2.7 Position Determination
2.7.3 Depth of the Main Interaction
In case of an irradiation of the MINIBALL detector perpendicular to the detector sur- face, the knowledge of the interaction depth is not required since the radial and angular
positionsr and'of the (first) interaction do not differ from the radial and angular posi-
tion of the point where the -ray enters the detector, the entry positionr(z(0)),'(z(0)).
Therefore, the positions from the PSA can be referenced directly to the front face of the detector (z(0)) as shown in figure 2.24.
In case of a non-perpendicular irradiation of a single MINIBALL detector the entry position and the interaction position do also differ in radial and angular direction. If the PSA position is referenced to the Average Interaction Depth (AID) z(E) the entry position of the -ray can be reconstructed with the knowledge of the source position as
shown in figure 2.24.
As the MINIBALL detector lacks an additional segmentation in depth, an experi- mental determination of the depth of the MI impossible. Since the knowledge of the interaction depth is necessary for the reconstruction of the interaction position, it has to be inserted into in the analysis as an external parameter. The average interaction depth (AID) of the first<z
FI (E )>and main<z MI (E
)>interaction was determined for var-
ious energies in a Monte-Carlo simulation [22]. These values are then put into a look-up table that is used to determine the average interaction depth. The AID determines the effective distance between detector and target, e.g. at an energy of 1 MeV the effective target-detector distance increases from 10.5 cm to about 13.5 cm.
2.7. POSITION DETERMINATION 57 500 1000 1500 2000 2500
Core
500 550 600 650 700 750 800Segment 1
300 350 400 450 500 0 5 10 15 20 25 30 35 40Segment 3
1000 1500 2000 2500 3000Segment 2
Time [25ns] ADC Value ADC Value ADC Value ADC Valueq
max -q
max+ 1 2 3 4 5 6Figure 2.22: The plot shows the extraction of the mirror charge amplitude from segment signal
showing induced signals only, a one segment event (OSE). The maximum mirror charge amplitude jq
max
jcan be determined directly from the detector waveform.
The mirror charge amplitude varies between 5 and 15 % of the net charge signal amplitude.
+
=
t
Amplitude
net charge signal
t
Amplitude
mirror charge signal
qmax
t
Amplitude
qmax
superposition of net and mirror charge signal
t90 t
90
t0 t
0
Figure 2.23: The extraction of the mirror charge amplitude for the case of a neighboring seg-
ment event (NSE) is schematically shown. The net charge signal is approximated by a linear signal using the timing parameterst
0and
t
90determined from the core
contact. The difference between the approximation and the segment signal gives the mirror charge signal.
z(E) 2 1 Collimated Source z Uncollimated Sources 3 r(z(0))non-perp r(z(E)) ≈ r ∝ tss r(z(0))perp
Figure 2.24: Perpendicular and non-perpendicular irradiation geometries for the MINIBALL
detector for a single interaction event, i.e. first and main interaction do coincide. Three different locations for -ray sources are indicated (1, 2 and 3). In case of
a perpendicular irradiation using a collimated source (1) the entry position does not differ from the (first) interaction position in radial and angular direction. In case of a non-perpendicular irradiation (2 and 3), the entry and (first) interaction positions differ also in radial and angular direction and therefore the positions obtained from the pulse shape analysis have to be referenced to the AID z(E).
Chapter 3
Realtime Pulse Shape Analysis
using the XIA DGF-4C CAMAC
module
”Great spirits often meet violent opposition with mediocre minds” - Albert Einstein
In thes chapter the realtime pulse shape analysis used for the MINIBALL project, using a digital electronics, namely the DGF-4C module from XIA [13], will be presented. The purpose of the realtime PSA1is a further reduction in data that has to be read out and stored. Instead of the detector waveform (40 parameters per channel at 40 MHz sam- pling rate) only a handy set of parameters (five per channel) is needed to characterize a
event in the MINIBALL detector. A measurement with a collimated -ray source was
performed to verify (and identify) the relationship between the detector pulse shape, i.e. the PSA parameters, and the collimator position.
3.1
The realtime pulse shape analysis program
The developed realtime PSA program, the user DSP code, was implemented for the dig- ital signal processor of the DGF-4C module. The details of the implementation are com- piled in appendix C.
As the FPGA on the DGF-4C board (RTPU) performs the first level processing, de- livering -energy E
and time of arrival TS, the DSP collects this information event-
by-event in its internal buffers together with the waveform of the leading edge of the detector pulse, read from a separate FIFO, to perform further pulse shape analysis and ballistic deficit compensation.
The developed program performs the MINIBALL PSA algorithms presented in sec- tion 2.7, delivering the steepest slope time t
ss and the maximum height of the induced
chargeq
max. In addition, the L-EBC and the Q-EBC timing algorithms (implemented us-
ing a LE method to determine the initial sample indexM) can be performed giving the
signal start timet EBC 0
and replacing the FT algorithm parametert FT 0
determined by the
1
Consider preprocessing as first level processing, PSA as second level processing.
DGF-4C module2. Additionally, the rise timet
90, the sample index of q
max, i.e. t(q
max )
and a parameter specifying the PSA module reporting an error condition are supplied3.
The segment containing the MI is identified by searching for the segment with the highest energy deposition. Using the PSA parameters, the drift time of the electrons is given by t e =t true ss =t dsp ss t dsp 0 witht dsp
ss the steepest slope parameter of the central
contact from which the start time of the detector pulset
0has to be subtracted to obtained
the time-to-steepest-slope t true ss
. The radial interaction position is then given by r = a t
+b, with a and b the calibration parameters that have to be determined. The
angular interaction position (the segment angle) is given by'= log jq + j jq j +d, with
andd the calibration parameters and jq +
j andjq j the absolute value of the maximum
mirror charge amplitude in the neighboring segments of the MI segment4. Together with the AID z(E
), the position of the (main) interaction inside the detector has been
determined by PSA. With the knowledge of the source position the entry position at the detector front face can be calculated.
In order to verify the functionality of the user DSP code, implementing the MINI- BALL PSA algorithms, the response of a MINIBALL cluster detector to a collimated
-ray source was determined.