LHC-ATLAS Phase-I upgrade: calibration and simulation of a new trigger readout system for the Liquid Argon calorimeter

The ATLAS Liquid Argon Calorimeter group has been working on an upgrade of its trigger readout electronics. As part of this upgrade, new trigger “Super Cells” will be introduced, increasing the granularity of the trigger readout by a factor of ten with respect to Run 2. While the production and installation of the new electronics is underway, a calibration framework for the energy and timing measurement of the Super Cell readout is also being developed. The framework is created by using data taken in calibration runs with a pulsing system to establish the Super Cell pulse shape and other parameters, i.e. pedestal level, equivalent transverse energy for one ADC bit, and coefficients of an optimal filtering algorithm for energy calculation. The new hardware has been verified to meet the design specifications using the framework. A new simulation of the calorimeter, using the calibrated parameters obtained during the commissioning of the new trigger readout system, is also being developed. The simulation takes into consideration the long bipolar pulse shape for any number of interaction per bunch crossing. This accounts for highly realistic out-of-time pileup effect.


Introduction
In 2021-2023 the LHC (Large Hadron Collider) will run with the same or higher beam luminosity than in Run 2, and luminosity increases are also planned for the High-Luminosity LHC. The trigger readout system of the Liquid Argon (LAr) Calorimeter of the ATLAS experiment [1] has been upgraded during the Phase-I upgrade from 2019 to 2020, in order to achieve a trigger rate compatible with the first stage trigger (100 kHz) without imposing higher energy thresholds. The new LAr trigger readout system has a ten times finer read out segmentation with respect to the Run 2 system to enhance the performance of the jet rejection. It consists of 34,000 readout segments, so-called Super Cells.1 With the Phase-1 upgrade, the energy threshold on the electromagnetic objects is expected to be lowered by 10 GeV with respect to the Run2 trigger readout system. The new system uses an optimal filtering algorithm to compute the transverse energy and the timing of the digitized signal pulse. The coefficients of the optimal filtering need to be calibrated by a test pulsing system. A framework for calibration and simulation of the new trigger readout system has been developed for validation and commissioning of the Phase-1 upgrade.

Upgrade of the trigger readout system
Super Cells will be introduced for the trigger readout of the LAr calorimeter for the Run 3 in order to use the shower shape information of electrons and photons. In the new trigger readout system, LAr Trigger Digitizer Boards (LTDBs) perform the digitization of the Super Cell analog signal at 1ATLAS uses a spherical coordinate system (r, θ, φ) with its origin at the nominal IP in the centre of the detector and φ being the azimuthal angle around the z-axis along the beam pipe. The pseudorapidity is defined as η = − ln tan(θ/2) using the polar angle θ. The transverse energy is defined by E T = E sin θ. A Super Cell consists of two to eight physical LAr cells depending on η region and layer. A ∆η × ∆φ ≈ 0.1 × 0.1 region in the low η region has one Super Cell for each of the 0 th and the 3 rd layers and four Super Cells for each of 1 st and the 2 nd layers. the front-end by the 12 bits ADC with a sampling frequency of 40 MHz. One LTDB typically corresponds to 320 Super Cells. The digitized data will be transmitted to the back-end system and be processed to obtain a precise measurement of the transverse energy and timing information of each Super Cell. There are 58 front-end crates (FECs) in total. Analog signals from the calorimeter have triangular shapes, and they are amplified and shaped with a CR-(RC) 2 bipolar filter in the front-end boards (FEBs) to minimize the pileup effects. 2 Transverse energy and timing are computed by the LAr Trigger prOcessing MEzzanine (LATOME) board with an optimal filtering algorithm in the back-end system. The optimal filtering algorithm provides the transverse energy of a Super Cell at the k th bunch crossing with the following formula: where a i are the optimal filtering coefficients, and p is the pedestal level of the Super Cell, which is defined as the average ADC value where no pulse is injected. The index i specifies a digit sample for optimal filtering and four consecutive samples are used. The b k i is correction term for low energy particles from collisions in the past, which depends on the LHC beam filling scheme. ADC values S k i and the b k i depend on the bunch crossing timing to calculate the transverse energy. R is the conversion factor of the computed amplitude in ADC counts to transverse energy.
Production of the new electronics (LTDBs and LATOMEs) and the installation work are under way. The front-end system must accommodate the new, additional LTDBs. Therefore, the baseplane, which transmits analog signals between boards in a crate, must be replaced. This work is the most time-consuming part. As of November 2019, the work for half the front-end crates has been done.

Test pulsing system
A simplified equivalent circuit of the test pulsing system for an individual, physical LAr cell is shown in figure 1. The signal pulse shape from the calorimeter for a real energy deposition is triangular. The triangle pulse is received by the FEB and reaches the LTDB through the base plane. The digitized bipolar pulse on the LTDB is transmitted to the LATOME and the transverse energy is extracted from the amplitude. For calibration, test pulses with exponential shapes3 are generated by the calibration board [2] in the front-end crate. Calibration pulses are sent to the calorimeter to measure realistic pulse responses. In calibration, the LATOME extracts dedicated consecutive 32 ADC samples for each of 320 Super Cells and transmits them to a PC where they are recorded. The first calibration data set of the newly installed LTDB in the end-cap was obtained in July 2019.
2Pileup signals arise from low energy collisions in the same or neighboring bunch crossings, which are irrelevant to physics analyses. The pileup effects are minimized by bipolar pulse shape itself, because positive and negative poles (undershoots) of different pulses cancel each other [1].
3A triangle pulse generator could be used in the calibration board, but the complex circuit required would cause more uncertainty in the responses.

Calibration flow
There are three types of calibration runs: pedestal run, delay run, and ramp run. A new calibration framework was verified using a set of data taken at the end of the autumn in 2019. The simplest calibration run is the pedestal run where no pulse is injected. For example, the pedestal p = 915.190 was measured in 12 bit ADC counts for a Super Cell at (η, φ) = (0.0125, −1.7211) in the middle layer (layer 2). The noise level and the auto-correlation are also measured for each Super Cell with the pedestal run. Figure 2 shows the result of a delay run, in which bipolar pulses are sampled over 24 sets of pulse phases.4 By overlaying the sequences of samples for different phases accordingly, the smooth pulse shape is obtained as if it was sampled every 25 24 ns. The amplitude of the bipolar pulses from the LAr calorimeter is proportional to the energy. In the Super Cell discussed above, 487 GeV was injected in transverse energy5 and observed approximately 1780 ADC counts above pedestal. The   transverse energy by ADC count (E T /ADC) is therefore about 274 MeV, which is consistent with the design value.
The last calibration run is the ramp run, the measurement of conversion factors from 12 bits ADC value to transverse energy (E T /ADC), which uses 15 different energy values injected with the same phase. The pulse amplitudes are computed using an optimal filtering algorithm to compare with the injected energy. Figure 3 left shows the result of the ramp run as a relation between output ADC count and injected transverse energy. The saturation level is visible (around 600-700 GeV) as well as the E T /ADC, which is calculated from the linear region before saturation. In this Super Cell, E T /ADC is 273.859 MeV which is consistent with the one derived from the delay run data. Figure 3 right shows E T /ADC of each Super Cell in the φ = −1.7211 region of the middle layer. The original pulse shape of the calibration run is different from the pulse shape in the physics run, as mentioned before, so the amplitude of the bipolar pulses also differs even if the same transverse energy is injected. A physics pulse shape is predicted from the calibration pulse shape obtained from the delay run data by using the so-called RT method [4] and correct E T /ADC.6 The ramp R in eq. (2.1) is the E T /ADC after the correction.
The linearity of the output ADC count vs injected transverse energy holds even if the injected E T exceeds 500 GeV, while the required value for a typical trigger tower is 255 GeV. Furthermore, E T /ADC in each Super Cell is consistent with the predicted value from the designed saturation level and ADC dynamic range. The calibration framework of the new trigger readout system of the LAr calorimeter has been validated for the first time.

Simulation of pileup effects with the measured pulse shapes
Optimal filtering coefficients a i are calibrated using the auto-correlation matrix and the derived physics pulse shape. Until Run 3 starts predicted auto-correlation matrices of physics runs are used. There is a simple way to predict the auto-correlation using a physics pulse shape and noise information obtained in a pedestal run, but there is no guarantee that the prediction algorithm works in a high luminosity environment. For example, a baseline shift caused by the bunch train structure 6Physics pulse shapes will be measured when physics runs start in 2021. of the LHC beam might have to be considered. Therefore, a simulator has been developed to investigate the optimal method to calculate the auto-correlation.7 In this simulator, it is easy to set a particular bunch train structure, a given number of interactions per bunch, the pulse shape, noise, sampling phase, and so on. Figure 4 shows the input and output of the simulation. Sequences of pulses are generated by adding multiple pulses which are created by multiplying and shifting the pulse shape according to the energy and timing, respectively, and according to the given hit information for each cell, no matter whether it is physical LAr cell or Super Cell. For example, users can program a sequence of high energy bipolar pulses such as in figure 4 (a). In this simulation, the signals to be analyzed are called events, and dedicated hit information including the pileup components is produced. In each cell, sequences of events ( figure 4 (a)), pileup ( figure 4 (b)), and electric noise (figure 4 (c)) are summed to produce a realistic sequence (figure 4 (d)). The zoomed plot of figure 4 (e) clearly shows the effects of pileup and electric noise. Finally, the sequence is digitized. At this point, it is ready for analysis by the optimal filtering algorithm for the energy and time reconstruction. Figure 5 shows an example of the result of the optimal filtering algorithm and selection in the simulator. The E T output should be given only for the corresponding bunch crossing. Shifts from the ideal time, denoted as τ, are the other quantity that the optimal filtering algorithm outputs. The red point is selected by the measured time phase, |τ| < 8 ns with E T > 1 GeV, which is consistent with the injected energy and timing. Now that there is an efficient pulse simulation for various bunch train structures and instantaneous luminosity conditions, the next step will be to investigate an optimal way to determine auto-correlation with the new tool. (f) Figure 4. Output of the simplified simulator for the new trigger system. A pulse shape generated by the SPICE (Simulation Program with Integrated Circuit Emphasis) [6] simulator is used as an example. The upper plots show a sequence of events (a), pileup (b), and electric noise (c). (d) shows the sum of these sequences. The zoomed plot is shown in (e), and the digitized output, which is multiplied by E T /bit, is shown in (f). Bunch train structure is not visible because is only about 1 ADC count at most.
7This simulator is new with respect to the conventional simulator, AREUS (ATLAS Readout Electronics Upgrade Simulation) [5], in that it simulates pulse shape with pileup by taking any complex train structure into account, with no limitation in the time period of pulse sequences.  Figure 5. Example of optimal filtering and selection in the simulator for the new system of the LAr calorimeter. A pulse shape generated by the SPICE simulator is used as an example. The point of passed E T is selected at the correct bunch crossing by the criteria based on the reconstructed transverse energy and time measurement.

Summary
The new trigger readout system of the ATLAS LAr calorimeter, which is part of the Phase-I upgrade, was presented. An optimal filtering algorithm will be used to calculate the energy and timing for the Level-1 trigger. In order to calibrate the optimal filtering coefficients for each Super Cell, a framework has been developed. The first set of coefficients was extracted using the data taken at the end of the autumn in 2019.
Optimal filtering coefficients are calibrated using the auto-correlation matrix. These calibrations may need to take into account the pileup effects with the bunch train structure of the LHC beam. Therefore, a simulator to seek an optimal way to obtain the auto-correlation matrix is being developed.