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Non-uniformities in the response of the calorimeter affect its
performance if they cannot be corrected by calibration.
In the case of a liquid krypton calorimeter with a tower
readout structure the electromagnetic
shower profile is rather narrow and very steep near its axis.
The average shower profile as measured with 120 GeV electrons is
shown in figure .
Up to 50 % of the visible shower energy is deposited in the
central calorimeter cell.
There are two main sources for a non-uniformity of the
calorimeter response with tower readout.
The first is the mechanical tolerance of the cell width and the
second is given by the presence of the charge collecting electrodes.
These electrodes are made of passive material and
only part of the charge produced close to the
electrodes is seen due to the effective pulse shaping time of
about 60 ns.
Both effects would average out in case of
uniform ionization across the calorimeter.
But, this is not the case for a shower profile as shown in
figure .
Both a left-right asymmetry in the two half-cells forming one
calorimeter cell and a decrease of the charge close to the
readout electrodes were observed in the data.
In the following, both effects are discussed in more detail.
For cells with an uniform electric drift field the initial
current is given by
where is the total ionization charge deposited in the cell,
the drift velocity and
the width of a cell.
In the case of the showers perpendicular to the
direction of drift and a cell size of the order of half a
Moliere radius, the density of the ionization is changing
strongly over the width of a cell.
Then the precision with which the cell width
is known
can become a limiting factor in the resolution of the calorimeter.
Since each cell consists of two half-cells, deviations
from the nominal width tend to be opposite for adjacent half-cells
and left-right asymmetries in the two half-cells can be observed.
Figure shows the response of the calorimeter
in one cell as a function of x,
the coordinate of the electron impact point
perpendicular to the readout electrodes, determined using
the drift chamber information.
This cell was chosen since it showed the largest observed left-right
asymmetry.
During the last period of the test run, extra spacers were
inserted to improve the constancy of the foil spacing.
The improvement of the response uniformity
can be seen in figure .
Monte Carlo simulation [12] confirmed that in order to maintain
the energy independent term in the resolution to less
than 0.5 %, the mechanical tolerances defining the width of the
cells must be kept to better than 1 % (i.e. 100
m)
for the geometry of this prototype.
The second effect is related to the fraction of ionization
deposited in the passive material of the electrodes and to the
effective shaping time during which the initial current
is measured.
Since
is of the order of 60 ns,
the ionization deposited in a region distant from the anode by less than
does not fully contribute
to the initial current measurement.
As a consequence, the current loss is small
if the shower core is far away from the anode,
but a larger amount of charge is lost if the particle impinges
close to the anode.
Independently of integration time, a larger fraction of ionization
ends in passive material when the shower is closer to either anode
or cathode.
As a result, the response of the calorimeter as a function
of the impact position shows depletions at the positions of the
electrodes.
These depletions are less pronounced at the cathodes.
To minimize non-uniformities, a small angle zig-zag of the
readout electrodes is planned for the final calorimeter.
In order to study the benefits of a small angle between
the calorimeter cell structure and the beam axis,
data were taken at calorimeter orientations of 0, 13 and
26 mrad with respect to the beam axis.
The depletion present at the centre of the cell is reduced
by this rotation.
Typical values for the depletion are reported in table .
The tilt smeared out and hence decreased the non-uniformities.
The remaining non-uniformities have been measured and subsequently corrected offline for the determination of the final energy resolution.