Aug 12, 1998 - GLAST Silicon Tracker Prototype. Simulations and Beam Test Results. B. B. Jones and W. F. Tompkins. Received. ; accepted. Draft: August 12 ...
GLAST Silicon Tracker Prototype
Simulations and Beam Test Results B. B. Jones and W. F. Tompkins Received
;
accepted
Draft: August 12, 1998
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ABSTRACT The proposed -ray telescope GLAST will provide important new observations in the energy range from 20 MeV to 300 GeV. The October 1997 test of the GLAST science prototype instrument in a -ray beam at SLAC allowed a comparison of beam test data with Monte Carlo simulations. Monte Carlo and beam test events were reconstructed with a Kalman lter, and the performance of the instrument was characterized. The Monte Carlo simulations accurately reproduced the instrument point-spread function beyond the 95% containment limit.
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1. Introduction The success of the EGRET -ray telescope has answered many questions, but it has also given rise to new ones. The bounty of unidenti ed EGRET sources undoubtably holds the key to understanding a wide variety of astrophysical systems. Several of these sources at low Galactic latitude are likely to be Geminga-like pulsars (Yadigaroglu & Romani 1995; Merck et al. 1996; Pohl et al. 1997). High-latitude sources may be unobserved AGN, or & Thompson may be a new class of sources not yet associated with -ray emission (Ozel 1996). Furthermore, EGRET has positively identi ed many -ray sources that deserve further study. While a number of -ray pulsars have been extensively studied (Fierro et al. 1995; Nolan et al. 1996), additional high-quality -ray data would discriminate between competing models of energy-generation mechanisms (Harding 1981; Cheng et al. 1986; Romani & Yadigaroglu 1995). Multiwavelength campaigns to simultaneously observe AGN from radio wavelengths to -rays have become an important tool in understanding energy generation in these distant yet powerful galaxies (Hartman et al. 1996; von Montigny et al. 1997). The recent discoveries of optical counterparts to -ray bursts (Costa et al. 1997) underscores the need for a large eld-of-view, high-energy -ray detector. In order to address these issues, we require a -ray telescope with a large e ective area, a narrow point-spread function, and good energy and timing resolution. A proposed future telescope to that end is GLAST , the Gamma-ray Large Area Space Telescope. GLAST will be based on solid-state silicon strip detector technology to provide high-quality e?e+ tracks from pair conversion events. These events can be reconstructed to give good directional information about the incident -ray. A calorimeter will provide energy information and possibly some directional information as well (Bloom 1996; Bloom et al. 1998).
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2. Beam Test In order to demonstrate the feasibility of such a project, as well as to con rm the simulations of the capabilities of the instrument, a science prototype was constructed at the University of California, Santa Cruz, the Naval Research Laboratory, and Goddard Space Flight Center. It was tested in the parasitic electron beam at the Stanford Linear Accelerator Center (SLAC) in October of 1997 (Ritz et al. in preparation). -Ray reconstruction software had been developed and tested with Monte Carlo simulations, and then was used to analyze the experimental results. Comparison of the actual beam test results with simulation con rmed that the simulations represent an accurate model of the beam test instrument, and by extension, of the baseline GLAST design.
2.1. The SLAC e? Beam The October 1997 beam test was conducted in End Station A at the Stanford Linear Accelerator Center. The nal beam as delivered to End Station A consisted of nearly monoenergetic bunches of electrons. The electron energy was tunable from approximately 5 GeV to approximately 40 GeV. The number of electrons per bunch was tunable over a wide range from less than one to many tens of electrons. To obtain -rays, a 3.5% X0 Cu foil radiator was inserted in the beam path. A large magnet steered the electrons into a hodoscopic calorimeter, while allowing the bremsstrahlung photons to continue directly into the prototype instrument. The energy of the electrons was measured to an accuracy of about 250 MeV, resulting in an energy-tagged photon beam (Cavalli-Sforza et al. 1993; Engovatov et al. 1997).
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2.2. The Prototype Instrument The beam test instrument, fully described elsewhere (Ritz et al. in preparation), is divided into three parts. The tracker consisted of 6 planes of silicon strip detectors, for precision measurement of the e?e+ tracks. The calorimeter was composed of segmented logs of CsI to measure deposited energy. It was composed of 8 layers of 6 logs, each 3 cm by 3 cm by 28 cm? with each layer in an alternating orientation, for a total depth of 13 radiation lengths. Thirty-two logs were made of CsI, with photodiodes at both ends to allow di erencing for longitudinal localization of energy deposition. The other 16 logs were made of Cu with holes bored into the material to simulate the equivalent number of radiation lengths of CsI. The anti-coincidence detector (ACD) was a set of plastic scintillators read out to photodiodes via wave-shifting bers. The ACD was segmented into tiles to allow localization of vetoing particles for use in backsplash studies. Each of these three components was connected to the data acquisition system of End Station A (Anthony & Szalata 1996). This work concentrates on data obtained from the silicon strip tracker. Competing physical e ects lead to the adoption of a number of tracker design con gurations. Multiple scattering of the e?e+ pair is the dominant source of error in reconstructing the incident angle of low-energy -rays. Multiple scattering refers to the process by which an electron passing through a material is de ected by many small scatters; it is generally inversely proportional to the electron energy (Barnett et al. 1996). However, at high energies the granularity of the strip pitch limits the resolution of the angle estimations. These two competing e ects make two parameters relevant to the design of a silicon-strip -ray telescope: the ratio of the strip pitch to the gap between planes, and the amount of radiator inserted between planes to facilitate conversions. Reducing the pitch-to-gap ratio improves the resolution of the instrument at high energies at the expense of either increasing the
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number of channels|corresponding to greater instrument complexity and power usage|or of increasing the spacing, thereby reducing the eld of view. Reducing the amount of radiating foil between planes decreases the amount of multiple scattering that each electron experiences, at the expense of reduced detection eciency. In order to explore this two-dimensional parameter space, the beam test instrument was built with adjustable spacing between planes, and with adjustable lead radiating foils between planes. Each of the six cards built for the instrument had two silicon-strip detectors (SSDs) attached to it; one with strips in the x direction and one with strips in the y direction. For consistency with GLAST documentation, a single detector in either direction will be referred to as a layer, while an x-y pair of detectors will be referred to as a plane. The test box was built with ten slots on 3 cm centers to accommodate the cards, allowing us to vary the pitch-to-gap ratio by putting the cards in di erent slots. The beam test SSDs were 5 cm by 5 cm square, with a strip pitch of 236 m and a thickness of 500 m. Each SSD had 192 instrumented strips, corresponding to 6 readout chips responsible for 32 strips each, and a total instrumented area of 4.6 cm by 5 cm. In addition, each slot could accommodate a radiator card, a special card with no SSDs, but instead with a thickness of lead (Pb) foil. Radiator cards were prepared with approximately 2% X0, 4% X0, and 6% X0 to allow us to vary the total radiator in the instrument.
2.3. Data Simulations before the beam test (Jones & Tompkins 1997) suggested two instrument con gurations that were adopted for study. The rst, so-called \pancake" mode, consisted of 6 planes of silicon, each containing an x and y layer, separated by 3 cm. This relatively
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compact con guration maximized the number of pair electrons contained within the tracker. However, at high energies when multiple scattering is small, the squat aspect ratio of this con guration accentuated the measurement error. The second mode, called \stretch," placed the planes as far apart as experimental conditions would allow. The rst ve planes were spaced 6 cm apart, and the last one was at 3 cm. This con guration allowed more low-energy pairs to escape the tracker, but minimized measurement error for the high-energy pairs. Data was taken in the stretch con guration with 2% X0 , 4% X0 , and 6% X0 radiators, as well as with the radiator cards removed. (\0% X0 ") In the pancake con guration, data was taken with no radiators, 2% X0, and 4% X0 . There was not enough time to take 6% X0 data in pancake con guration. All together, over 100 runs of -ray data were taken, with approximately 375,000 good -ray events after all cuts. More events (over 100,000) were measured in stretch con guration with 6% radiators than in any other con guration due to the high conversion probability in the thick radiators. The fewest events ( 20; 000) were measured in stretch con guration with no Pb radiators; nevertheless, there were still sucient statistics to make good measurements of the distribution widths.
3. Simulations Simulations of the GLAST instrument have been successfully done using computer code called glastsim. The code is based on gismo, a toolbox of routines that simulates the interaction physics for a large number of particles with a large number of materials (Atwood 1992). These particles and their interactions are taken from EGS, a database established
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by the particle physics community for the simulation of high-energy physics experiments (Nelson et al. 1985). For the purposes of the science prototype beam test, we further modi ed glastsim to simulate the prototype instrument that we would actually be using. In the interest of realism, as much of the experimental apparatus was included in the simulation as possible, including the process by which the -rays were produced. Simulated electrons were generated incident on a 3.5% Cu radiator, and allowed to bremsstrahlung according to the interaction cross-section. A magnetic eld swept the electrons aside, allowing the bremsstrahlung -rays to continue into the simulated instrument. Once the -ray entered the silicon tracker, it was allowed to pair produce using the standard EGS -ray interactor. The standard interactor has a very accurate representation of the pair-conversion cross section as a function of the energy split between the electron and positron, but does not accurately model the QED opening angle distribution. For most instrument studies, this e ect is not important. For a small number of simulations, the full di erential interaction cross-section for unpolarized photons was used (Yadigaroglu 1997). Upon exiting (or missing) the tracker, the resulting particles were collected in a CsI calorimeter. The Monte Carlo calorimeter consisted of 8 layers of 8 CsI logs, each 3 cm by 3 cm, identical to the prototype calorimeter. When the Monte Carlo data was read into the analysis code, energy deposition into logs that were not instrumented was ignored. Once the -ray generation mechanism was veri ed, some simpli cations were made to reduce the computer time required for the simulations. Since only a small number of the electrons incident on the Cu foil converted to -rays, it was signi cantly faster to simply inject a bremsstrahlung spectrum of -rays directly. Tracking the particle shower in simulations of the calorimeter is complicated and thus quite slow, so some simulations were done with monoenergetic incident -rays, without a calorimeter.
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4. Analysis
-Rays
that pair produce o er an opportunity for detection. By tracking the resulting e+ e? pair, we can estimate the incident -ray energy and direction. The reconstructed energy will be the sum of the e+ and e? energies, corrected for energy loss in the instrument, and the incident direction is the energy-weighted average of the e+ and e? directions. The problem of establishing the most likely electron tracks falls naturally into two steps: nding and tting. The rst step consists of choosing which hits in the tracker are part of the track in question. Designing good algorithms to do this is an art; in fact, it is similar in some ways to the pattern recognition problems being worked on by computer scientists. The second step consists of making the best estimate of the track of the electron that caused those hits. The latter is a science|an optimization problem|and is by far the more tractable problem.
4.1. Track Reconstruction Given a set of strip addresses which have been hit, we must reconstruct the electron tracks and determine the parameters of the incident -ray. There may be noise hits, spurious tracks, missing hits, or ambiguous tracks. We are limited by measurement error, and by energy-dependent multiple scatter. Even if we have two well-de ned tracks, we don't necessarily know the energy in each electron, only the combined energy deposited in the calorimeter. Furthermore, the x and y projections of the instrument are read out separately. Given a track in the x projection, the question of which y track corresponds to it is ambiguous. Clearly, a good method of nding and tting electron tracks will be critical. The Kalman lter is the optimal method for tting particle tracks (Kalman 1960). A practical implementation has been developed by Fruhwirth (1987). Two e ects hinder our
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e orts to accurately reconstruct the particle tracks, multiple scattering of the electrons (e+ and e? will be referred to collectively as \electrons"), and measurement error. The lter must balance the competing e ects of multiple scattering and measurement error. If the measurement error were negligible compared to the multiple scattering, as expected at low energies, the lter would simply \connect the dots," making a track from one hit to the next. Most of the information about the -ray direction would come from the rst two hits, where the cumulative e ects of multiple scattering are the least. However, if the measurement error is signi cant and multiple scattering is negligible (as it will be for high energy photons), all hits have information, and we should essentially t a straight line to the hits. The Kalman lter balances these two limits properly in the intermediary energy regime, and thus earns its title as the optimal linear lter; in the limit that all errors and multiple scattering are Gaussian, it is the optimal lter. Track nding is a more subjective problem. The identi cation of which hits belong to a track is a pattern recognition problem which does not admit an analytic solution. The basic algorithm we have adopted is based on the ltering procedure described above. At each plane, we use a Kalman lter to predict the most likely location of the hit. We then assume, in most cases, that the nearest hit to that predicted location is the one which belongs to the track. This simple criterion is complicated by caveats that allow for tracks leaving the tracker and for tracks sharing the same hit.
4.2. Alignment The position of each of the tracker planes was not measured prior to the beam test, but rather was determined by an examination of high energy tracks. These straight tracks were t with a line in each projection, and the median of the residuals for a given plane was taken to be the o set of that plane. In order to avoid aliasing e ects, a small amount
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of random noise was added to the strip positions before the line ts. This tting procedure was then repeated (using the corrected positions), and iterated until the measured positions converged. The results indicate that the tracker was very nearly aligned already, with the largest o set being 250 m. This alignment procedure measured the strip positions to about 50 m. The rotational orientation of the tracker planes was checked via the same method, and was found to be consistent with no rotational mis-alignment.
4.3. Data Selection The SLAC main electron beam runs nominally at 120 Hz. The state of the beam test instrument, including all strips hit, all energy deposited in the calorimeter, and all ACD tiles hit was read out for each beam spill. With an average of one electron per pulse, approximately 30% of spills had no electrons in them at all. Spills with one or more electrons shed bremsstrahlung photons with a probability dependent on the thickness of the Cu radiator foil|usually 3.5%. Therefore only a fraction of the 2:1 108 triggers recorded on tape were useful. A ltering program (not to be confused with Kalman ltering) was developed to extract the useful triggers. The criteria for accepting a trigger as a useful event was the detection of hits in three successive tracker planes, or of more than 6 MeV for low gain or 160 MeV for high gain in the calorimeter. These criteria were adopted so as to be sure to accept any particle that passed through the tracker, whether or not it hit the calorimeter, as well as any event that did not interact with the tracker, such as a
-ray that did not convert until it entered the calorimeter. The three-in-a-row requirement for the tracker was designed to ensure that random noise hits in the tracker would not pass the acceptance criteria. When the Cu foils were in place to produce -rays from the main electron beam, approximately 20% of the triggers were accepted. When the foil was
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removed, and the electron beam was directly incident on the instrument, nearly all the triggers were retained. These \useful events" were then analyzed by the reconstruction software. Many of them had no interactions in the calorimeter and were thus thrown away. In addition, any event with one or fewer hits in either projection was thrown away. The remaining events were reconstructed, but not all of these were satisfactory to be included in the analysis. The rst requirement was that the hodoscopic calorimeter reported only one electron in the spill. The presence of multiple beam electrons in the spill greatly increases the chance of multiple bremsstrahlung -rays entering the tracker at the same time. Second, each anti-coincidence tile was required to have less than 1/4 the energy of a minimum ionizing particle (MIP). While the ACD is designed to detect charged particles, it represents 0.5% X0 of material, which can cause -rays to pair convert. If a -ray pair converts in an ACD tile, each electron will deposit 1 MIP, times the fraction of the tile through which the electron passes. For example, if the -ray converted halfway through the tile, then the two electrons would deposit 2 (1=2 1MIP) = 1 MIP. The 1/4 MIP threshold will therefore reject all events where a -ray converts in the top 7/8 of the thickness of the tile. Of course, there are two layers of scintillator on the top of the instrument, so any conversions in the rst layer will deposit 2 MIP in the second layer. Thus this cut eliminates 15/16ths of the events which convert in the ACD, as well as any charged particle events. In addition, cuts were made based on the characteristics of the tracks themselves. All tracks were required to have at least three real hits, exclusive of \virtual" hits placed on noisy strips or outside of the tracker. A \reduced 2 " was formed, based on the Kalman ltering technique (Fruhwirth 1987; Jones 1998). The total track 2 was divided by the number of hits in the track, and this reduced 2 was required to be less than 5. The nal cut demanded that all tracks start at least 4.7 mm (20 strips) from the edge of the active
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area of the tracker. Electrons from -rays that convert that close to the edge are likely to exit the tracker preferentially, and will introduce a bias to the distribution of reconstructed
-ray directions. The eciency of each cut is given in Table 1.
Monte Carlo cuts. In an e ort to make the beam test data as directly comparable with Monte Carlo simulations as possible, the Monte Carlo data was subjected to very similar cuts. The Monte Carlo included an anti-coincidence system, and a similar cut was made to reject events which converted in the plastic scintillator. All of the cuts based on track parameters were made in the exact same way for both the Monte Carlo and the beam test data. Since most of the Monte Carlo simulations were done with incident -rays drawn from a bremsstrahlung energy spectrum, there was no need to make cuts to ensure only one
-ray in the tracker. The particular cuts made were chosen to simplify analysis of the beam test data. They are not meant to represent the types of cuts that will be appropriate for GLAST . GLAST will be faced with a very di erent environment in space, replete with background particles. GLAST will be illuminated from all directions with both -rays and charged particles. It also has a very di erent geometry, which will require combining data from di erent towers and accounting for gaps. The relevant feature of the cuts made here are that they are very nearly identical for the beam test instrument and the Monte Carlo simulations. This will allow direct comparison of their results. However, the instrumental parameters measured for the beam test instrument will not be directly scalable to GLAST .
5. Results The Kalman lter was implemented to t each instrument projection (x and y) separately. Because the incident -ray direction was known from the beam position, the
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68% Containment 95.5% Containment
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Fig. 1.| x-projected point-spread widths for Pancake con guration with no Pb radiators (left) and 4% Pb radiators (right). Circles indicate the 68% containment width, and squares indicate the 95.5% containment width. Error bars are 2 statistical errors, and shaded regions represent the 2 con dence regions of the Monte Carlo estimates. distribution of reconstructed -ray angles is a good estimate of the instrument projected point-spread function. Since the multiple scattering and measurement errors are non-Gaussian, there are non-Gaussian tails to the point-spread function. Therefore, we measured the point-spread width with the 68% and 95.5% containment radii rather than the standard deviation. The measured projected point-spread widths for both the Monte Carlo simulations and the beam test data are shown for each instrument con guration in Figures 1 and 2. There is good agreement between the two in both the 68% and the 95.5% containment radius. In stretch mode, all of the measurements lie within the 2 statistical error bars of the Monte Carlo results. In pancake mode, the 95.5% containment radii of the actual projected point-spread widths were slightly larger than expected at the highest energies (above a few GeV). The 68% containment radii were well represented by the Monte Carlo at all energies.
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Fig. 2.| x-projected point-spread widths for Stretch con guration with no Pb radiators (left) and 4% radiators (right). Circles indicate the 68% containment width, and squares indicate the 95.5% containment width. Error bars are 2 statistical errors, and shaded regions represent the 2 con dence regions of the Monte Carlo estimates. The containment radii in each projection fall o with increasing energy somewhat faster than the 1=E we might expect purely from multiple scattering. There are a number of reasons for this. First of all, the containment radii at low energies are smaller than expected theoretically because of self-collimation. The nite width of the detector prevents events from being reconstructed with large incident angles. At higher energies, measurement error becomes a signi cant contributor to the point-spread width. While these e ects cause deviations from theoretical estimates of the point-spread width, they are well represented by the Monte Carlo (See Figure 3).
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Degrees
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Fig. 3.| Reconstructed -ray angle distributions for beam test and Monte Carlo data for pancake 4% X0 (left) and stretch with no Pb radiators (right). Thin lines are the beam test distributions, thick lines are the normalized Monte Carlo distribution.
6. Conclusions The agreement between the Monte Carlo simulations and the beam test data is clearly encouraging to the GLAST collaboration. However, some care must be taken to interpret these results in light of their implications for GLAST . Primarily, it is important to remember that the point-spread widths measured may not be used as an estimate of the GLAST point-spread width; they are two separate instruments with di erent characteristics. Furthermore, the beam test instrument was measured in a controlled, low background beam environment, while GLAST will be operating in space, bombarded by charged particles and albedo -rays. However, this does not mean that these results are irrelevant to GLAST . The veri cation of the Monte Carlo code implies that simulations of GLAST with gismo should yield accurate estimates about the nal instrument parameters without building many expensive prototypes. Point-spread functions derived from Monte Carlo simulations of
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the entire instrument should be used in accurate science simulations to determine the practical limits for measurements of astrophysical interest, such as source confusion limits and point-source sensitivity. The agreement between the beam test data and simulations suggest that these GLAST science simulations will give accurate results. [acknowledgements here]
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Jones, B. B., 1998, Data Analysis Techniques for EGRET and GLAST , Ph.D. thesis, Stanford University Jones, B. B. & Tompkins, W. F., 1997, Preliminary Tracker Simulation Results, World Wide Web, http://egret0.stanford.edu/bbjones/presimres.pdf Kalman, R. E., 1960, Transaction of the ASME|Journal of Basic Engineering, 35{45 Merck, M. et al., 1996, A&AS, 120, 4, 465 von Montigny, C. et al., 1997, ApJ, 483, 161 Nelson, W. R., Hirayama, H., & Rogers, D. W. O., 1985, The EGS4 Code System, Tech. Rep. SLAC-265, Stanford Linear Accelerator Center Nolan, P. L. et al., 1996, A&AS, 120, 4, 61 M. E. & Thompson, D. J., 1996, ApJ, 463, 105 Ozel, Pohl, M., Kanbach, G., Hunter, S. D., & Jones, B. B., 1997, ApJ, 491, 149 Ritz, S., Atwood, W. B., et al., in preparation, Nucl. Inst. & Meth. Romani, R. W. & Yadigaroglu, I.-A., 1995, ApJ, 438, 314 Yadigaroglu, I.-A., 1997, Experimental Astronomy, 7, 3, 221 Yadigaroglu, I.-A. & Romani, R. W., 1995, ApJ, 449, 211
This manuscript was prepared with the AAS LATEX macros v4.0.
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Cut Triggers Kept Hodoscope 42-55 % ACD 57-84 % Three Hits 77-87 % 2 73-82 % Edge 89-96 % All Cuts 15-25 % Table 1: Cut Eciencies
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