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 
[7].
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.
