Detsim, from Detector Simulation, is a the city that simulates the detector response for fast-simulated events. A fast-simulated event consist of a collection of hits of position and energy desposition in the gaseous volume (right figure below). The detector response are the signals measured in the light-sensors in the form of time ordered waveforms (left figure below).
We can differenciate two simulation modes implemented in NEXUS: the full-simulation and the fast-simulation. In what follows, primary particles are defined as the particles of the simulated event. The rest of the particles produced in the simulation would be considered as secondary particles. For example, 0\nu\beta\beta primary particles are e^+ e^-. Ionization electrons, scintillation photons, and EL photons are secondary particles. The simulation modes are described below.
Full-Simulation: In this mode the propagation of all particles (primary and secondary) is carried out until they reach the sensors. Particles are considered as individual entities with a unique ID-number, making it possible to trace their interactions throughout the detector. Therefore the overall simulation would be composed by the simulation of each individual particle. This is a CPU-time-consuming task, growing with the number of particles involved, which scales with the energy of the simulated event. Since each of the emitted photons is also simulated, the final result of the simulation will be a number of photons arriving at the photo-sensors. The output of the simulation is given as zero-suppressed time histograms with the photo-electrons generated in each sensor (left figure). This simulation mode is both CPU-time-consuming and memory demanding, with a time-scale on the order of 2 min to simulate a 41.5 keV ^{83m}Kr event and > 1 hour for a Q_{\beta\beta} \sim 2.5 MeV event. The advantage of this simulation mode is its extreme detail and that its outcome is the actual signal measured at the light sensors.
Fast-Simulation: In this mode the simulation is stopped after the creation of the ionization electrons and scintillation photons. The ionization electrons and scintillation photons are produced by the direct propagation of primary particles, or by secondary particles emitted by the primaries, like delta electrons or bremsstrahlung that subsequently interact. Once they are created, the simulation stops, and neither drift nor light propagation is simulated. The ionization electrons and scintillation photons created are collected in voxels of a certain volume (usually around 1x1x1 mm^3 voxels). Each voxel represents an energy deposition, a so-called hit, and is characterized by a 3D position \boldsymbol{r} = (x, y, z), the energy E required to produce them, and the delay time t from the start of the event (right figure). The collection of hits for a given even is saved, defining a track in the detector’s active volume. The fast-simulation is very fast compared with the full-simulation mode, on the \mu s scale. However, since the simulation is stopped we do not know the signal that would be measured at the sensors.
Detsim input are NEXUS fast simulation tracks, these files must contain only the following non-empty information.
/MC/hits
/MC/: the data in the nexus input file is copied in the output file/Run/event_map: mapping between nexus event id and IC event id. This mapping is needed because detsim might split nexus events into multiple IC events/Run/events: IC event number and simulated timestamps based on rate configuration parameter/Run/runInfo: run number of each event/pmtrd: the PMT waveforms for each PMT/sipmrd: the SiPM waveforms for each SiPM/Filters/active_hits: nexus events without hits inside the active volume are filtered
| Parameter | |
|---|---|
| Electron simulation | inverse ionization yield w_{io} |
| fano-factor F | |
| drift velocity v_d | |
| lifetime \tau | |
| diffusion D_L, D_T | |
| Photon simulation | inverse scintillation yield w_{sc} |
| EL gain G_{EL} | |
| conde-policarpo factor J_{CP} | |
| Signal simulation | EL drift velocity v^{EL}_d |
| S1 Light Tables | |
| S2 Light Tables | |
| point spread function (PSF) | |
| Waveform creation | pre-trigger time |
| buffer length | |
| PMT waveforms bin width | |
| SiPM waveforms bin width |
The city flow parts are shown in the diagram
Hits filtering. Hit position determines in which region of the detector the energy deposition occurs. Energy depositions, ie ionization electrons, can only be created in the gaseous part of the detector which is composed by the active, buffer and EL regions. The ionization electrons drift towards the EL only if they are produced in the active region, therefore only hits at this region are selected in the S2 simulation. On the other hand, scintillation photons can be emitted and produce signal from anywhere inside the gas, thus the S1 simulation keeps all the hits in the active and buffer regions. Hits in the EL-region are removed to avoid duplication of S1 and S2 LTs and implementation complications. This is a good approximation since the S1 of tracks with hits in the EL-region is overlapped with the subsequent S2, and the event would be reconstructed anyway as an no-S1 event.
Electron simulation. This step starts by computing the ionization electrons produced in each hit, which is the value of the hit energy divided by the inverse ionization yield w_{io}. Defining n=E/w_{io}, the number of ionization electrons in a hit n'_{ie} is simulated following the distribution
n'_{ie} \sim
\begin{cases}
\text{Pois}(n) & \text{if} ~ n F < 1 \\
\text{Gauss}(\mu=n, \sigma=\sqrt{n F}) & \text{if} ~ n F \geq 1
\end{cases},
motivated by the definition of the fano-factor F. Next the electrons are drifted toward the EL region. During the drifting some of the electrons are absorbed due to impurity attachment, a process described by an exponential with characteristic lifetime \tau. Or equivalently, the time it takes the drifting electrons to be absorbed t_{abs} is given by
t_{abs} \sim \text{Exp}(\lambda = \tau^{-1}).
\label{eq:detsim-absorption-time}
Then the number of electrons that survive n_{ie} can be computed by
n_{ie} = \sum_{i=1}^{n'_{ie}}
\begin{cases}
1 & \text{if} ~ t_{abs}^i < t_{drift} \\
0 & \text{if} ~ t_{abs}^i \geq t_{drift}
\end{cases},
where t_{drift}=z/v_{d} is the time it takes to the ionization electrons produced at z to reach the gate with drift velocity in the active volume v_d. The last electron physical process to simulate is the diffusion, characterized by the longitudinal and transverse diffusion coefficients D_{L} and D_{T} respectively. The position of each electron arriving at the gate is diffused following
\begin{aligned}
X_{diff}&\sim\text{Gauss}(x,~D_{T}\sqrt{z}),\\
Y_{diff}&\sim\text{Gauss}(y,~D_{T}\sqrt{z}),\\
Z_{diff}&\sim\text{Gauss}(z,~D_{L}\sqrt{z}).\end{aligned}
where x, y, z are the initial position of the electrons, ie the hit position in which they are created.
Photon simulation. The S1 photons are generated from the initial hits through the inverse scintillation yield w_{sc}
n_{S1} \sim \text{Pois}(E/w_{sc})
The S2 photons are computed using the number of ionization electrons arriving at the EL n_{ie},
n_{S2} \sim\text{Gauss}\left(n_{ie}G_{EL}, \sqrt{n_{ie}G_{EL}J_{CP}}\right),
where G_{EL} is the EL gain (number of photons emitted by a single electron) and J_{CP} is the conde-policarpo factor.
Signal simulation. In this stage we compute the photon-electrons (pes) measured in each sensor and their arrival times. The treatment is different for S1 and S2 signals and also for PMTs and SiPMs.
S1. In the photon simulation block, we computed the number of scintillation photons produced by each hit. By the definition of the S1 LT, the number of photo-electrons generated by the scintillation photons at x, y, z is given by
S_{S1}(\text{PMT}) \sim \text{Pois}(n_{S1} \times \text{LT}_{S1}(x, y, z|\text{PMT})).
\label{eq:poisson-S1}
The next step is to simulate the arrival time of the photons to the sensors, which is given by
t_{arrival} = t + t_{decay} + t_{travel}
\label{eq:s1-tarrival}
where t is the hit production time, t_{decay} the scintillation decay time and t_{travel} is the time it takes the photons to go from the hit position to the particular PMT. The travel time is neglected in detsim since its simulation would require a complete photon propagation. The photon travel time is in fact negligible compared to the drift time of the ionization electrons that produce the S2, thus we can safely omit it (recall that S1 is used to compute the drift time of the event, namely its longitudinal position). The decay time is simulated for xenon using its fast and slow scintillation components given by
t_{decay} \sim 0.1 ~ \text{exp}(-t/\tau_{f}) + 0.9 ~ \text{exp}(-t/\tau_{s})
where \tau_{f} = 4.5~\text{ns} and \tau_{s} = 100~\text{ns} are the fast and slow scintillation decay times, respectively. For each measured photo-electron, a t_{arrival} is computed. The total S1 signal would be given by the time histogram of the arrival times for the generated photo-electrons. The S1 signal at the SiPMs is not simulated.
S2. The computation of the number of photo-electrons in the PMTs is similar to that of the S1,
S_{S2}(\text{PMT}) \sim \text{Pois}(n_{S2} \times \text{LT}_{S2}(x, y|\text{PMT})),
but the arrival times are treated differently. The arrival time will be given by the sum of the production time, the drift time and the EL emission time,
t_{arrival} = t + t_{drift} + t_{EL}.
The drift time is given by t_{drift}=z/v_{d}. The t_{EL} is the emission time at the EL gap. Assuming that photons are emitted uniformly throughout the EL gap,
t_{EL} \sim \text{Uniform} \left( 0, T_{EL} \right) \quad \text{with} \quad T_{EL}=\frac{w_{EL}}{v^{EL}_{d}},
where w_{EL} is the width and v^{EL}_{d} the drift velocity in the EL. Notice that we are implicitly neglecting the travel time from the emission point to the sensor, which is much lower that the drift and EL times.
The signal in the SiPMs is computed with the PSF function. Recall that the PSF is z dependent, covering the EL width in several partitions. For an ionization electron arriving at the EL at position x, y and emitting n_{S2} total photons, the signal produced at the SiPM at distance d would be
S_{S2}(\text{SiPM}, z_p) \sim \text{Pois} \left( n_{S2}/n_z \times \text{PSF} (d|z_{p}) \right),
where n_z is the total number of EL partitions. Notice that this is the signal produced by photons emitted at partition z_p, which are assumed to be uniformly emitted throughout the EL width. The arrival times would also depend on the partition
t_{arrival~p} = t + t_{drift} + t_{drift~p} + t_{EL~p}
where t_{drift~p} = |z_p|/v^{EL}_d and
t_{EL~p} \sim \text{Uniform} \left( 0, \Delta T_{p} \right) \quad \text{with} \quad \Delta T_{p}=\frac{w_{p}}{v^{EL}_{d}},
where w_p is the partition width. Again, in both PMTs and SiPMs the arrival time is computed for each measured photo-electron.
Waveforms creation. By definition, a waveform is a time histogram of the arrival times. Therefore this step consists of histograming the photo-electron’s arrival times for each sensor. The PMT and SiPM waveforms are assumed to have the same buffer-length but different bin width. By convention the waveform times go from 0 to buffer-length, and in order to mimic the DAQ triggering system we add an extra pre-trigger buffer time that fixes the start of the signals inside the buffer.