Radioactive Particle Tracking (RPT) and Benchmarking for High Velocity Conditions
2.2 Radioactive particle tracking technique
2.2.3 Calibration
channels increase the resolution of spectra. Figure 2.9 shows the energy spectra of scandium-46 with peak from MCA with 1024 channels.
Figure 2.9 Energy spectra of Scandium - 46 Single Channel Analyzer
From the spectrum it can inferred that, it contains all the energy levels including Compton backscattered photons and electronic noise. These unwanted photons can be removed through single channel analyzer (SCA) by using a threshold. Single channel analyzer (SCA) discriminates the incident photons between the LLD (Low level discriminator) threshold and ULD (Upper level discriminator) threshold. SCA can be used for high frequency acquisition, as there are only threshold limits, it process the data faster than MCA.
noted down. Similarly, tracer particle is placed at different known locations inside the vessel and distance-count map is generated for all the detectors. Ideally, tracer particle should be placed at all the possible locations inside the vessel to achieve high accuracy.
However, practically it is not possible to place the particle at all the locations. Further, it requires huge time and effort, which make the process tedious. To avoid this, Monte Carlo code for photon emission, transmission and detection developed by Larachi et al. (1994), later on modified by Upadhyay (2010) was applied, to mathematically generate the counts recorded on the detector for a known particle location. However to optimize the unknown fitting variables of Monte Carlo program, ‘in – situ’ calibration at few points is required (Upadhyay, 2010). In current work, Monte Carlo code is used to obtain the position – count map numerically using limited data of experimental calibration.
Monte Carlo simulation
An alternate way of constructing the distance - count map is by modeling the emission, transmission and subsequent detection of photons at the detector. While this is not intended to replace the real RPT calibration, however it provides a way of making the calibration part of the experiment more efficient. Also, it provides valuable information that can complement the experimentally acquired photon counts and allow for more accurate reconstruction. This modeling for gamma ray interaction is done by Monte Carlo simulation. In the Monte Carlo program, photon histories are tracked in their way from source, through the medium and their final detection at detector (Larachi et al., 1997; Beam et al., 1978). Both the geometry and radiation effects are accounted for estimation of detector efficiencies in capturing and recording the photons. To account the geometry effect, solid angle (angle created by the tracer particle to the detector) effect is accounted, which significantly affect the detector counting efficiency. Absolute efficiency can be
is far from the detector axis the side face of the detector is more important than the front face.
3
1
exp 1 exp
N
abs j j D
j
r n l d d
r
(2.2)Where,
n
the unit normal vector to the curved surface of the detector r is the radius vector from source to detector
D is the mass attenuation coefficient of the detector crystal material is the penetration depth of photons in the detector crystaljis the mass attenuation coefficient of all the materials that comes in the path of photons between the source and the detector
In equation 2.2, mass attenuation, solid angle subtended by the detector disk and surface on the tracer particle and penetration depth of photons in the detector are unknowns.
Penetration depth of photons can be obtained by geometrical arguments and explained in detail later. Solid angle is a complex function as particle emits photons in all the directions and each direction has different path length. It is calculated by tracking large number of photon histories in different direction through Monte Carlo method. Source strength, attenuation and dead time for each detector are evaluated using limited experimental values by suitable optimization algorithms.
In Monte Carlo method, domain is first chosen i.e. solid angle subtended. There are three possible type of particle position with respect to the detector location. As shown in Figure 2.10, if the particle is in position S1, photon can enter through both the flat and curved surface of the detector. If the particle in position S2, photon can enter only through the curved surface and if it is in position in S3, photon can enter only through the flat surface.
d
Depending on the particle position, solid angle subtended is different. The angular extremities max, min, max, min and cri, which define the boundary of the surface as shown in the Figure 2.10 and arrived by the arguments as given by Beam et al. (1978).
Different photon histories where each photon defined by and in between the angular extremities are generated by using random generators (Beam et al., 1978). Depending on the exact orientation of the detector, all directions in the solid angle given by the
,combination are not equivalent. Appropriate statistical weights
,
according to the sampled direction is assigned to each photon sample. Beam et al., (1978) calculated individual directional weights
,
by geometrical arguments. So, the averaged value of solid angle is given by,
1
1 N
j j
N j
(2.3)Figure 2.10 Schematic diagram for relative positioning of source and detector
Penetration depth of the photon in the crystal depends on the point of entry and exit. There are four possible ways in which the photon can enter and pass through the crystal, viz., Lateral entrance, bottom exit
Lateral entrance, lateral exit Top entrance, bottom exit Top entrance, lateral exit
Figure 2.11 Four possible cases in which photon can travel through a cylindrical detector
Entry point is determined through angle, and using geometrical arguments penetration depth is arrived (Figure 2.11). If depth of penetration is greater than chord length of detector, it is not consider as a count. Only the photons having depth of penetration less than the length of detector i.e. photon which will absorb by the detector crystal is considered as a count.