- Email: [email protected]
Determination of Z coordinate from track width in MiniTPC
Nuclear Instruments and Methods in Physics Research A 851 (2017) 35–38
Contents lists available at ScienceDirect
Nuclear Instruments and Methods in Physics Research A journal homepage: www.elsevier.com/locate/nima
Determination of Z coordinate from track width in MiniTPC
MARK
⁎,1
D.C. Feng, M. Garcia-Sciveres, J.A. Kadyk , A. Wang Lawrence Berkeley National Laboratory, 1 Cyclotron Rd., Berkeley CA 94720, USA
A R T I C L E I N F O
A BS T RAC T
Keywords: Neutron recoil tracks Drift coordinate by diffusion GEMs Pixel chip TPC WIMP detection
A gas-filled Time Projection Chamber and a radioactive neutron source were used to study recoil tracks produced by scattering of the multi-MeV neutrons on gas nuclei. Since the event readout is triggered by the first electron arrival, the initial time and position in the electron drift direction are unknown, leading to a translational uncertainty in this direction. By using the track width due to electron diffusion, the coordinate along the drift direction was determined. With a suitable width calibration at a known drift distance, it is found that width measurements of the track can provide useful information for establishing a well-defined gas fiducial volume for the interactions. The coordinate determination is also sufficiently precise that it can be used as a third parameter in kinematic reconstruction of the neutron collision, providing improved knowledge of the neutron collision process. Despite a wide range of track ionization levels resulting from the broad spectrum of neutron energies and varying angles of scatter, the coordinate determination is not sensitive to the track ionization.
1. Introduction In a Time Projection Chamber (TPC) [1] with pixel chip readout, the transverse spatial coordinates, X and Y, of a particle scattering event or track can be easily measured, but a measurement of the longitudinal coordinate, Z, along the electron drift direction, cannot be made directly. More specifically, one can only measure the “relative” Z coordinates, i.e. the Z positions relative to the first pixel hit of the event, using the time measured for each hit and the known electron drift velocity in the TPC, 11.5 mm/µs for these tests [2]. It is therefore possible to create an accurate 3D image of the track as it passes through the TPC, up to an unknown translation along the Z axis, since the event starting time is unknown. This is a continuation of studies for the detection and measurement of recoil tracks in a gas medium, with the potential of detection and measurement of dark matter particles [3]. The investigation described here is to use the well-known process of electron diffusion to determine the absolute Z coordinates of particle tracks [4]. Specifically, we studied electron tracks created by nuclear recoils induced by collisions of fast neutrons with gas nuclei in the TPC. The electric field in the TPC causes the electron track to drift downward, and diffusion causes the track to grow wider as it drifts. The measured width of a track, as determined by the distribution of electrons produced on the track, scales as √Z due to diffusion [5], since the absolute Z coordinate is the same as the drift distance. In particular, the measured width of tracks is larger for those
⁎
1
produced nearer the top (larger Z) of the TPC than those nearer the bottom (smaller Z), due to the larger drift distance in the TPC. As discussed here, it appears that such an absolute Z determination is quite feasible and insensitive to the track ionization. Even though the Z measurement is limited to a precision much poorer than that of the X and Y pixel coordinates, it is still a potentially quite useful measurement. The advantages of obtaining the absolute Z with useful precision are clear: 1) this provides additional information for the kinematic reconstruction of an observed event, and 2) events can be restricted to a well-defined gas fiducial volume, so that the background and contamination arising from interactions outside of the gas fiducial volume become negligible. 2. Experimental setup and methods A simple sketch of our apparatus in shown in Fig. 1. Fast neutrons were obtained using a plutonium-beryllium (Pu/Be) neutron source and these were allowed to recoil in the TPC gas volume with nuclei of the gas constituents, 80% helium and 20% isobutane (iC4H10). The (Pu/Be) source had a neutron rate of about 104 per second, yielding an neutron recoil rate of several per minute in the gas fiducial volume. This gas mixture was chosen because of the several target nuclei of quite different masses, and for the excellent quenching properties of isobutane. Data collection and tests were all done at a gas pressure of
Correspondence to: Lawrence Berkeley National Laboratory, 50A-2158, Cyclotron Rd., Berkeley, CA 94720, USA. E-mail address: [email protected] (J.A. Kadyk). Alternate Address: 1060 Mariposa Ave., Berkeley, CA 94707.
http://dx.doi.org/10.1016/j.nima.2017.01.061 Received 17 October 2016; Received in revised form 21 January 2017; Accepted 26 January 2017 Available online 26 January 2017 0168-9002/ © 2017 Elsevier B.V. All rights reserved.
Nuclear Instruments and Methods in Physics Research A 851 (2017) 35–38
D.C. Feng et al.
Fig. 1. Diagram of the detector. This diagram shows the outer thin-walled aluminum containment vessel for gas mixture, and the TPC inside. A uniform electric field is established inside the TPC between the cathode drift mesh at the top and the doubleGEM at the bottom. Further details may be found in the text and references [3]. The three numbered stars indicate the locations where the neutron source was placed to create neutron collision tracks for data collection: ★1 above the TPC, ★2 below the TPC, and ★3 in the TPC mid-plane.
1.0 atm. Several thousand events of neutron recoil data were taken at each of the three ★ locations in Fig. 1, in order to gather data at differing recoil track directions and heights in the TPC. The TPC is made of a thin Kapton sheet formed into a cylinder with a diameter of 75 mm and a length of 120 mm. The top of the TPC is enclosed by a metallic cathode drift mesh and the bottom of the TPC by the double-GEM electron avalanche multiplier. There is a series of 20 narrow, circular and parallel, copper bands on the inner Kapton surface, spaced apart in Z by 5 mm. Applying a uniform potential gradient to the copper bands generated a uniform electric field of 300 V/cm in the TPC, which drifted electrons downward toward the double-GEM. A more detailed description of the apparatus can be found in the references [3]. Electrons in tracks formed by the recoil particles were multiplied by the double-GEM and measured by the FE-I4, a fine-resolution pixel chip developed for use in the ATLAS experiment at CERN. The pixel chip has a sensitive region of 20 mm×16.8 mm, respectively in X and Y, and contains 26,880 pixels in total, each pixel with dimensions 250 µm along X and 50 µm along Y. For each pixel a charge threshold requires at least 3000 electrons to register a “hit”, and the pulse height above this threshold was registered as the Time-over-Threshold, or ToT, which is a measure of the charge collected by each pixel hit. The avalanche gain of the double-GEM is about 8000 during these tests, and therefore most electron clusters on each track were recorded as one or more pixel hits [6]. The pixel chip also records the time of each hit in time samples according to a 12 MHz pixel readout clock speed, resulting in time bins of 0.083 µs. Using the clock speed and electron drift velocity, we calculated relative Z positions with a resolution of 0.95 mm. The track direction, track width, and average ToT were then determined from these measurements. For each recoil track, we performed a least-squares 3D line fit using all the hits associated with
Fig. 2. (a) 3D reconstruction of a nearly vertical scattered track, by a least-squares line fit. (b) Plot of the track width vs. segments along the track. Segments are measured by the distance, s, along the track, where we define s=0 as the smallest Z position of the hits on the track. The s coordinate increases in the direction of increasing Z from the beginning of the track at s=0.
the track. This provided the measured direction of the fitted track. The root mean square (RMS) distance of the hits to the fitted line then determined the RMS track width measurement. The line fit is found to be a good approximation to the actual track since the recoiling nuclei do not sustain much subsequent scattering. We also calculated the average ToT of all the hits on a track as a measure of the ionization density along the track. 3. Results We collected tracks with the source at location ★2 (as labeled in Fig. 1) to study the diffusion of vertical tracks. Fig. 2a shows one such vertically oriented recoil track reconstructed in 3D. This track points in an upward direction 14.8° from the vertical, and is about 80 mm long within the TPC fiducial volume. Each gray dot on the figure indicates the location of a single pixel hit, and a 3D line is fitted to these pixel hits. Fig. 2b shows the RMS track width as measured in 4 mm segments along the track length. The width for each 4 mm segment of the track is shown vs. s, which is the distance along the track, defining s=0 to be at the smallest Z position of the track. It can be seen that the track width increases with distance along the track, corresponding to larger drift distances, as expected from the √Z scaling behavior. 36
Nuclear Instruments and Methods in Physics Research A 851 (2017) 35–38
D.C. Feng et al.
width is determined primarily by diffusion due to drift, and that the scaling law √Z applies, the diffusion constant, or the mean width for tracks at Z=10 mm, would be 0.68*√(10/60) mm=0.28 mm. This is close to the value we expect from published data for diffusion at a 10 mm drift (~0.21 mm) [7], and is consistent with the precision of this analysis. It is usually important to know the confidence level with which events originated within the Z boundaries of the gas volume fiducial region instead of in outside material. To calculate this, we assume that the standard deviation of error on a measured width distribution remains the same (0.12 mm) at Z=10 mm as at Z=60 mm, that the mean width of tracks originating at Z=10 mm is the above calculated value of 0.28 mm, and that the width distribution can be approximated as nearly Gaussian. As one example, assume we are given a track whose minimum Z coordinate is measured as 10 mm. Then, the mean width of the track indicates that Z > 0 with a confidence level of 0.28/0.12 σ=2.3 σ. With this level of confidence, tracks seeming to originate from Z=10 mm can be trusted to have truly originated in the gas volume (Z > 0 mm) with 2.3 σ, or about a 95% confidence level. In this case, the fiducial length is slightly reduced by 10 mm from the TPC bottom, and would be reduced by a similar amount from the top. To calculate how much the fiducial volume is reduced on the bottom and top of the TPC, there must be a calibration of the track width at one or more known or estimated Z positions, such as in this case the one calibration point at Z=60 mm. For this example, the reduction in fiducial volume due to the restriction in Z is significant but not large compared to the TPC length of 120 mm. The precision in Z determination for purposes of kinematic fitting can be estimated by considering the case for an event at Z=60 mm, the center of the TPC. Assuming only that the track width W scales as √Z, then: W=A√Z, where A is a diffusion proportionality constant. Error propagation between the width and Z variables yield: log(W)=log(√Z) + log(A), dW/W=dZ/(2*Z), and dZ/Z=2*(dW/W). Taking the measured mean value of W from Fig. 4, and the above value of dW as the standard deviation on the mean for W, we obtain: dZ/Z=2*(0.12 mm/ 0.68 mm)=0.35. For horizontal tracks originating from Z =60 mm, this yields an estimated error on Z of 0.35*60 mm=21 mm. Improved measuring techniques, such as measurements of horizontal tracks at other Z values, such as Z=40 mm and Z=80 mm, should refine the precision of these distance determinations, and allow smaller volume cuts. It should be mentioned that there is some scattering of the recoil tracks, due to nuclear scatters of these slow tracks. A more accurate estimate of intrinsic track width measurement may be obtained by making RMS fits within finite segments of each track, then averaging the result. This would cause changes in track direction, e.g. due to scattering, to become less of a bias, resulting in a smaller measured track width, and a more precise result than fitting the entire track as a line fit. This refinement has not been attempted in this analysis.
Fig. 3. Scatter plot of average ToT vs. RMS track width for a data set of 8200 nearly horizontal recoil tracks. The neutron source is at position ★3. Each point represents one recoil track that drifted about 60 mm.
We then gathered data with the source at location ★3 to collect nearly horizontal tracks, originating near the TPC midplane. These tracks were required to have directions within 10° of the horizontal plane. Therefore, they should all have nearly equal drift distances of 60 mm. As a result, they should also have nearly the same diffusion broadening, except for statistical and systematic errors. There was a small fraction of events filtered out to remove those that could not be analyzed properly. For example, tracks with too few (under 100) or too many (over 20,000) hits, ones that were too short (under 10 mm), or those which failed the line fit were rejected from the sample. Originally, there was a concern that the variation of ionization density between tracks would significantly affect the track width determination, and this would prevent using width as a direct measure of diffusion and the drift distance. Fig. 3 displays the average ToT plotted vs. RMS track width for these nearly horizontal tracks. The figure shows that there is only a small correlation between the track width and average ToT, with a calculated correlation coefficient of 0.0081. The correction to the measured width of tracks due to the ToT ionization measurement is therefore small, and has been neglected in this simplified analysis. Since the width is determined by an initial width, followed by broadening due to diffusion, the Z coordinate is now determined within the precision of this method. The next plot, Fig. 4, shows a distribution of the widths of the nearly horizontal tracks. The track width distribution has a mean of 0.68 mm and a standard deviation of 0.12 mm, and resembles a Gaussian distribution except with a "tail" at smaller widths. This tail may be partly due to the small ToT-RMS width correlation. Assuming the
4. Discussion and conclusions It is shown that for tracks in a gas-filled TPC of 120 mm length, the measurement of electron drift distance, Z, can be measured by means of an RMS track width measurement, allowing absolute Z coordinate determination with useful precision. It appears that this technique, using the diffusion scaling law, √Z, does not have a large dependence upon the ionization density. A calibration of width uses horizontal tracks at a Z coordinate of 60 mm, or half the TPC length. The RMS width determination using this sample of tracks is approximately 0.68 mm, for the horizontal tracks measured with the source at this TPC midplane position. Restriction of events to be entirely inside the gas fiducial volume is feasible: scaling current results to a measurement at Z=10 mm gives an estimate of being inside the Z=0 mm TPC volume boundary of 2.3 σ, corresponding to a 95% confidence level. There is an approximate error in Z of 21 mm for a track originating at the TPC
Fig. 4. Width distribution for the dataset of horizontal tracks. The dataset contained 8200 tracks, with a mean width of 0.68 mm and a standard deviation of 0.12 mm. In the figure, each bin has a width interval of 0.01 mm.
37
Nuclear Instruments and Methods in Physics Research A 851 (2017) 35–38
D.C. Feng et al.
Department of Energy under Contract No. DE-AC02-05CH11231.
midplane. This is sufficiently precise that this knowledge of the Z coordinate should be useful in kinematic reconstruction. The present study is intended only as a demonstration of the capability of the technique described, and does not provide an optimization for best results. More precise Z determinations should be possible by making width calibration measurements at other values of Z, and by making the correction due to the small correlation between width and ToT. The foregoing analysis was based upon the sample of recoil events obtained with the source in the location ★3 of Fig. 1. This is the optimum location relevant to this analysis, by having nearly equal drift distances for track electrons. However, there are approximately equally large samples of recoil events at the locations ★1 and ★2, and one such event is shown in Fig. 2, but these are not relevant to the present analysis, which depends upon using a sample of tracks having nearly equal drift distances. We wish to thank Mayra Lopez-Thibodeaux for work at an early stage of program development, and instructions to one of the authors on use of these programs. We also thank the Lawrence Berkeley Laboratory Radiation Protection Group for supplying the neutron source used for all the tests. This work was supported by the Director, Office of Science, Office of High Energy Physics, of the U.S.
Authors All authors have contributed to research described, and have approved this article. Funding body and financial support LBNL. No involvement in project except for funding. References [1] D.R. Nygren, A Time Projection Chamber, Proceedings of the 1975 PEP Summer Study, LBL Berkeley, 1975. J. Marx, D. Nygren, The Time Projection Chamber, Phys. Today, Oct. 1978. [2] CERN 84-08 (1984), Fig. 77. The very small fraction of TMAE in these mixtures, 0.05%, is expected to have negligible effect upon the drift velocity. [3] NIMA 738 (2014) 111–118. NIMA 589 (2008) 173–184. [4] NIMA 789 (2015) 81–85. [5] For an elementary explanation of width due to diffusion, see CERN 84-08, A. Peisert, F. Sauli, equations (1)–(6). [6] NIMA 301 (1991) 202–214. See especially Fig. 11. [7] Y. Assran, A. Sharma, arXiv: 1110.6761, 2011.
38
Contents lists available at ScienceDirect
Nuclear Instruments and Methods in Physics Research A journal homepage: www.elsevier.com/locate/nima
Determination of Z coordinate from track width in MiniTPC
MARK
⁎,1
D.C. Feng, M. Garcia-Sciveres, J.A. Kadyk , A. Wang Lawrence Berkeley National Laboratory, 1 Cyclotron Rd., Berkeley CA 94720, USA
A R T I C L E I N F O
A BS T RAC T
Keywords: Neutron recoil tracks Drift coordinate by diffusion GEMs Pixel chip TPC WIMP detection
A gas-filled Time Projection Chamber and a radioactive neutron source were used to study recoil tracks produced by scattering of the multi-MeV neutrons on gas nuclei. Since the event readout is triggered by the first electron arrival, the initial time and position in the electron drift direction are unknown, leading to a translational uncertainty in this direction. By using the track width due to electron diffusion, the coordinate along the drift direction was determined. With a suitable width calibration at a known drift distance, it is found that width measurements of the track can provide useful information for establishing a well-defined gas fiducial volume for the interactions. The coordinate determination is also sufficiently precise that it can be used as a third parameter in kinematic reconstruction of the neutron collision, providing improved knowledge of the neutron collision process. Despite a wide range of track ionization levels resulting from the broad spectrum of neutron energies and varying angles of scatter, the coordinate determination is not sensitive to the track ionization.
1. Introduction In a Time Projection Chamber (TPC) [1] with pixel chip readout, the transverse spatial coordinates, X and Y, of a particle scattering event or track can be easily measured, but a measurement of the longitudinal coordinate, Z, along the electron drift direction, cannot be made directly. More specifically, one can only measure the “relative” Z coordinates, i.e. the Z positions relative to the first pixel hit of the event, using the time measured for each hit and the known electron drift velocity in the TPC, 11.5 mm/µs for these tests [2]. It is therefore possible to create an accurate 3D image of the track as it passes through the TPC, up to an unknown translation along the Z axis, since the event starting time is unknown. This is a continuation of studies for the detection and measurement of recoil tracks in a gas medium, with the potential of detection and measurement of dark matter particles [3]. The investigation described here is to use the well-known process of electron diffusion to determine the absolute Z coordinates of particle tracks [4]. Specifically, we studied electron tracks created by nuclear recoils induced by collisions of fast neutrons with gas nuclei in the TPC. The electric field in the TPC causes the electron track to drift downward, and diffusion causes the track to grow wider as it drifts. The measured width of a track, as determined by the distribution of electrons produced on the track, scales as √Z due to diffusion [5], since the absolute Z coordinate is the same as the drift distance. In particular, the measured width of tracks is larger for those
⁎
1
produced nearer the top (larger Z) of the TPC than those nearer the bottom (smaller Z), due to the larger drift distance in the TPC. As discussed here, it appears that such an absolute Z determination is quite feasible and insensitive to the track ionization. Even though the Z measurement is limited to a precision much poorer than that of the X and Y pixel coordinates, it is still a potentially quite useful measurement. The advantages of obtaining the absolute Z with useful precision are clear: 1) this provides additional information for the kinematic reconstruction of an observed event, and 2) events can be restricted to a well-defined gas fiducial volume, so that the background and contamination arising from interactions outside of the gas fiducial volume become negligible. 2. Experimental setup and methods A simple sketch of our apparatus in shown in Fig. 1. Fast neutrons were obtained using a plutonium-beryllium (Pu/Be) neutron source and these were allowed to recoil in the TPC gas volume with nuclei of the gas constituents, 80% helium and 20% isobutane (iC4H10). The (Pu/Be) source had a neutron rate of about 104 per second, yielding an neutron recoil rate of several per minute in the gas fiducial volume. This gas mixture was chosen because of the several target nuclei of quite different masses, and for the excellent quenching properties of isobutane. Data collection and tests were all done at a gas pressure of
Correspondence to: Lawrence Berkeley National Laboratory, 50A-2158, Cyclotron Rd., Berkeley, CA 94720, USA. E-mail address: [email protected] (J.A. Kadyk). Alternate Address: 1060 Mariposa Ave., Berkeley, CA 94707.
http://dx.doi.org/10.1016/j.nima.2017.01.061 Received 17 October 2016; Received in revised form 21 January 2017; Accepted 26 January 2017 Available online 26 January 2017 0168-9002/ © 2017 Elsevier B.V. All rights reserved.
Nuclear Instruments and Methods in Physics Research A 851 (2017) 35–38
D.C. Feng et al.
Fig. 1. Diagram of the detector. This diagram shows the outer thin-walled aluminum containment vessel for gas mixture, and the TPC inside. A uniform electric field is established inside the TPC between the cathode drift mesh at the top and the doubleGEM at the bottom. Further details may be found in the text and references [3]. The three numbered stars indicate the locations where the neutron source was placed to create neutron collision tracks for data collection: ★1 above the TPC, ★2 below the TPC, and ★3 in the TPC mid-plane.
1.0 atm. Several thousand events of neutron recoil data were taken at each of the three ★ locations in Fig. 1, in order to gather data at differing recoil track directions and heights in the TPC. The TPC is made of a thin Kapton sheet formed into a cylinder with a diameter of 75 mm and a length of 120 mm. The top of the TPC is enclosed by a metallic cathode drift mesh and the bottom of the TPC by the double-GEM electron avalanche multiplier. There is a series of 20 narrow, circular and parallel, copper bands on the inner Kapton surface, spaced apart in Z by 5 mm. Applying a uniform potential gradient to the copper bands generated a uniform electric field of 300 V/cm in the TPC, which drifted electrons downward toward the double-GEM. A more detailed description of the apparatus can be found in the references [3]. Electrons in tracks formed by the recoil particles were multiplied by the double-GEM and measured by the FE-I4, a fine-resolution pixel chip developed for use in the ATLAS experiment at CERN. The pixel chip has a sensitive region of 20 mm×16.8 mm, respectively in X and Y, and contains 26,880 pixels in total, each pixel with dimensions 250 µm along X and 50 µm along Y. For each pixel a charge threshold requires at least 3000 electrons to register a “hit”, and the pulse height above this threshold was registered as the Time-over-Threshold, or ToT, which is a measure of the charge collected by each pixel hit. The avalanche gain of the double-GEM is about 8000 during these tests, and therefore most electron clusters on each track were recorded as one or more pixel hits [6]. The pixel chip also records the time of each hit in time samples according to a 12 MHz pixel readout clock speed, resulting in time bins of 0.083 µs. Using the clock speed and electron drift velocity, we calculated relative Z positions with a resolution of 0.95 mm. The track direction, track width, and average ToT were then determined from these measurements. For each recoil track, we performed a least-squares 3D line fit using all the hits associated with
Fig. 2. (a) 3D reconstruction of a nearly vertical scattered track, by a least-squares line fit. (b) Plot of the track width vs. segments along the track. Segments are measured by the distance, s, along the track, where we define s=0 as the smallest Z position of the hits on the track. The s coordinate increases in the direction of increasing Z from the beginning of the track at s=0.
the track. This provided the measured direction of the fitted track. The root mean square (RMS) distance of the hits to the fitted line then determined the RMS track width measurement. The line fit is found to be a good approximation to the actual track since the recoiling nuclei do not sustain much subsequent scattering. We also calculated the average ToT of all the hits on a track as a measure of the ionization density along the track. 3. Results We collected tracks with the source at location ★2 (as labeled in Fig. 1) to study the diffusion of vertical tracks. Fig. 2a shows one such vertically oriented recoil track reconstructed in 3D. This track points in an upward direction 14.8° from the vertical, and is about 80 mm long within the TPC fiducial volume. Each gray dot on the figure indicates the location of a single pixel hit, and a 3D line is fitted to these pixel hits. Fig. 2b shows the RMS track width as measured in 4 mm segments along the track length. The width for each 4 mm segment of the track is shown vs. s, which is the distance along the track, defining s=0 to be at the smallest Z position of the track. It can be seen that the track width increases with distance along the track, corresponding to larger drift distances, as expected from the √Z scaling behavior. 36
Nuclear Instruments and Methods in Physics Research A 851 (2017) 35–38
D.C. Feng et al.
width is determined primarily by diffusion due to drift, and that the scaling law √Z applies, the diffusion constant, or the mean width for tracks at Z=10 mm, would be 0.68*√(10/60) mm=0.28 mm. This is close to the value we expect from published data for diffusion at a 10 mm drift (~0.21 mm) [7], and is consistent with the precision of this analysis. It is usually important to know the confidence level with which events originated within the Z boundaries of the gas volume fiducial region instead of in outside material. To calculate this, we assume that the standard deviation of error on a measured width distribution remains the same (0.12 mm) at Z=10 mm as at Z=60 mm, that the mean width of tracks originating at Z=10 mm is the above calculated value of 0.28 mm, and that the width distribution can be approximated as nearly Gaussian. As one example, assume we are given a track whose minimum Z coordinate is measured as 10 mm. Then, the mean width of the track indicates that Z > 0 with a confidence level of 0.28/0.12 σ=2.3 σ. With this level of confidence, tracks seeming to originate from Z=10 mm can be trusted to have truly originated in the gas volume (Z > 0 mm) with 2.3 σ, or about a 95% confidence level. In this case, the fiducial length is slightly reduced by 10 mm from the TPC bottom, and would be reduced by a similar amount from the top. To calculate how much the fiducial volume is reduced on the bottom and top of the TPC, there must be a calibration of the track width at one or more known or estimated Z positions, such as in this case the one calibration point at Z=60 mm. For this example, the reduction in fiducial volume due to the restriction in Z is significant but not large compared to the TPC length of 120 mm. The precision in Z determination for purposes of kinematic fitting can be estimated by considering the case for an event at Z=60 mm, the center of the TPC. Assuming only that the track width W scales as √Z, then: W=A√Z, where A is a diffusion proportionality constant. Error propagation between the width and Z variables yield: log(W)=log(√Z) + log(A), dW/W=dZ/(2*Z), and dZ/Z=2*(dW/W). Taking the measured mean value of W from Fig. 4, and the above value of dW as the standard deviation on the mean for W, we obtain: dZ/Z=2*(0.12 mm/ 0.68 mm)=0.35. For horizontal tracks originating from Z =60 mm, this yields an estimated error on Z of 0.35*60 mm=21 mm. Improved measuring techniques, such as measurements of horizontal tracks at other Z values, such as Z=40 mm and Z=80 mm, should refine the precision of these distance determinations, and allow smaller volume cuts. It should be mentioned that there is some scattering of the recoil tracks, due to nuclear scatters of these slow tracks. A more accurate estimate of intrinsic track width measurement may be obtained by making RMS fits within finite segments of each track, then averaging the result. This would cause changes in track direction, e.g. due to scattering, to become less of a bias, resulting in a smaller measured track width, and a more precise result than fitting the entire track as a line fit. This refinement has not been attempted in this analysis.
Fig. 3. Scatter plot of average ToT vs. RMS track width for a data set of 8200 nearly horizontal recoil tracks. The neutron source is at position ★3. Each point represents one recoil track that drifted about 60 mm.
We then gathered data with the source at location ★3 to collect nearly horizontal tracks, originating near the TPC midplane. These tracks were required to have directions within 10° of the horizontal plane. Therefore, they should all have nearly equal drift distances of 60 mm. As a result, they should also have nearly the same diffusion broadening, except for statistical and systematic errors. There was a small fraction of events filtered out to remove those that could not be analyzed properly. For example, tracks with too few (under 100) or too many (over 20,000) hits, ones that were too short (under 10 mm), or those which failed the line fit were rejected from the sample. Originally, there was a concern that the variation of ionization density between tracks would significantly affect the track width determination, and this would prevent using width as a direct measure of diffusion and the drift distance. Fig. 3 displays the average ToT plotted vs. RMS track width for these nearly horizontal tracks. The figure shows that there is only a small correlation between the track width and average ToT, with a calculated correlation coefficient of 0.0081. The correction to the measured width of tracks due to the ToT ionization measurement is therefore small, and has been neglected in this simplified analysis. Since the width is determined by an initial width, followed by broadening due to diffusion, the Z coordinate is now determined within the precision of this method. The next plot, Fig. 4, shows a distribution of the widths of the nearly horizontal tracks. The track width distribution has a mean of 0.68 mm and a standard deviation of 0.12 mm, and resembles a Gaussian distribution except with a "tail" at smaller widths. This tail may be partly due to the small ToT-RMS width correlation. Assuming the
4. Discussion and conclusions It is shown that for tracks in a gas-filled TPC of 120 mm length, the measurement of electron drift distance, Z, can be measured by means of an RMS track width measurement, allowing absolute Z coordinate determination with useful precision. It appears that this technique, using the diffusion scaling law, √Z, does not have a large dependence upon the ionization density. A calibration of width uses horizontal tracks at a Z coordinate of 60 mm, or half the TPC length. The RMS width determination using this sample of tracks is approximately 0.68 mm, for the horizontal tracks measured with the source at this TPC midplane position. Restriction of events to be entirely inside the gas fiducial volume is feasible: scaling current results to a measurement at Z=10 mm gives an estimate of being inside the Z=0 mm TPC volume boundary of 2.3 σ, corresponding to a 95% confidence level. There is an approximate error in Z of 21 mm for a track originating at the TPC
Fig. 4. Width distribution for the dataset of horizontal tracks. The dataset contained 8200 tracks, with a mean width of 0.68 mm and a standard deviation of 0.12 mm. In the figure, each bin has a width interval of 0.01 mm.
37
Nuclear Instruments and Methods in Physics Research A 851 (2017) 35–38
D.C. Feng et al.
Department of Energy under Contract No. DE-AC02-05CH11231.
midplane. This is sufficiently precise that this knowledge of the Z coordinate should be useful in kinematic reconstruction. The present study is intended only as a demonstration of the capability of the technique described, and does not provide an optimization for best results. More precise Z determinations should be possible by making width calibration measurements at other values of Z, and by making the correction due to the small correlation between width and ToT. The foregoing analysis was based upon the sample of recoil events obtained with the source in the location ★3 of Fig. 1. This is the optimum location relevant to this analysis, by having nearly equal drift distances for track electrons. However, there are approximately equally large samples of recoil events at the locations ★1 and ★2, and one such event is shown in Fig. 2, but these are not relevant to the present analysis, which depends upon using a sample of tracks having nearly equal drift distances. We wish to thank Mayra Lopez-Thibodeaux for work at an early stage of program development, and instructions to one of the authors on use of these programs. We also thank the Lawrence Berkeley Laboratory Radiation Protection Group for supplying the neutron source used for all the tests. This work was supported by the Director, Office of Science, Office of High Energy Physics, of the U.S.
Authors All authors have contributed to research described, and have approved this article. Funding body and financial support LBNL. No involvement in project except for funding. References [1] D.R. Nygren, A Time Projection Chamber, Proceedings of the 1975 PEP Summer Study, LBL Berkeley, 1975. J. Marx, D. Nygren, The Time Projection Chamber, Phys. Today, Oct. 1978. [2] CERN 84-08 (1984), Fig. 77. The very small fraction of TMAE in these mixtures, 0.05%, is expected to have negligible effect upon the drift velocity. [3] NIMA 738 (2014) 111–118. NIMA 589 (2008) 173–184. [4] NIMA 789 (2015) 81–85. [5] For an elementary explanation of width due to diffusion, see CERN 84-08, A. Peisert, F. Sauli, equations (1)–(6). [6] NIMA 301 (1991) 202–214. See especially Fig. 11. [7] Y. Assran, A. Sharma, arXiv: 1110.6761, 2011.
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