Position Sensitive Twin Ionization Chamber for Nuclear Fission Investigations

Abstract. In this work we report the recent achievements in design of twin back-to-back ionization chamber (TIC) for fission fragment (FF) mass, kinetic energy and FF orientation. Correlated FF kinetic energies, their masses and the angle of the fission axes in 3D Cartesian coordinates can be determined from analysis of the heights and shapes of the pulses induced by the fission fragments on the anodes of TIC. Anodes of TIC were designed as consisting of isolated Δ-shaped strips connected to nodes of the chain filter, made of serially connected twoport networks. Double charge division method was implemented by digitizing four waveforms at the endpoints of the chain filters. It was shown how the fission fragments emission point on the target plane may be determined using the measured data. Position sensitive neutron induced fission detector for neutron imaging applications with both thermal and low energy neutrons was found as another possible implementation of the designed TIC. Preliminary measurements with the thermal neutron induced fission were done with RC chain filters and the results were demonstrated.


Introduction
Nuclear fission model and prompt fission neutron emission (PFN) was first developed by N. Bohr and J. Wheeler, where nuclei considered as a drop of charged liquid, which surface constantly distorted in competition between attractive nuclear and repulsive Coulomb forces.Rarely large distortion brought the nuclear into the configuration, where repulsion could not be compensated by nuclear force and the system split, sometimes after neutron emission.In this case the neutrons, called scission neutrons in order to distinguish them from the PFN, which are emitted from the fully accelerated fission fragments.The configuration of nuclear shape just before split can be monitored experimentally by measurement of fission fragment (FF) kinetic energy release along with PFN velocity and the angle between fission axis and PFN measured in single fission event.In new experimental approach developed in ref. [1] authors investigated PFN emission in spontaneous fission of 252 Cf using twin Frisch-grid ionization chamber (TIC) for FF kinetic energies and PFN emission angle along with PFN velocity measurement with help of liquid scintillator (NE213 or equivalent liquid) based neutron detector (ND).The authors demonstrated a power and high capacity of the new approach, which was further elaborated by replacing the traditional analog electronics by modern digital pulse processing (DPP) described in ref. [2].The PFN detection efficiency of the method was limited by use only two fast neutron detectors, allocated along the TIC axis, because of the FF angle in TIC could be measured in respect to the certain axis.If the PFN detector allocated along this axis, then the measured angle was the same as between FF and PFN emission.Therefore the next modification of the method was intended to measure correlated FFs angles in respect to three axes of 3D Cartesian coordinate frame in the event by event basis.If the PFN detectors allocation in the same Cartesian frame was fixed and well known, then the angle between FF and PFN emission could be evaluated for each fission event.It should be noticed that two correlated FF was emitted along the straight line called fission axis for the considered fission event.That means that for each fission event the coordinates of two points on the fission axis could be measured refs [2,3].This gives the possibility to evaluate the 2D coordinates of the crossing point of the fission target plane with fission axis -neutron capture location.The modification was expected to improve the quality of experiments with targets like 239 Pu, 235 U, 237 Np in resonance neutron induced fission.In addition the slight modification of the developed 2D coordinate readout principle expected became very competitive solution for the neutron imaging, tomography and similar applications.

Ramo-Shokley Theorem and Charge Division
Using the Ramo-Shokley theorem (see ref. [4]) calculation of so called weighting potential in 3D Cartesian coordinate system was done.According to the theorem condition the weighting potential in the TIC volume was calculated for one Δ-electrode potential raised to 1, leaving other electrodes grounded.If the strips operated at positive potential relative to the cathode surface, then ionization electrons would be attracted along the real field lines (calculated for homogeneous electric field between anode-cathode).From the calculated weighting potential F(x, y, z) the slices F(x, y=const, z) were derived and plotted in Fig. 2 to demonstrate the charge division along the Y-coordinate of the anode plain.Full scale of X, Y, Z -coordinates was 400, 300, 300 units respectively.It should be noticed that weighting potential almost has zero values everywhere except the close vicinity of the anode plane.If the cathode-anode distance was chosen large to keep the FFs stopping far enough from the anode plane, then there was no need in Frisch-grid as screening electrode.From the Y-dependence of weighting potentials the linear behaviour of the charge division between complementary Δ-electrodes was concluded.This fact was utilized to evaluate the Y-coordinate value from the induced signals on the anode.The charge induced on the Δelectrode was calculated according to Ramo-Shockley theorem as: where ∆F is the difference of weighting potentials between the point of charged particle q origin and the point where the charged particle was collected at the anode surface and Q is the induced charge.The FFs create ionisation electrons along their deceleration path in the TIC working gas.In description of pulse formation in TIC the charge "centre of gravity" considered as a good measure of FF coordinate.Therefore in this paper all calculation of FF coordinates referred to that value, calculated according to the formula: ( where integration was done along the FF deceleration path, ) (x  is the density distribution of ionization electrons along the FF deceleration path and Q f is the full charge of ionization electrons.

Charge Division on the Chain Filter
The position information along the X-coordinate was obtained by two methods: the charge attenuation and the pulse delay.Both methods based on the charge split at the node of chain filter.Chain filter was created by serially connected two-port networks created by resistor R, inductance L and capacitance C of Δ-electrode as shown in Fig. 3. Induced charge splits into the respective inputs of pair of symmetric two-port networks.If the chain filter ends loaded with wave impedance, then the charge splits into two equal portions between two ends of chain filter.The operational calculus is conventional method to study of signal propagation along the serially connected two port networks (chain filter).Circuit diagram of the chain filter made of passive electrical components depicted in Fig. 3 Laplace transform could be found using transform tables [5]: Eq. 4 describes propagation of the unit step signal over chain filter made of inductance and capacitance (resistance is very small).In case when the resistance could not be neglected, then the result is as follows: .
Eq. 5 describes propagation of the unit step signal over chain filter made of resistance and capacitance (inductance very small).The wave impedance and the speed of signal propagation given by the following formulas for both cases, considered above: It should be noticed that in case of resistive chain filter the pulse height of the unit step attenuated exponentially, passing the chain filter.

Numerical Simulations
The dependence of output pulse height on the sequential numbers of two-port networks, composing the chain filter, consisting of 16 two-port networks plotted in Fig. 4. The calculation was done using digital RC-filter representing two-port network.The attenuation of the unit step signal height by factor exp(-m/T) on passing sequentially the m two-port networks was calculated and plotted on the left of Fig. 5 and T value was found by fitting.The T parameter could be used to correct the attenuation of total charge induced on the strips.The coordinate m of the charge "centre of gravity" were evaluated from the simulated pulses using the following formula: where A and B were the pulse heights calculated for two-port network with sequential number m and 16-m respectively.Result demonstrated almost perfect linear dependence on the network number (left graph on Fig. 5).Another way to determine the coordinate m was connected to measurement of delay between unit step signal and its response at the ends of two port networks as demonstrated in the right plot of Fig. 4.

Experimental Measurements
Experiments were performed with chamber with anode of rectangular shape made of 16 strips each consisted of 2 Δ-electrodes as shown in Fig. 6.After amplification the signals were recorded by four WFD and collected on PC memory for further off-line data analysis.There were four waveforms recorded for each fission event, which were used for FF charge "centre of gravity" evaluation.The organization of the measurement apparatus provided the possibility to made measurement of each coordinates in (8) , and two different independent ways.This was used to evaluate the precision of the coordinate measurement as demonstrated in the Fig. 7.For example coordinate X was measured as: , where A, B, C, D were the pulse heights, obtained from the correlated waveforms, and recorded for the same fission event.These measured coordinates were used to made 2D plot P(x, y) in coordinates x, y calculated for each fission event using formulas: The function P(x, y) was plotted on the left of Fig. 7 and demonstrates scattering of the points due to random errors.The function G(x, y) was constructed in the way similar to P(x, y) using the following formulas: From the values of Y 1 ,Y 2 coordinates of 2D function G(x, y) were constructed using the following formulas: It should be noticed that measurements was done with one of the TIC chambers due to target backing was tick enough to absorb the complementary FF.That is why in performed experiment fissile nucleus position could not be measured directly.The kinetic energy release of FF was analyzed using all four waveforms, recorded in event by event basis.These waveforms first were corrected for attenuation in the chain filter as was described above.The corrected waveforms were unfolded to single one taking into account that sampling of the four signals actually was made sequentially with 1 GHz frequency.That means that first signal sampled at first rising edge of 1 GHz oscillator, second signal at the next edge and so on.The unfolded signal was used for evaluation of the Z-coordinate of FF charge "centre of gravity" and the angles between FF and Cartesian frame axes as it was described in refs.[2,3,7].Using coordinates, kinetic energy, and the angle measured for one of the FF the coordinates, the similar parameters for correlated FFs were evaluated neglecting the target thickness.Correlated FF kinetic energy was calculated using total kinetic energy value for 235 U(n th ,f) reaction known from the literature [6].The location of the point on the target plane then was evaluated as the crossing point of straight line drawn between two "center of gravity" points of two correlated FF.The evaluated accuracy of the coordinates was found to be better than 0.2 mm.

Conclusions
Theoretical and experimental investigation of signal propagation trough the chain filter made of serially connected two-port networks was performed with objective of position sensitive ionization chamber design for PFN emission investigation with arbitrary allocated fast ND.Relations between 2D Cartesian coordinate (X,Y) information and response of chain filter was found and investigated by digital simulation.It was shown that coordinate information can be obtained by both the double charge division and time delay method.Implementing both methods provided better accuracy in coordinate measurement.Dependence of pulse height data on coordinate was investigated for resistive chain filter.The procedure of pulse Color Scale Title height data correction was developed.Measurement of neutron imaging with U-235 target was done to demonstrate the quality of the double charge division method for position sensitive ionization chamber.Good position resolution was demonstrated: 0.7 mm for X and 0.5 mm for Y coordinates.New design for He-3 imaging proportional chamber with double charge division method could utilize the double charge division method to improve the coordinate resolution in comparison with double delay line readout system.Digitization electronics was implemented for data acquisition system, and the data analysis software was developed and tested in experiments.The data analysis was done using DPP algorithms developed by authors in previous publications in Ref. [7] as the recursive procedures.

Fig. 1 .
Fig. 1.The allocation of the electrodes for one of the TIC.

Fig. 4 .
Fig. 4. step signal attenuation after passing m times the two-port networks (on the left) and the pulses obtained after differentiating the unit step signals (on the right).

Fig. 5 .
Fig. 5. Attenuation of unity sep signal height after passing number m of two-port networks (on the left) and position evaluated from simulated data (on the right).

Fig. 6 .
Fig. 6.Sketch of data readout system used in the experiment.

Fig. 7 .Fig. 8 .
Fig. 7. Two dimensional plots demonstrating the scattering of measured data in respect to average values for X and Y coordinates in the anode plain.