one fill and two further scans performed at the start of the following fill are shown in figure . (The reflection profiles are offset in the vertical direction for clarity.)
The total shift observed in the position of the reflection over the first fill was on the pseudo energy axis. This was a result of a decrease in lattice parameter of the monochromator. The overall fractional change in energy observed was . It is also apparent that additional shifts in the energy are introduced after reinjection of electrons. This is due to non-reproducibility of the electron orbit position and angle. The total fractional energy shift after reinjection was . It is difficult to estimate exactly what the fractional contributions to energy instability due to the thermal instability of the monochromator and to source movement are but given that the expected energy shifts corresponding to temperature drifts of were we can conclude that changes in the electron orbit trajectory produce comparatively small energy shifts during a storage ring fill but may result in shifts of a few tenths of an electron-volt after reinjection.
These experiments demonstrated the need for some form of energy stabilisation for the X31 beam line. This could have been achieved by a new monochromator set up with an improved cooling system. This however left the question of electron orbit instability unresolved. The second possibility was the control of the energy of the monochromatic X-rays via the energy calibrator as described in section . The latter approach was adopted for the MAD experiments which are described in the following chapters since it made the experiments as independent as possible of source and monochromator problems.