The new high-performance detector for measuring fragment starting time and position at the dispersive plane has been designed and constructed. Its schematic layout is shown in Fig. 2(a). It is composed of a 100 mm×100 mm×1 mm EJ 232 scintillator sheet and a plastic scintillator strip array with a sensitive area of 100 mm×100 mm.
The scintillator sheet is read out on four sides, each by 10 silicon photomultipliers (SiPMs) from Hamamatsu Photonics (MPPC S13360-6075PE). The 10 SiPMs are mounted on a Printed Circuit Board (PCB) and connected in series, which is good for getting a better time resolution because detected light yields increase and smaller capacitance makes a rise time faster[18]. The start time of fragments can be defined as a quarter of the sum of times measured by the SiPMs attached to the four sides of the scintillator sheet. This can effectively eliminate the effect of the fragment hitting positions on the time resolution.
The plastic scintillator strip array is placed downstream of the scintillator sheet. It has 50 detector modules, and each module consists of an EJ212 scintillator strip with a dimension of 120 mm×2 mm×0.5 mm and two SiPMs (MPPC S13360-3050PE) coupled to both ends for readout. The fragment position information at the F1 with a resolution of 2 mm in the horizontal direction can be obtained from this scintillator strip array.
All the SiPMs output signals from the scintillator sheet and the scintillator strip array is fed into a specific high-resolution time measurement module. It is a 6U PXI module and can measure the time information with a 25 ps time resolution for 16 SiPM signals simultaneously[19].
The new ToF start detector has been installed in the F1 dispersive plane at the RIBLL2. It is inserted into a vacuum box shown in Fig. 2(b). This vaccum box has thin windows in both sides, and each window has an area of 100 mm×100 mm covered by a 0.1 mm thick stainless steel foil. When inserted, the center of the new start detector will overlap with the center of two windows. The mobility of the detector is accomplished by connecting the vaccum box to the F1 chamber using a long bellows seal. By compressing the bellows, the detector can be moved within a range of 200 mm, which assures the detector is online or offline.
In the experiment, the 78Kr beam passing through the target was utilized to test the performance of the new ToF start detector. Fig. 3(a) shows the measured ToF spectrum, where the ToF is calculated by the time difference between the scintillator sheet detector at the F1 and the stop detector at the ETF. A room-mean-square(RMS) ToF resolution of ~221.9 ps was obtained. The main contributions to this ToF resolution include time resolution of time detectors, energy straggling of the beam in the target, and variance in the flight path length. According to ion-optical transformation, both the energy straggling and the flight path length is related to the fragment positions at the F1 dispersive plane. A correlation between the ToF and the position at the F1 is plotted in Fig. 3(b), and a dependence of ToF on positions is observed. To correct the effect of position on ToF, we introduce the following formula
Here ToF and ToFraw are the measured ToF and corrected ToF, respectively. The c is the correction coefficient. It can be obtained by linearly fitting Fig. 3(b). Using this formula the ToF spectrum was corrected and shown in Fig. 3(c). An obvious improvement in the time resolution from ~221.9 to ~186.7 ps is obtained after this correction. It is slightly better than the calculated value of Eq. (1).
Assuming that the intrinsic time resolution of the readout of both ends of a detector are the same, then for a detector illuminated by a small beam spot the width of the time difference between the times measured from both ends can indicate $ \sqrt 2 $ times of the timing resolution of the detector. Fig. 3(d) shows the time difference spectra between the times measured from the left and right sides of the ToF start and stop detectors in the 78Kr experiment. The horizontal beam spot size on the ToF start and stop detectors is limited to be 10 mm using the position information measured with the plastic scintillator strip array and MWDC detectors, respectively. According to the fitting results, the time resolutions of the ToF start and stop detectors is evaluated to be ~58.7 and ~140.5 ps, respectively. The worse time resolution of the ToF stop detector is caused mainly by poor H6410 photomultiplier performance, which has a slow rise time (~2.7 ns) and large transit time spread (~1.1 ns). By using the fast time photomultiplier likes R2083 from Hamamatsu Photonics or SiPMs connected in series likes readout in the ToF start detector in place of H6410 photomultiplier, the time resolution of the ToF stop detector can be expected to be improved.
According to the coincidence measurements of ΔE, ToF, and Bρ, the atomic number Z and the mass-to-charge ratio A/Q of the fragments produced in the reaction 78Kr+Al2O3(1.84 mm) at 300 MeV/nucleon were determined and shown in Fig. 4(a). In the calculation of A/Q, the fragment Bρ values were fixed at 5.44 Tm. From the results, it is obvious that all the elements can be clearly separated. The fragment charge spectrum obtained from the projection on the Z axis is shown in Fig. 4(b). The charge resolution is approximately ~0.25 charge units (RMS) for the lower Z elements, which have small energy loss in the MUSIC. With the increase of the charge number, the charge resolution becomes slightly better and a good charge resolution of ~0.19 charge units (RMS) was achieved for the As element. Compared to the charge resolution, however, a poor fragment mass resolution was obtained even for the light fragments, and the isotopes from Ca to Se can not be identified unambiguously. This is mainly because of the large Bρ spread resulted from the fully opened slits at the F1. In this case, a precise Bρ measurement should be used instead of the constant value.
In the case of the horizontal plane, the ion-optical transformation is given by
Here x1 is the horizontal position at the image position. The x0 and a0 represent the horizontal position and angle at the object position, respectively. The first-order matrix elements (x|x), (x|a), and (x|δ) denote the image magnification, the angular dependence, and the momentum dispersion, respectively. The Bρ0 is the central magnetic rigidity. Using this relationship, the precise Bρ determination could be realized with the measured coordinate information at the object and image positions.
Using Eq. (3), the Bρ values have been determined with the designed matrix elements. For fragments transported from the F0 to the F1, the design values of (x|x), (x|a), and (x|δ) are 0.54, 0, and 11.69 mm/%, respectively. Assuming negligible spot size at the F0 object position, the Bρ values can be calculated simply from the following equation
Here xF1 represents the positions in the horizontal plane at the F1. Using the designed dispersive value of 11.69 mm/% and the horizontal positions measured with the new ToF start detector at the F1, the Bρ values of the fragments were determined and the A/Q values were recalculated and shown in Fig. 5(a). All the isotopes from Be to Se can be distinguished obviously compared to Fig. 4(a). But for the fragments in the region of Ca to Se, the mass resolution is still poor. That is because the designed (x|δ) value was used in the calculations. The difference between the designed and experimental momentum-dispersion values results in a non-negligible deterioration of the Bρ and mass resolutions.
According to the measured various correlations between the F1 and ETF foci, the experimental image magnification and momentum dispersion can be derived using Eq. (3). For example, in the experiment, the angular dependence (x|a) equals zero if the focusing is realized. The gradient of the correlation between the xF1 and xETF gives the (x|x) element if the events with (Bρ- Bρ0)/Bρ0≈0 are selected, and the correlation between the (Bρ- Bρ0)/Bρ0 and xETF allow us to determine the (x|δ) element if the events with xF1≈0 are selected.
To further improve the Bρ resolution, the derivation of the first-order matrix elements has been made in this 78Kr fragmentation experiment with the selected isotope 75As33+ which is circled with a solid line in Fig. 5(a). The (Bρ- Bρ0)/Bρ0 values were obtained from the ToF measurement. The correlation between xETF and xF1 for (ToF-ToF0)/ ToF0<0.02% and between xETF and (Bρ-Bρ0)/Bρ0 for xF1<2 mm with the selected isotope is plotted in Fig. 5(b) and (c), respectively. The experimental image magnification of –1.0±0.09 and momentum dispersion of (14.24±0.83) mm/% are obtained with these correlations. The increase in momentum dispersion is mainly caused by the additional 9o dipole magnet near the ETF focus labeled as D01 in Fig. 1. Using the experimentally derived matrix elements, the Bρ values of the fragments were recalculated and the A/Q values were again determined and shown in Fig. 6(a). It is obvious that there is a significant improvement compared to Fig. 5(a) and the fragments up to Se element can be identified unambiguously.
The A/Q spectra of Ne, Ca, and As isotopes are shown in Fig. 6(b), (c), and (d), respectively. The fitting results display that the mass resolution gets better with the increase of fragment mass number. That is because in the data processing we focused mainly on heavy isotopes that are difficult to the identification. The 75As isotope, which has higher yields, was selected for the derivation of the experimental matrix elements. This may cause the light mass isotopes to have poor mass resolutions. However, the current mass resolution is enough for the light isotopes. The absolute RMS A/Q resolution for 75As33+ is as high as σA/Q~5.8×10-3, revealing the importance of the derivation of experimental matrix elements for the precise Bρ determination.
In data processing, the effect of the angular dependence (x|a) in Eq. (3) was ignored. That is because only the position information can be used without angles. If the incident angles at the F1 and ETF foci can be measured in the future, the (x|a) element can be derived from the experimental data likes the (x|x) and (x|δ) elements. This may further improve the accuracy of the Bρ determination and get better particle identification.