1 Introduction

Detectors made of organic plastic scintillation materials are commonly used in nuclear physics experiments to measure time-of-flight, hit position, and energy loss of traversing ions. The intrinsic detection efficiency is typically 100%, these detectors are available at low cost and are easy to handle. Their properties, like scintillation-light emission wavelength and decay times, match the requirements given by modern nuclear-physics setups and, thus, are an ideal choice for many experiments at various facilities.

In this paper, we present the design, construction and performance of the new time-of-flight detector (ToFD) that consists of plastic scintillator bars and will be deployed at the R\(^3\)B (Reactions with Relativistic Radioactive Beams) setup at GSI Helmholtzzentrum für Schwerionenforschung in Darmstadt, Germany.

1.1 The R\(^3\)B setup

R\(^3\)B is a versatile setup for nuclear-physics experiments in inverse kinematics at relativistic energies. This setup provides high efficiency, large acceptance, and high resolution for kinematically complete studies of reactions involving heavy-ion beams of short-lived nuclei. The physics program of the R\(^3\)B collaboration is dedicated to reaction studies, with emphasis on nuclear structure, astrophysics and nuclear dynamics; technical applications are also considered.

The setup will be located at the focal plane of the high-energy branch of the Super-FRS [1, 2] at FAIR, which will deliver high-quality secondary beams up to uranium at intensities ranging from a few hundred to several million particles/second. The experimental setup of R\(^3\)B is configured to accept the highest beam energies provided by the Super-FRS corresponding to 20 Tm magnetic rigidity, capitalizing on the highest possible transmission of secondary beams.

The R\(^3\)B setup has been designed and built by the R\(^3\)B collaboration on the basis of more than 20 years of experience with the reaction setup LAND [3] at GSI, introducing substantial improvements with respect to resolution and an extended detection scheme.

One of the major improvements is the new large-acceptance super-conducting dipole magnet GLAD [4], which allows to perform experiments with beams with a rigidity up to 20 Tm. For nuclei in the lead-uranium region, this corresponds to kinetic energies of 1 GeV/nucleon at which the ions are fully stripped, thus, enabling unambiguous identification of the reaction products.

In order to fully exploit the potential of FAIR beams at the R\(^3\)B setup - heavy beams and high intensities - the planned detector systems have to be able to cope with such new conditions.

The layout of the R\(^3\)B experimental setup is sketched in Fig. 1. To perform kinematically complete measurements, it is mandatory to detect all particles emerging from the reaction - photons, neutrons, light-charged particles and heavy residues on an event-by-event basis. The key components of the setup are a station for tracking and identification of the incoming beam, the target area surrounded by the R\(^3\)B silicon tracker [5] and the gamma-ray and light charged-particle calorimeter CALIFA [6], the super-conducting large-acceptance dipole magnet GLAD, the large-area neutron detector NeuLAND [7], the fragment and the proton arms with tracking and time-of-flight detectors [8]. For a detailed explanation of the setup and the physics program we refer the reader to the R\(^3\)B Letter-of-Intent [9].

Fig. 1
figure 1

R\(^3\)B experimental setup: The ion beam enters from the left and hits a solid target or a liquid-hydrogen target in the target area. The target is surrounded by CALIFA, a gamma spectrometer and target recoil calorimeter. After a reaction in the target, the fragments are deflected by the magnetic field of GLAD. Fiber detectors behind the magnet record the position of the fragment track. The ToFD detector measures the time-of-flight and the energy loss of the ions. Neutrons from reactions are unaffected by the GLAD magnet and hit NeuLAND

Full size image

1.2 A new time-of-flight wall

The ToFD detector, made from plastic scintillators, will be situated about 20 m down-stream from the reaction target, behind the large dipole magnet GLAD. It will serve for a list of major tasks for a large variety of experiments performed at R\(^3\)B. All heavy fragments produced in the reaction target will be recorded in the ToFD detector. Their specific energy loss and arrival time at the detector plane are essential for their identification in mass and nuclear charge. In addition, the detector will be one of the main trigger sources for the entire setup, it will measure the time between consecutive events to avoid event mixing, and it will provide absolute position information for the alignment of the whole tracking system.

In the following, the requirements, construction, working principles, and tests with a fast LED, laser and ion beams will be presented.

2 Design goals

Detectors based on plastic scintillators with fast timing response can be found at various positions of the R\(^3\)B setup. The ToFD detector, located behind the dipole magnet at the end of the evacuated beam line for fragments, measures the time-of-flight (\(t_\text {flight}\)) and the nuclear charge (Z) of heavy fragments after the reaction in the target. The nuclear charge of reaction products is obtained by precise energy-loss measurements (\(\varDelta E\)) of the fragments passing through the scintillator material. The new detector should be able to separate the nuclear charge Z from Z-1 even for the heaviest fragments. In case of Pb fragments, a relative nuclear-charge precision \(\sigma _{Z}/Z\) of better than 0.4% is required to separate Z from Z-1Footnote 1. This translates into an energy-loss measurement with a relative precision \(\sigma _{\varDelta E}/{\varDelta E}\) better than 1%.

Another requirement on the performance of the new ToFD detector comes from the identification of residues in mass. The mass-over-charge ratio of the fragment can be calculated from the measured time-of-flight and the measured trajectory through the dipole field according to the following equation:

$$\begin{aligned} \frac{A}{Z} = \frac{e}{m_{0}c} \cdot \frac{B \rho }{\beta \gamma }, \end{aligned}$$
(1)

where A is the mass number, Z is the charge of the nucleus, e is the electron charge, \(m_{0}\) is the atomic mass unit, c is the speed of light, \(B\rho \) is the magnetic rigidity, \(\beta \) is the velocity relative to the speed of light, and \(\gamma \) is the corresponding Lorentz factor.

Once the nuclear charge Z is obtained from energy-loss measurements, the relative uncertainty in the mass determination can be calculated as:

$$\begin{aligned} \frac{\sigma _{A}}{A} \approx \frac{\sigma _{B\rho }}{B\rho } + \gamma ^{2} \cdot \left( \frac{\sigma _{t_\text {flight}}}{t_\text {flight}} + \frac{\sigma _{L}}{L} \right) , \end{aligned}$$
(2)

where \(t_\text {flight}\) is the time-of-flight between the start detector and the ToFD detector, and L corresponds to the flight path. Also here, the strongest constraint comes from the identification of the heaviest residues in the lead-uranium region, where the relative difference in mass between two neighbouring nuclei amounts to \(\sim 0.5\%\). In order to resolve the masses\(^1\), the relative uncertainty in mass must be of the order \(\sigma _{A}/A < 2\cdot 10^{-3}\). This would also match the uncertainty of the magnetic rigidity of about \(10^{-3}\) that can be obtained via particle tracking. For typical beam energies of 1 GeV/nucleon (\(\gamma \sim \) 2), the time-of-flight of the heaviest residues has to be measured with a relative uncertainty of less than \(2\cdot 10^{-4}\) (sigma) in order to obtain the desired mass resolution. Considering a flight path of \(\sim \)20 m, this results in an ultimate time-of-flight precision better than 14 ps for nuclei in the lead-uranium region at 1 GeV/nucleon kinetic energy. For several other cases the required time-of-flight precision (assuming a 20 m flight path) is given in Table 1.

Table 1 Required time-of-flight precision for several different cases to fulfill \(\sigma _{A}/{A} < 2\cdot 10^{-3}\), assuming a flight path of 20 m
Full size table

Furthermore, since the unreacted beam also hits the ToFD detector, it must be able to maintain its performance even at high beam rates of up to \(1\cdot 10^{6}\)particle/s, and the associated electronics must have multi-hit capabilities. Here, it is important to note, that not only the energy- and time-precision have to remain stable at different counting rates, but also the mean positions of measured energy-loss and time signals must not shift with counting rate. If, for example, at different rates the measured energy-loss signal shifts in its position by more than 1%, this could lead to wrong nuclear-charge identification.

The final detector, designed to fulfill the specifications mentioned above, consists of four planes of scintillators, and has an active area of about 1200\(\times \)100 mm\(^2\). Each plane contains 44 vertical scintillator bars; each bar has the dimensions 27\(\times \)1000\(\times \)5 mm\(^3\). The scintillator bars are read out by Photo-Multiplier Tubes (PMTs) on both far ends. The width of a single bar is matched to the size of a PMT, in order to completely omit light guides, and couple the scintillator bars directly to the PMTs, thus maximizing the light collection. To use the detector at high counting rates, it is required (see Sect. 4.2) that the PMTs are equipped with fully active voltage dividers, and that the signals delivered by the detector are adjusted to a voltage region were the PMTs have the best performance with regard to rate stability and nuclear-charge resolution. Thus, associated read-out electronics must be able to work with small currents from the PMTs.

To design the detector, we have performed simulations of the time resolution to investigate the influence of different components on the detector resolution, and to choose appropriate scintillator material and PMTs, see Sect. 3. We carried out different measurements with a prototype detector using LEDs, laser, and relativistic heavy ion beams to test timing and the quality of energy-loss measurements, see Sect. 4.

3 Simulations

GEANT4 [10] simulations with optical photons were performed to model the timing response of the detector and to evaluate the contribution of the various processes that determine the timing precision. However, simulations with photon tracking are computationally intense and, therefore, calculations using the statistical model (see below) were also performed. The statistical model is presented first as it captures the main factors affecting the time resolution in scintillators.

3.1 Time precision using the statistical model

The statistical model as originally described in Ref. [11] was used to study different effects influencing the time precision and search for a compromise between best-performance capabilities and costs. Several statistical processes limit the attainable time precision of scintillation detectors, such as:

  • time spread in the energy transfer to the optical levels of the scintillation,

  • decay time of the excited states,

  • fluctuations in the propagation time of photons through the scintillator,

  • creation of photo-electrons within the photo cathode of the photomultiplier, and

  • the associated electronics.

First studies on the statistical limitations on the achievable time precision using scintillation detectors have been done in the early 1950s by Post and Schiff [11]. The basic idea of their model is that the probability \(P_{M}(t)\) that M photo-multiplier pulses occur between the time zero (defined as the time of the initial excitation of the scintillator), and the time t is given by the Poisson distribution:

$$\begin{aligned} P_{M}(t)=\frac{1}{M!}\cdot [N(t)]^{M}\cdot \exp \left[ -N(t)\right] , \end{aligned}$$
(3)

where N(t) is the average expected number of photomultiplier pulses in the range [0, t], with \(R_{\text {tot}}=\int \limits _{0}^{\infty }N(t)\text {d}t\) being the average total number of created photoelectrons. Starting from this probability distribution, the probability that the \(Q^{th}\) photoelectron is detected in the time interval \([t,t+\text {d}t]\) can be calculated as [11]:

$$\begin{aligned} W_{Q}(t)= & {} P_{Q-1}(t)\cdot \frac{dN(t)}{dt} \nonumber \\= & {} \frac{1}{(Q-1)!}\cdot [N(t)]^{Q-1}\cdot \exp \left[ -N(t) \right] \cdot \frac{\text {d}N(t)}{\text {d}t}.\nonumber \\ \end{aligned}$$
(4)

The time precision \(\sigma _{t}\) can then be calculated from the variance of the time signal:

$$\begin{aligned}{} & {} \sigma _{t}^{2}=\langle t^{2}\rangle - \langle t\rangle ^{2}=\frac{1}{W_{Q}^{\text {tot}}}\cdot \int \limits _{0}^{t}t^{2}\cdot W_{Q}(t)\text {d}t\nonumber \\{} & {} \qquad -\bigg ( \int \limits _{0}^{t}t\cdot W_{Q}(t)\text {d}t\bigg )^{2}, \end{aligned}$$
(5)

where \(W_{Q}^{\text {tot}}\) is the total probability that the \(Q^{th}\) photoelectron occurs in the range \([0,\infty ]\) and is given as [11]:

$$\begin{aligned} W_{Q}^{\text {tot}}=1-\exp {\left( -R_{\text {tot}}\cdot \sum _{i=1}^{Q} \frac{R_{\text {tot}}^{i-1}}{(i-1)!} \right) }. \end{aligned}$$
(6)

As a result of this approach, the limiting factors obtained for the time precision are the average total number of photoelectrons \(R_\textrm{tot}\) (\(\sigma _{t} \sim 1/R_{\text {tot}}^{1/2}\)) as well as the involved scintillator decay timing constants. Based on these ideas, many different studies dedicated to the timing properties of scintillator detectors have been performed [13,14,15,16,17,18,19,20,21,22,23].

Usually, the function \(\text {d}N(t)/\text {d}t\) is given as a convolution of the different above-mentioned contributions influencing the time precision. On the other hand, as these processes (photon production and photon transport, photoelectron conversion, and signal processing) are statistically independent, one can calculate the timing precision for each of them (\(\sigma _{i}\)) using above equations, and then obtain the total time precision as a quadratic sum of individual components, i.e. \(\sigma _{t}^{2}=\sum \sigma _{i}^{2}\). This allows to separately study and optimize the influence of different contributions from scintillator, photomultiplier, and electronics to the timing precision.

The intrinsicFootnote 2 contribution of a scintillation detector to the overall time precision is determined by the time-distribution of the produced light signal and by the amount of produced light. In case of a plastic scintillator, it has been shown [24,25,26,27] that the best-suited distribution shape for the produced light signal \(\text {d}N(t)/\text {d}t\) is given by a convolution of an exponential and a Gaussian function:

$$\begin{aligned}{} & {} \frac{\text {d}N(t)}{\text {d}t} \sim f_{G}(t) *\exp \left( -t/\tau \right) , \nonumber \\{} & {} \quad f_{G}(t)=\frac{1}{\sigma \cdot \sqrt{2\pi }\cdot \exp \left( -\frac{(t-3\sigma )^{2}}{2\cdot \sigma } \right) }, \end{aligned}$$
(7)

where \(\sigma =\tau _{\text {rise}}/\ln (9)\) and \(\tau =\tau _{\text {decay}}\), with \(\tau _{\text {rise}}\) and \(\tau _{\text {decay}}\) being, respectively, rise and decay times of a given scintillator material as given by the supplier.

Concerning the use of Eq. 7, as the involved functions are Gaussian and exponential, time-consuming numerical convolutions are not necessary. A convoluted function is known as exponentially modified Gaussian function (ExGaussian) and can be easily calculated as [28]:

$$\begin{aligned} \begin{aligned} \frac{\text {d}N(t)}{\text {d}t}={}&\frac{1}{2\cdot \tau }\cdot \exp \left( \frac{\sigma ^{2}}{2\cdot \tau ^{2}} - \frac{t-3\cdot \sigma }{\tau } \right) \\&\left[ 1-\text {erf} \left( \frac{\sigma }{\sqrt{2}\cdot \tau } - \frac{t-3\cdot \sigma }{\sqrt{2}\cdot \sigma } \right) \right] . \end{aligned} \end{aligned}$$
(8)

To calculate the intrinsic resolution of a scintillation detector, we see from Eqs. 4 and 5 that apart from the light-pulse shape \(\text {d}N(t)/\text {d}t\) the average expected number N(t) of light pulses in the range [0, t] is also required. For an ExGaussian function one would obtain:

$$\begin{aligned} N(t)= & {} R_{\text {tot}}\cdot \frac{f(t)-f(0)}{0.5-f(0)}, \nonumber \\ f(x)= & {} {} 0.5\cdot \Bigg \{ \text {erf}\left( \frac{x-3\cdot \sigma }{\sqrt{2}\cdot \sigma }\right) \nonumber \\{} & {} \quad - \exp \left( \frac{\sigma ^{2}}{2\cdot \tau ^{2}}-\frac{x-3\cdot \sigma }{\tau }\right) \cdot \nonumber \\{} & {} \qquad \left[ 1+\text {erf}\left( \frac{x-3\cdot \sigma }{\sqrt{2}\cdot \sigma }-\frac{\sigma }{\sqrt{2}\cdot \tau }\right) \right] \Bigg \}. \end{aligned}$$
(9)

For small-size (a few cm) scintillation detectors, the light-production mechanism described above plays the dominant role. For timing properties of larger-size detectors, light transport becomes more important, see e.g. Ref. [12] and references therein. In this case, the light pulse which arrives at the photomultiplier, \(\text {d}N_{\text {SCI}}(t)/\text {d}t\), can be considered as a convolution of two contributions due to light-production processes, \(\text {d}N_{\text {LP}}(t)/\text {d}t\), and from the light-transport processes, \(\text {d}N_{\text {LT}}(t)/\text {d}t\):

$$\begin{aligned} \frac{\text {d}N_{\text {SCI}}(t)}{\text {d}t}=\frac{\text {d}N_{\text {LP}}(t)}{\text {d}t}*\frac{\text {d}N_{\text {LT}}(t)}{\text {d}t}, \end{aligned}$$
(10)

where \(\text {d}N_{\text {LP}}(t)/\text {d}t\) is given by Eq. 8.

To calculate the contribution from the light transport, we have followed the work of Ref. [12]. We assume, for simplicity, that photons created in the interaction between a traversing particle and the scintillation material are coming from a point-like source positioned at a distance L from the end face of a scintillator which is coupled to a PMT. Assuming an isotropic distribution of created photons, we obtain that \(\text {d}N_{\text {LT}}/\text {d}t=-2\cdot \pi \cdot L\cdot n_{\text {sci}}/(c\cdot t^{2})\), with \(n_{\text {sci}}\) being the refractive index of the scintillation material, and c the velocity of light in vacuum. It is important to note that absorption processes of photons (\(L_{att}\) being the attenuation length) during their transport also influence the propagation-time distribution. Taking this effect into account, we can write for \(\text {d}N_{\text {LT}}(t)/\text {d}t\):

$$\begin{aligned} \frac{\text {d}N_{\text {LT}}(t)}{\text {d}t}=-2\cdot \pi \cdot \frac{L\cdot n_{\text {sci}}}{c\cdot t^{2}}\cdot \exp \left( -\frac{c\cdot t}{n_{\text {sci}}\cdot L_{\text {att}}}\right) . \end{aligned}$$
(11)

The above function is non-zero only for propagation times between minimum propagation time \(t_\text {min}\) and maximum propagation time \(t_\text {max}\). If we neglect scattering processes of photons on the surface of the scintillator, we can obtain a direct correlation between the propagation time t of a given photon and its initial axial angle \(\theta \):

$$\begin{aligned} t=\frac{L\cdot n_{\text {sci}}}{c\cdot \cos {\theta }}. \end{aligned}$$
(12)

The minimum propagation time \(t_\text {min}\) is obtained for a direct photon trajectory, i.e. for \(\theta =0\): \(t_\text {min}\) = \(L\cdot n_{\text {sci}}/c\), and the maximum \(t_\text {max}\) propagation time is given by a maximum axial angle for which the photons are still reflected in the direction of a photomultiplier: \(t_\text {max}=L\cdot n_\text {sci}/(c\cdot \cos {\theta _\text {max}})\). As a good approximation we can calculate \(\theta _\text {max}\) as \(\theta _\text {max}= \pi /2- \theta _\text {tot\_refl}\), where \(\theta _\text {tot\_refl}\) is the critical angle for total reflection.

Knowing the light-pulse shape seen by a PMT (see Eq. 10) and using the statistical model, one can calculate the contribution of the scintillator \(\sigma _{\text {sci}}\). The contribution from the PMT is determined by its transient-time-spread (\(t_{tts}\)) and is calculated as: \(\sigma _{\text {PMT}} = t_{tts} / (2.35 \cdot \sqrt{R_{\text {tot}}})\). Then, the total time precision \(\sigma _{t}\) becomes: \(\sigma _{t} = \sqrt{\sigma _{\text {sci}}^{2}+\sigma _{\text {PMT}}^{2}+\sigma _{\text {el}}^{2}}\), where \(\sigma _{\text {el}}\) is the contribution from electronics. For simplicity, we assume that the traversing particle is passing through the centre of a bar. We have taken numerical values of \(R_{\text {tot}}\) that correspond to the number of photoelectrons created due to passage of relativistic 1 GeV/nucleon ions ranging from \(^{12}\)C to \(^{238}\)U through the given thickness and type of scintillation material. To do this, we have calculated the energy loss of the passing ions using the ATIMA code [29], with the number of electrons per MeV deposited energy as given by the scintillator supplier, calculated the quenching factor suited for heavy-ion beams at relativistic energies according to Ref. [30], with the geometrical efficiency from GEANT simulations (see below), and considered the quantum efficiency of a given photomultiplier as provided by the supplier.

For calculations presented here, we have assumed three different scintillation materials: EJ200, EJ204 and EJ232 from Eljen Technolgy [31], see Table 2; very similar properties are also reported for BC408, BC404 and BC422, respectively, from Bicron. We have considered only these three materials, as these are all characterized by short rise and decay times. These are mandatory conditions to reach excellent time precision and to operate in high count-rate experiments. The R8619-20 photomultiplier from Hamamatsu was chosen for the ToFD and thus used in these calculations. For the contribution of electronics \(\sigma _{\text {el}}\), for a single readout channel a value of 13 ps is assumed. This is a typical electronic single-channel time-precision of a FQT-TAMEX3 board, which is chosen for the final detector, see Sect. 4.1.

Table 2 Characteristics of considered scintillation materials from Eljen Technology [31]
Full size table

Table 3 presents the time precision required to separate A from \(A-1\) in different mass regions. In the same table, also shown is the achievable time precision of the new ToFD detector calculated using the statistical model described above. Due to the higher deposited energy, and thus higher light production, the calculated time precision improves with increasing nuclear charge of the considered fragment. For all three scintillation materials, the calculated time precision is better than the design goals. The best precision, especially for light nuclei, is achieved with EJ232. Nevertheless, due to the porosity of EJ232, it is not possible to produce bars of the size required for the ToFD detector, and it was therefore excluded from further consideration.

Table 3 For each considered fragment, the time precision required \(\sigma _{t}^{\text {required}}\) to separate A and \(A-1\) in the R\(^3\)B setup is shown. Also results of simulations for three different scintillator-material types are included (columns 3–5). A 1 GeV/nucleon kinetic energy and a flight path of 20 m is assumed
Full size table

For the EJ200 and EJ204 scintillation materials, Fig. 2 shows the different contributions to the total time precision of the new ToFD detector assuming a \(^{208}\)Pb beam at 1 GeV/nucleon.

The contribution of the photomultiplier to the time precision is negligible, due to the high amount of photons produced after the passage of relativistic heavy ions through the detector. Thus, there is no need to use very fast and expensive photomultipliers in order to obtain the required time precision.

The contribution of the electronics for the whole detector is about 5 ps. Such a good electronic resolution can be achieved using a FQT-TAMEX3 board [44] developed in the EE department at GSI, see Sect. 4.1. Please note, that each of the four layers of bars measures the time-of-flight, and hence, we obtain a better electronic resolution for the whole detector than for one channel.

The contribution from the light production and light transport in the scintillator material to the total time precision is of the same order as the contribution from the electronics.

Fig. 2
figure 2

Different contributions to the total time precision of the new ToFD detector calculated for \(^{208}\)Pb at 1 GeV/nucleon assuming EJ200 (top) or EJ204 (bottom) scintillation material: Photomultiplier (dash-dotted line), electronics (thin full line), scintillator (dashed line), and total (thick full line)

Full size image

3.2 GEANT4 simulations

The geometry of the individual scintillators as well as the full detector assembly was studied using the GEANT4 simulation toolkit [32] including the package for optical photon tracking. The simulations included light production by fragments traversing the scintillators, tracking of the photons to the PMTs at the far ends of the scintillators, quantum efficiency of the photo-cathode, convolution with the single-electron response of the PMT, and leading-edge timing at a given threshold.

For the production of the scintillation light in GEANT4 the bi-exponential function is used:

$$\begin{aligned} I_{t} = \frac{I_0}{\tau _\text {decay}-\tau _\text {rise}}(\exp [-t/\tau _\text {decay}]-\exp [-t/\tau _\text {rise}]), \end{aligned}$$
(13)

where \(I_0\) is the photon yield, and \(\tau _\text {rise}\) and \(\tau _\text {decay}\) are the rise and decay times of the scintillator material. Please note, that the bi-exponential function given above, which is used in GEANT4, is well-suited for a liquid scintillator, but not for the shape of a light pulse from a plastic scintillator [24,25,26,27].

One of the most important ingredients to calculate the expected timing precision is the number of photons produced by the impinging ion. The energy loss can be calculated rather accurately, but the light output is quenched and depends on the ionization density. The calculation of the quenching factor produces one of the largest systematic uncertainties in the prediction of the time precision.

In GEANT4, Birk’s formula is implemented in order to calculate the photon yield \(\text {d}L/\text {d}x\) as a function of the energy loss per path length \(\text {d}E/\text {d}x\):

$$\begin{aligned} \frac{\text {d}L}{\text {d}x}=L_0\cdot \frac{\text {d}E/\text {d}x}{1+k_\textrm{B} \cdot \text {d}E/\text {d}x}. \end{aligned}$$
(14)

\(k_\textrm{B}\) is Birk’s constant and the proposed value for polystyrene-based scintillators is 0.126 mm/MeV (see also Ref. [33]). With this value, GEANT4 predicts that about 400,000 photons are produced for each incoming Ni fragment. However, if one compares this with the results of the statistical model calculation where Ref. [30] was used to calculate the quenching factor, the GEANT4 value is smaller. It should be noted that the quenching factor calculated with Birk’s law in Ref. [33] is used for minimum-ionizing particles and Ref. [30] is more suited for heavy ions. Therefore, we adapted a value for Birk’s constant which produces for the Ni beam the same amount of photons as in the statistical model. In Sect. 6, these values are also compared to measurements.

In the simulations, the scintillator bar is read out at both ends by PMTs with a diameter of 25 mm, and photons were then tracked until they reached the corresponding PMT. The arrival-time distribution of photons is shown in the top part of Fig. 3.

Fig. 3
figure 3

Arrival-time distribution of the photons at the PMT (top) and the resulting electric pulse (bottom)

Full size image

In the next step, the quantum efficiency of 28% of the photo-cathode was taken into account and the \(t_{tts}\) of the PMT was simulated by adding a transit time, which followed a truncated Gaussian distribution with the corresponding width given by the PMT’s properties. In addition, the single-electron response (SER) of a PMT was recorded and digitized. In this way, an electronic pulse (see Fig. 3 bottom) could be reconstructed by adding the SER at each time a photo-electron was registered in the simulations. A comparison between the top and bottom parts of Fig. 3 shows clearly the influence of the PMT. The rise time of the signal gets longer and the width larger. Using the time when the signal was above a given threshold, a leading-edge discriminator is simulated.

By plotting the arrival-time distributions of the n\(^\text {th}\) electron for many events (see Fig. 4), we can obtain the expected time precision as the spread (sigma) of the distribution.

In this way, simulations for a 500 MeV/nucleon Ni beam impinging on a scintillator with dimensions 27\(\times \)800\(\times \)5 mm\(^3\) have been performed. These simulations can be directly compared to the measurement performed during the GSI S438 beam time in 2014.

Fig. 4
figure 4

Examples of arrival-time distribution of the \(1^\textrm{st}\) (top) and the \(20^\textrm{th}\) (bottom) photo-electron. The spread of the distribution yields the achievable time precision

Full size image

3.3 Comparison between GEANT4 simulations and statistical model

The predictions of the statistical model and GEANT4 simulations for the time precision of the ToFD detector are shown in Fig. 5. In both cases the same experimental conditions were assumed that were met during the S438 beam time: \(^{58}\)Ni beam at 500 MeV/nucleon kinetic energy impinging on the detector made out of EJ204 scintillation material. For the contribution from each single electronic channel 25 ps was used as it was measured during the experiment with the test electronics.

Fig. 5
figure 5

Time precision of the new ToFD detector calculated with GEANT4 (top) and the statistical model (bottom) assuming a \(^{58}\)Ni beam at 500 MeV/nucleon. Shown are different contributions to the total time precision (full thick line): electronics (thin full line), photomultiplier (dashed-dotted line), light production and light transport (dashed line)

Full size image

The agreement between these two sets of calculations is rather good. In both cases, the strongest contribution comes from the electronics. As already mentioned, using the FQT-TAMEX3 read-out for the final detector, we are able to reduce the contribution from the electronics by a factor of two compared to the old electronics. The contributions from the scintillation material - light production and light transport are also rather similar in both cases. Although the two sets of simulations use different shapes for the light pulses, due to the large amount of produced photons, details of the light-pulse shape do not have a strong influence. Somewhat different are the predictions for the contribution of the photomultiplier which in the statistical model is smaller than in the GEANT4 simulation. This can be explained, as in the GEANT4 simulations details of the single-electron response of the photomultiplier have been considered, which was not the case in the statistical model, see Sect. 3.1. Nevertheless, both models show that the design goals concerning timing precision with the new ToFD detector can be fulfilled with the particular combination of components and design parameters.

4 Prototype developments and results

Energy and time precision of the ToFD detector have been studied using a fast LED, a picosecond pulsed diode laser and several different heavy-ion beams at relativistic energies. The prototype detector consisted of 4 layers. Each layer was composed of 6 bars with a length of 800 mm and a width of 27 mm, but those in the first two layers had a thickness of 3 mm, and those in the last two layers a thickness of 5 mm (see Fig. 6). The bars were made of scintillation material EJ204 and were read out at both ends with the R8619-20 PMTs from Hamamatsu. Tests performed with a fast LED have shown (see below) that these PMTs are best suited for our purposes.

Fig. 6
figure 6

Schematic view of the ToFD prototype detector used in the test experiment. On the left part of the figure the front view of the prototype is shown. The inset on the right shows holding structures for scintillator bars and photomultipliers

Full size image

4.1 Readout electronics

To fulfill the design goals of the new ToFD detector, appropriate read-out electronics had to be developed. The electronics need to measure the time and the charge of the PMT pulse with sufficient precision. And, as already discussed above, in order to cope with high-counting rates, new read-out electronics has to have multi-hit capability. The final electronics consists of a front-end board called FQT and a FPGA-based TDC with the name TAMEX3. It is described in detail in this Section. However, many results with prototype detectors shown in this paper were achieved with other electronics. Therefore, we describe in this Section the used electronics in chronological order.

When starting on the R &D for a new ToFD detector, a read-out system based on the general purpose Pre-Amplifier-Discriminator (PADI [43]) together with VFTX modules [35] were available. For the signal shape produced by the ToFD detector, a time precision of about 15 ps per channel can be expected with the PADI system, while the charge is measured by a Time-over-Threshold (ToT) method. In a ToT approach [41], the input signal is compared to a pre-defined threshold value in order to convert collected charge to a digital time signal with a width corresponding to the input charge. A disadvantage of the standard ToT method is the non-linearity between the collected charge and the width of the digitized signal [42] which in our case would result in large difficulties to identify and separate heavy fragments in the lead-uranium region in nuclear charge.

To overcome this problem, a new development based on the TacQuila board, developed originally for the FOPI experiment [37, 38], was initiated. TacQuila is based on a high resolution Time-to-Amplitude Converter ASIC chip for time measurement, and has compact read-out functionality. A time precision of up to \(\sim \)10 ps per channel [34] can be achieved using this board. The TacQuila board runs in a free common-stop mode relative to an external clock. TacQuila-based read-out comprises also a 16-channel Front-End Electronics (FEE) board for signal amplification, splitting and discrimination [39]. Additionally, a control board TRIPLEX [40] offers individual thresholds for each channel, a multiplicity signal, an analogue sum, an ‘OR’ signal, a pulser to trigger the timing branch and a multiplexer. Charge is measured via a Charge-to-Time-Digital-Converter (QTC) board - the input charge signal is shaped and integrated, as in the case of the QTC board, and the signal integration enables a linear charge measurement. The Time-over-Threshold of the integrated signal is then taken as a measure of the deposited energy and for nuclear-charge identification. This overcomes the problem with the non-linearity of the ToT method discussed above.

For the purpose of the R\(^3\)B experiments, on the basis of the TacQuila board, a new front-end electronic board named FQT (Front-End, charge Q and Time) has been developed, and the new version of the system is also adopted for the ToFD detector. The new multichannel electronic card, called FQT-TAMEX3 system [44], is a combination of the new FEE board FQT and an FPGA-based TDC from the VFTX module [36]. The time precision is 13 ps per channel, and the module is multi-hit capable. The FQT board combines the QTC board, the control board TRIPLEX, and the FEE board all in one PCB, whereas for the TacQuila readout these were all on separate boards. Combining several boards into just one reduces the number of required PCBs and the required space, as well as the price per channel.

In the FQT board, the incoming signals are shaped and integrated, thus providing the linearity required for the charge measurement. Tests performed with the new card have shown that the linearity of the charge measurements persists over a large range of PMT signal amplitudes [45]. Digital time signals produced by the FQT board are sent to a TAMEX3 card to determine their leading and trailing edges. The time measurement is split into a fine and a coarse measurement, corresponding to a time relative to the next clock cycle and the number of the clock cycles, respectively. The Time-over-Threshold is then obtained as a difference between trailing and leading times of the integrated signal, and is used in the data analysis as a measure of the energy deposited in the detector by traversing particles. The system also includes a backplane, which enables connections to the low-voltage power supply as well as to an optical link for communication and data transfer. The FQT-TAMEX3 is used for the final detector.

At the time the detector prototype was tested, this electronic card was still under development. Thus, for the prototype testing we have used the PADI-VFTX combination, as well as a prototype of a TAMEX board combined with the LAND front-end [34]. As the TAMEX prototype did not have a QTC included, for several tests with LED we have also used a separate QTC module IWATSU CLC101 [46] combined with the VFTX module. This setup was only used for tests on measurements of the precision in the energy deposit, as the IWATSU CLC101 module has a time precision of the order of 100 ps, and thus is not suitable for our timing measurements.

Fig. 7
figure 7

New multi-channel electronic card FQT-TAMEX3. The card consists of two boards which are plugged together via a multi-pin connector. The board on the right is the front-end-electronics FQT and on the left one can see the FPGA-TDC Tamex

Full size image

4.2 Energy precision of the prototype detector

The energy precision of a prototype of the new ToFD detector was investigated using a test stand with a fast LED, a test stand with laser and also during the GSI beam time in April 2014 (experiment S438). These tests had several measurement goals: Testing the influence of the photomultiplier’s properties on the energy-loss resolution at different counting rates, testing the position-dependence of the measured energy-loss signal, and testing the nuclear-charge resolution for different relativistic beams. The goal of these tests was to find conditions enabling energy resolution of better than 1%, stable over different counting rates in the range 1 kHz-1 MHz.

4.2.1 Photomultiplier choice

Due to the large number (352) of read-out channels, the photomultiplier to be used for the new ToFD detector has to be cost-effective, its diameter should match the width of the bars to obviate any light guides, and in order for the detector to be used in high count-rate experiments it must have a stable gain. The last point implies that the PMT power-supply circuit must have a fully active voltage divider. An active voltage divider ensures that in case of large currents the voltages at the last dynodes, and consequently the gain of the PMTs are kept constant. Without an active voltage divider, the gain of the PMT varies, see e.g. Figure 12.15 in Ref. [47], and thus the peak position in the energy spectrum is strongly dependent on the counting rate. This results in a reduced nuclear-charge resolution for varying beam rates or, in the worst case, no resolution at high rates at all. Another advantage of using a photomultiplier with an active voltage divider is the decreased power consumption.

For the purposes of the NeuLAND detector, Hamamatsu has equipped the R8619 photomultiplier (see Table 4 for its properties) [48] with a fully active base following the work of Kalinnikov et al. [49]. The original version R8619 has only a partly active base (with a capacitor connected to the last three dynodes). The modified version is called R8619-20, and is also used for the new ToFD detector. The photomultiplier is directly glued to the scintillator bar using a silicone glue without any light guides.

The photomultiplier and its influence on the energy precision of a new ToFD detector have been tested using a test stand [50] with a fast LED. The type of LED used in these tests was Osram LB Q39E [51]; it emits blue light with 420 nm wavelength. To obtain realistic conditions, the LED was pulsed in random mode using the programmable pulse generator LeCroy 9210 with external trigger [52]. With this pulse generator, signals of different shapes at different rates can be generated. For comparison, we also studied the original version R8619.

Table 4 Characteristics of the Hamamatsu R8619-20 photomultiplier [48]
Full size table

The pulse frequency of the LED was varied between 5 and 800 kHzFootnote 3. The analog outputs of the PMTs were sent directly to a charge-to-time converter QTC module IWATSU CLC101 [46] where they were shaped and integrated. These signals were then recorded by the FPGA TDC VFTX2 [53] developed at GSI. The voltage of the PMTs was varied in order to extract different charges. The charge resolution, \(\sigma _{Q}\), and shifts of the mean value in the charge spectrum have been recorded at different rates. The results of the test with LED are presented in Figs. 8 and 9.

Fig. 8
figure 8

Relative charge resolution (\(\sigma _{Q} / Q\)) at different rates measured using R8619 (bottom) and R8619-20 with a fully active voltage divider (top) at three different values of extracted PMT charges

Full size image

The relative charge resolution (\(\sigma _{Q} / Q\)) measured with the two photomultipliers at different rates is shown in Fig. 8. While at low extracted-charges both PMTs give very similar results, for larger charges only the R8619-20 PMT with a fully active divider guarantees a stable resolution even for the highest counting rates.

Similar behaviour is seen in Fig. 9, where the shift in the peak position relative to the 5 kHz case as a function of the counting rate is shown for three different values of extracted PMT charges. For the photomultiplier with a fully active base, the shift in the mean charge with increasing rate is smaller than in the case of a PMT with a partly active base. We can see, that for smaller extracted charges, the relative shift in the peak position in the charge spectrum stays below 1% over the whole counting-rate range (5–800 kHz).

The stability of the energy-loss measurement at different counting rates with the new ToFD detector has also been studied with a \(^{58}\)Ni beam at 500 MeV/nucleon during the S438 experiment at GSI. For this, the detector prototype as shown in Fig. 6 was used. In these tests, only R8619-20 PMTs were used.

Fig. 9
figure 9

Shift in the peak position in the charge spectra for different rates measured at three different values of extracted PMT’s charges. Top: R8619-20 photomultiplier with active base, bottom: R8619

Full size image

Figure 10 shows nuclear charges determined using the prototype detector for the incoming \(^{58}\)Ni beam and its reaction products. The voltage of the PMTs was set to 500 V, corresponding to a PMT signal height of about 200 mV (top left and right, and bottom left in Fig. 10) and to 400 V corresponding to 60 mV signal height (bottom right in Fig. 10). By fitting the main peak we obtain a nuclear-charge resolution of \(\sigma _{Z}\) = 0.19 charge units (for \(Z=28\)) at the lowest rate of 5 kHz, which corresponds to \(\sigma _{Z}/Z\) = 0.68%. Even at the highest rate of 1000 kHz an excellent relative nuclear-charge resolution of 0.84% has been obtained, which is well below the required value of 1.5% to separate Ni from Co.

A summary of all measurements with \(^{58}\)Ni beam is shown in Table 5. Nuclear-charge resolution as well as the shift in the position of the main Z = 28 peak relative to the 5 kHz measurement are presented. One can see that up to about 300 kHz counting rate, the shift is about 1% or less. Only at higher rates the shift becomes larger than 1% which is not acceptable.

The situation can be considerably improved if one performs measurements with a smaller amplitude of the PMT signals. By decreasing the HV values to 400 V, corresponding to about 60 mV PMT signal height, we reached, during the experiment, very stable nuclear-charge measurements, where the relative shift in Z remained below 1% also for the highest rates of 1000 kHz while still keeping the excellent nuclear-charge resolution, see Fig. 10 bottom right. Of course, one has to compromise in the usable dynamic range, as is clearly seen from the figure.

4.2.2 Position-dependence of the energy-loss signal of the prototype detector

Due to light attenuation along a scintillator bar, the energy \(E_{\text {PMT}}\) measured by a single PMT depends on the position of the fragment impact along the bar [54]: \(E_{\text {PMT}}=E_{0}\cdot \exp (-\lambda \cdot x_{\text {PMT}})\), where \(E_{0}\) is the deposited energy, \(\lambda \) the absorption coefficient, and \(x_{\text {PMT}}\) the distance between the impact point of the fragment and the PMT. If a scintillator bar is read out at both far ends, as it is in our case, then the deposited energy \(E_{0}\) can be obtained from the geometrical mean of the energies obtained by the two PMTs:

Fig. 10
figure 10

Nuclear charge of the reaction products for a \(^{58}\)Ni beam at 500 MeV/nucleon measured with the prototype of the ToFD detector at several counting rates. The spectrum is obtained from the scintillator bars read out with PADI coupled to VFTX. Top left: 5 kHz count rate; top right: 375 kHz; bottom left: 1000 kHz; bottom right: 1000 kHz and 400 V

Full size image
$$\begin{aligned} E_\textrm{geom}= & {} \sqrt{E_{\text {PMT1}}\cdot E_{\text {PMT2}}}\nonumber \\= & {} E_{0}\cdot \sqrt{\exp (-\lambda \cdot x_{\text {PMT1}})\cdot \exp (-\lambda \cdot x_\text {PMT2})}\nonumber \\= & {} E_{0}\cdot \exp (-\lambda \cdot L/2), \nonumber \\\Rightarrow & {} E_{0} = \sqrt{E_\text {PMT1}\cdot E_\text {PMT2}}\cdot \exp (\lambda \cdot L/2) \end{aligned}$$
(15)

where \(L=x_\text {PMT1}+x_\text {PMT2}\) is the bar length.

Ideally, the measured energy as calculated according to Eq. 15 should be independent of the impact position of the fragment. In reality, this is not the case. Additional effects such as light refraction on the surface of the scintillator or light reflections at the ends of the scintillator have an influence on the number of photons detected by each PMT, and thus on the measured energy. As these effects depend on the impact position of the fragment, they result in position-dependence of the measured energy beyond Eq. 15. In order to obtain the required nuclear-charge resolution, one has to avoid or correct for the position-dependence of the measured deposited energy.

Table 5 Nuclear-charge resolution measured with the ToFD prototype at different counting rates. Also shown (last column) is the shift in the position of the main peak relative to the 5 kHz run
Full size table

Firstly, we have tested the influence of different wrapping materials on the measured energy. We have performed two sets of measurements, one using a laser test-stand and one using \(^{48}\)Ca beam at 550 MeV/nucleon kinetic energy. For the laser test-stand [55], a Picosecond pulsed Diode Laser PDL 800-D from PicoQuant GmbH [56] was used. With the driver, which is part of the laser system, it was possible to change the repetition frequency as well as the light output, thus simulating different experimental conditions. In both cases, several wrapping materials were tested: no wrapping, TYVEK [57], 3M Enhanced Specular Reflector (ESR) film [58] and standard aluminum foil.

Both sets of measurements show a strong influence of the wrapping material on the position-dependence of the deposited energy. As an example, we show in Fig. 11 results measured with a \(^{48}\)Ca beam and with Al-foil (top), no wrapping (second from top), with ESR as wrapping material (third from top) and TYVEK (bottom). In each figure the deposited energy, calculated as \(\sqrt{E_{\text {PMT1}} \cdot E_{\text {PMT2}}}\), is plotted as a function of the beam-impact position. The beam-impact position is calculated with the time difference of the PMT signals at both ends of the scintillator.

The influence of position dependence was smallest for aluminum wrapping. In case of ESR material, the behavior of energy with position is opposite to the case with no wrapping: the measured energy decreases while approaching the photomultipliers. Figure 11 also shows, that in case of all wrapping materials the measured energy is higher as compared to the case of no wrapping. This is due to photons which finally reached the PMTs after many reflections on the wrapping material. In experiments with low-photon statistics this effect is desirable. In our case, these late photons do not improve the energy resolution (as heavy-ion beams produce enough photons) but instead result in long tails in the measured energy signals [59]. These long tails do not improve the energy resolution, but they introduce pile-up at high counting rates. Thus, we have rejected any refractory material, even aluminum, as the wrapping material in order not to be limited in counting rate due to long signals.

Fig. 11
figure 11

Non-calibrated deposited energy as a function of the \(^{48}\)Ca impact position for bars without any wrapping material (second from top), for bars wrapped with Al-foil (top), ESR (third from top) and TYVEK (bottom)

Full size image

As a final configuration, we have opted for a non-refractory light-tight 10 \(\mu \)m-thick black foil as a wrapping material. This option was chosen in order to avoid cross-talk between two neighbouring bars without introducing long tails in the signal shape, as in this case all photons leaving the scintillator are absorbed by the foil. The position dependence of the energy-loss signal in the case of bars wrapped with a black foil is almost identical to the case of no wrapping.

By looking at Fig. 11, one can see strong edge effects approaching the ends of the bars at \(+40\) cm and \(-40\) cm. In order to avoid these effects, we have decided to make the final detector somewhat larger than the active area required in the R\(^3\)B setup by increasing the length of the bars from 80 cm (as it was in the prototype detector) to 100 cm for the final detector.

In order to correct offline for the observed position dependence of energy-loss signals, we have tested several functions [59]. The best results have been obtained by fitting a two-component exponential function to the measured energy of a single PMT, as proposed in Ref. [60]:

$$\begin{aligned} \begin{aligned} E_{\text {PMT},i} = {}&E_{\text {PMT},i}^{0} \cdot \exp (-\lambda _{i,1} x_{\text {PMT},i}) \\&\quad + E_{\text {PMT},i}^{0} \cdot \exp (-\lambda _{i,2} x_{\text {PMT},i}), \\&i=1,2, \end{aligned} \end{aligned}$$
(16)

where \(E_{\text {PMT},i}^{0}\), \(\lambda _{i,1}\), and \(\lambda _{i,2}\) are fit parameters.

In this way, we improve the precision of an energy-loss measurement by a factor of 1.6 in the experiments with heavy-ion beams (see below and Table 6). Equivalent results to the above-described approach are obtained using the geometric mean and then correcting the position dependence of each bar with a polynomial of second order.

4.2.3 Tests of the prototype detector with heavy-ion beams

To test further the accuracy of the new detector concerning nuclear-charge precision for heavier beams, we have performed tests with a stable \(^{124}\)Xe beam at 600 MeV/nucleon and a radioactive \(^{194}\)Bi beam at 700 MeV/nucleon. The measured nuclear-charge spectra for these two cases are shown in Fig. 12. Even in case of Bi, there is a clear separation between single nuclear charges.

Fig. 12
figure 12

Nuclear-charge spectra of reaction products from \(^{124}\)Xe at 600 MeV/nucleon (top) and \(^{194}\)Bi at 700 MeV/nucleon (bottom). The background present in both spectra is due to a large amount of different materials and detectors that were located in front of the ToFD prototype during the test experiments

Full size image

In Table 6 a summary of the nuclear-charge precision measured with several different heavy-ion beams during the test beam time is shown. The charge resolution was obtained by a Gaussian fit of individual peaks. It can be seen, that in all cases the design goals are met.

Please note that the measured values given in Table 6 are the “worst-case” values. In all beam tests listed above, the prototype detector was tested in a parasitic mode, at the end of the beam line in air, with many other detectors and layers of matter in front of it. These conditions do not correspond to the experimental conditions in which the ToFD detector will be used.

Table 6 Nuclear-charge resolution measured with the new ToFD prototype and corrected for the position dependence as described in Sect. 4.2.2. Also shown (last column) is the nuclear-charge resolution required to separate Z from \(Z-1\)
Full size table

4.3 Time precision of the prototype detector

First tests of the timing precision of the ToFD prototype have been performed during the S438 experiment using \(^{58}\)Ni beam at 500 MeV/nucleon and at various counting rates. Later, additional tests using \(^{124}\)Xe at 600 MeV/nucleon, and \(^{194}\)Bi (secondary beam) at 700 MeV/nucleon were performed.

For the determination of the time precision we plot the time difference of hits between the first and second plane of the detector and perform a Gaussian fit. In the case of \(^{58}\)Ni beam at 500 MeV/nucleon with 5 kHz rate a value of \(\sigma _t\) = 41 ps is obtained. For an overview of all measured rates, see Table 7.

Assuming that the scintillators of the two planes have similar performance, \(\sigma _t\) = 41/\(\sqrt{2}\) ps = 29 ps is obtained for the time precision of one scintillator. To estimate the performance of the full detector where the time will be measured with four planes and against a start detector with much better time precision, this value is divided by \(\sqrt{4}\), yielding \(\sigma _{t}^{\text {det}}\) = 14 ps. For a flight path of 20 m, this would correspond to a relative time precision of \(\sigma _t / t\) = 0.016%, which is smaller than the design goal of 0.02%. Even at 1000 kHz one could reach a time precision for the whole detector of 23 ps, which is rather close to the design goal. Please note, that the contribution from the electronics amounted to 25 ps per read-out channel in the \(^{58}\)Ni run. The developments which took place since then have resulted in an electronic time precision of 13 ps per channel.

Table 7 Time precision measured with the new ToFD prototype between two bars at different counting rates for PMT signal heights of \(\sim \)200 mV. Also shown (last column) is the time precision expected for the full detector with four planes. Data were measured with \(^{58}\)Ni at 500 MeV/nucleon
Full size table

The measured time precision of 14 ps agrees very well with the results of simulations presented in Sect. 3.3. In the simulations, see Fig. 5, we obtain about 15 ps for low values of photoelectron threshold and about 10 ps for the higher photoelectron thresholds. This good agreement between simulation and experimental data confirms that our design goal of \(\sigma _t / t\) = 0.02% for the relative time precision can be reached with the new detector.

Table 8 summarizes the time-precision measurements of the ToFD prototype. Comparing these values with the values given in Table 1 one clearly sees that the new detector fulfills the design goals on time precision. However, one should keep in mind, that the values measured here give the intrinsic time precision of the detector. In an experiment, one needs time-of-flight information for fragments having different nuclear charges and having different velocities. Since a leading-edge discriminator is used in the electronics, the measured time-of-flight is influenced by a walk effect. Thus, although the ToFD detector has an excellent intrinsic time precision, the overall timing for all charges in the experiment depends critically on the quality of the walk correction.

Table 8 Time precision between two bars of the ToFD detector. Also shown are corresponding time precisions of the whole detector, and the time precision required to separate \(A_{\text {proj}}\) from \(A_{\text {proj}}-1\) at the corresponding beam energy. We see, that in all cases the measured time precision of the prototype detector is better than required
Full size table

5 Mechanical design

The mechanical design of the ToFD detector (see Fig. 13) foresees a modular design with two frames, each frame containing two layers of scintillator bars.

The two frames can be combined to form a light-tight housing or used individually at different positions in the setup. At the front and the rear side, the detector is closed by two end-covers holding a thin black plastic foil with a thickness of 100 µm in order to make the assembly light-tight. The frames of the ToFD detector, are quadratical and can be mounted with bars in vertical or horizontal alignment dependent on the experiment.

Each plane contains 44 vertical scintillator bars with the dimensions 1000\(\times \)27\(\times \)5 mm\(^3\). The bars of two successive planes are shifted by half a bar width. In this way the small gap between two bars is covered by the previous or by the next plane. Each bar is read out by PMTs on both far ends. The mounting of the PMTs and the scintillators is done in a way to ensure quick replacement if necessary. Especially for high beam rates one expects radiation damage of the bars which are hit by the unreacted beam and, therefore, a more frequent exchange of scintillators in this region is required.

Fig. 13
figure 13

Mechanical design of ToFD: The detector is mounted on an \(\textit{x/y}\)-table, which allows to move the detector through the beam. In this way the position calibration, gain matching and time-offset determination can be performed. The bands at the top and bottom are made of Mu-metal and can be used for magnetic shielding of the PMTs when the detector is mounted close to the superconducting magnet GLAD. The electronics is mounted on the left and right side (green boxes)

Full size image

The detector is positioned on a table, see Fig. 13, which allows to move the detector in the x- and y-direction. This facilitates the calibration of the whole surface of the detector with unreacted incoming beam.

The high voltage distribution is realized by CAEN multi-pin HV modules. Each module has 28 channels and 16 multi-pin connectors are distributed along the frames. The signal cables are connected to 8-fold MMX connectors, matching the 8-fold geometry of the front-ends of the readout electronics.

6 Results of the final detector

After the design studies and prototype tests, the final ToFD detector was built and used for the first time for experiments carried out during the FAIR phase-0 physics program in 2019. A calibration and analysis code was developed and included in R3BRoot [61], which is the simulation and analysis framework of the R\(^{3}\)B collaboration. In this Chapter we want to outline the calibration procedure and show first results obtained with the new detector.

The calibration procedure consists of several steps. The beam spot of the unreacted beam on the detector is only a few cm in diameter. In a first step, the detector is moved in the x-direction through the beam and all bars are irradiated in the center. The measured spectra are analyzed and with a semi-automatic procedure the voltages of all PMTs are adjusted to obtain a similar gain.

After adjusting the HV, the detector is moved once more in x-direction through the beam. The beam hits the center of the bars and the time-offsets of all PMTs are determined in a way that the time difference between the two PMTs attached to the same bar is zero. In the same step, a time synchronisation is also done so that all barsFootnote 4 show the same time-of-flight relative to a start detector.

Afterwards, the x/y-table is moved by a well defined distance in y-direction and with another movement in x-direction the position calibration in y-direction is obtained. The position along a bar can either be calculated by the time difference or by the ratio of the energy deposit.

Finally, the detector is moved in a meander pattern through the beam, making sure that the full length of each bar is hit by the ions. With this data the correction of the position-dependent charge measurement is performed.

After these calibration steps, which can be performed in a rather short time of a few hours, the detector is ready for the experiment. To demonstrate the performance of the detector we present results from the S473 experiment, where a stable \(^{120}\)Sn beam at 800 MeV/nucleon impinged on a 4.5 mm thick carbon target. Both the unreacted beam and the reaction products hit the ToFD detector. The diameter of the beam spot of the unreacted beam is rather small and only a few scintillator bars in the center of the ToFD detector are hit. The reaction products are distributed over a larger area. In the current study we have selected an area which is outside of the beam spot of the unreacted beam in order to give more emphasis to the reaction products. Otherwise the spectra are dominated by contributions from the unreacted beam.

To determine the time precision, the nuclear charge of the reaction products is plotted against the time difference between plane 1 and 2 (see Fig. 14). One can see how the time precision gets worse for smaller nuclear charges which is mostly due to lower photon statistics for smaller nuclear charges. A Gaussian fit on the events with nuclear charge 50 yields a time precision of \(\sigma _{t}\) = 37 ps. This corresponds to \(\sigma _{t}\) = 13 ps for the full detector with four planes.

Fig. 14
figure 14

The measured time difference between plane 1 and 2 for particles with different nuclear charges. A projection of selected nuclear charges on the x-axis yields the time precision. For charge 50 \(\sigma _{t}\) = 37 ps is obtained

Full size image

The electronics used for the detector has a leading-edge discriminator which results, as already mentioned, in a strong walk effect. In Fig. 14 this cannot be seen since all bars have a similar walk effect, and for time differences within the detector the effect is mostly negated. However, for the time-of-flight of the particle from the start detector to the ToFD detector this effect can be seen and the precision of the full time-of-flight measurement depends on the walk correction.

Figure 15 shows the measured nuclear-charge distribution of the fragments. An excellent nuclear-charge precision of \(\sigma _{Z}\) = 0.22 charge units or 0.44% was obtained. This can be even slightly improved by applying a velocity correction, since the fragments have a spread in velocities after a rather thick carbon target. The results were obtained by averaging the charge measurement of all 4 planes and using the bars on one side of the detector excluding the central part where the nuclear-charge spectrum is dominated by the unreacted beam particles.

Fig. 15
figure 15

Nuclear charge of the reactions products from the reactions of \(^{120}\)Sn beam at 800 MeV/nucleon with a carbon target and measured with the new ToFD detector

Full size image

In order to obtain the correct nuclear charge, the measured ToT-spectra of all bars have to be calibrated. The peaks in the spectra are located and by counting down the charge, from the known nuclear charge of the unreacted beam, the corresponding nuclear charges are assigned. Afterwards a fit of a polynomial function of second degree is used as calibration. Since the measured ToT is proportional to the energy loss of the ions in a scintillator bar, a quadratic dependence is expected. However, as discussed in Sect. 3, quenching can reduce the light production in a scintillator. In Fig. 16 the obtained experimental function is compared with the methods used for the simulations. The measured relation between the charge from the ToT-signal and the nuclear charge is almost linear and lies between the values given in Ref. [30] and the calculation with Birk’s law (see Eq. 14) used for the simulations. However, also other effects, e.g. saturation in the PMT or non-linearities in the electronics chain, can cause a similar behaviour. Therefore, not all losses can be uniquely attributed to quenching.

Fig. 16
figure 16

Comparison of light quenching factors for Ref. [30] (dashed line), Birk’s law (dash-dotted line) and measured with the reaction products of a \(^{120}\)Sn beam (solid line). For comparison, also a quadratic function assuming no quenching is plotted (dotted black line). All lines are normalized to a nuclear charge value of 10

Full size image

7 Summary

A new time-of-flight wall has been designed as part of the R\(^3\)B setup at GSI and FAIR, prototypes have been tested and the final detector has been built. The detector is used to detect and resolve nuclear-charge and mass of heavy-ion fragments up to the lead-uranium region at relativistic energies.

The detector has an active surface of 1200\(\times \)1000 mm\(^2\), and consists of four planes of scintillators. Each plane contains 44 vertical scintillator bars with the dimensions 27\(\times \)1000\(\times \)5 mm\(^3\). Each bar is read out by photomultipliers on both far ends. The width of the single bar is matched to the size of a PMT, in order to omit light guides, and couple the scintillator bars directly to the PMTs, maximizing the light collection.

First results obtained for in-beam measurements during the FAIR Phase-0 program show that the design goals - a relative energy-loss precision of \(\sigma _{\varDelta E}/{\varDelta E} < 1\%\) and a relative time precision of \(\sigma _t/t< 0.02 \%\) - are fully met. This will allow, together with an elaborate particle-tracking system, the full identification of heavy-ions up to the lead-uranium region in mass and nuclear charge.