Efficient positron trapping and extraction with a center-hole SiC remoderator

Trapping technologies of positrons, the antimatter counterpart of electrons, are indispensable for various atomic, molecular, and optical experiments and for material analyses that use positron swarms. Efficient trapping of high-intensity positron beams generated by electron linear accelerators (LINACs) will improve the quality and throughput rate of experiments but have yet to be practically realized. In the present work, we demonstrate the efficient trapping and extraction of a LINAC-based positron beam by using a silicon carbide (SiC) remoderator with a center hole. The positron beam was remoderated by 4H-SiC wafers in the back-reflection geometry followed by accumulation in an electromagnetic trap with CF4 cooling gas. A rotating electric field was driven to spatially compress the accumulated positrons, enabling the lossless extraction of the positrons through the SiC hole. A trapping efficiency in the higher 20% range was achieved. The proposed trapping scheme employing a center-hole SiC remoderator is thus a practical technique to accumulate and cool positron beams generated by LINACs.


Introduction
Over the last few decades, trapping technologies of positrons, the antimatter counterpart of electrons, have been advanced by the development of particle beam and plasma science. A series of operations such as the accumulation, cooling and manipulation of positrons in an electromagnetic trap enables us to generate high-density cold positron swarms, which can be used as sources for exotic atoms and molecules involving positrons [1][2][3], quantum degenerate gas of positronium, which is the bound state of an electron and a positron [4], and electron-positron-pair plasmas [5]. Furthermore, well-cooled positron beams extracted from such traps (so-called trap-based positron beams) [6] are of high quality and operability, making trap-based beams powerful tools for investigating atomic and molecular interactions with positrons [7,8], optical spectroscopy of positronium systems [9] and material characterization [10].
Various techniques are available to accumulate positrons (see the review [11] for details). For instance, an accumulation scheme with nitrogen buffer gas [12,13] has become widespread, providing the highest trapping efficiency of 20%-30%. In this scheme, the a 1 Π electronic excitation of nitrogen molecules is used to dump the energy of incoming positrons. Radioisotope-based slow positron beams generated by combining 22 Na positron sources with various moderators are conventionally fed into a buffer-gas trap. Positron beams supplied by nuclear reactors and electron linear accelerators (LINACs) have intensities a few orders of magnitude greater than that of typical radioisotope-based beams. For example, LINAC-based positron beams with intensities of 10 7 -10 8 e + s −1 are available at the European Organization for Nuclear Research (CERN)'s antiproton decelerator (AD) by the gravitational behaviour of antihydrogen at rest (GBAR) Collaboration [14], the slow positron facility (SPF), Institute of Materials Structure Science (IMSS), High Energy Accelerator Research Organization (KEK) [15], and the National Institute of Advanced Industrial Science and Technology (AIST) [16]. Feeding such beams into a buffer-gas trap should improve the trapping rate and thereby increase the number of accumulated positrons. Independent attempts to accumulate LINAC-based positron beams were made at CERN AD by the GBAR Collaboration [17,18] and at AIST [19]. However, the trapping efficiencies of these attempts were 4%-6%, which were most likely due to the broadening of the parallel energy distribution in the trap magnetic fields (50-60 mT) and their beam intensities were not fully utilized. The energy range in which positrons are efficiently trapped in collisions with nitrogen buffer gas is as narrow as ∼3 eV [20], so the larger energy spread of the LINAC-based beam [19] could significantly decrease the trapping efficiency.
A different approach to accumulate the LINAC-based beam is now under development by the GBAR Collaboration using a silicon carbide (SiC) remoderator instead of a nitrogen buffer gas [21]. Since n-type SiC crystals have negative positron work functions of approximately −2 eV, and the positron diffusion lengths in these materials are remarkably long, positrons impinging upon SiC are moderated and then efficiently re-emitted from the surface with a low energy of approximately 2 eV [22][23][24][25][26]. The efficiency of this re-emission process for n-type SiC can reach 60% for positrons of less than 1 keV incident energy [23,26], although the epithermal positron component may be included [25]. Furthermore, the energy spread of re-emitted positrons has also been measured to be about 1 eV (σ) using a retarding potential method [25,26], in which the positrons are selectively repelled by varying retarding voltage to measure their energy distribution. Therefore, positrons incident upon the SiC are efficiently converted to a low-energy, monoenergetic beam. Such SiC remoderators are thus promising for use as energy dumpers to replace the buffer gas in trapping schemes, especially for positron beams with large energy spreads. The GBAR Collaboration reported a tentative trapping efficiency of 40% [21] using epitaxial grown n-type 4H-SiC in the reflection geometry, with positrons re-emitted from the SiC being stored by an electrostatic potential barrier formed in front of the SiC. The remaining issue for this scheme is how to extract the accumulated positrons from the trap, since the SiC is positioned at the trap exit. A system that performs this extraction is under study; it has a movable SiC holder or diocotron mode manipulation [21].
In the present work, we demonstrate the efficient trapping and extraction of a LINAC-based positron beam with a center-hole SiC remoderator. The irreversible shapes of incoming and outgoing beams in the trap enable the efficient extraction of the accumulated positrons through the hole in the SiC. Positrons accumulated in the trap with the SiC remoderator are spatially compressed by using the rotating-wall technique and then extracted through the hole. This practical positron trapping technique based on a SiC remoderator allows the efficient accumulation of LINAC-based positron beams. This paper gives the details of the apparatus and reports the performance of the system.

Experimental setup
The demonstration used a slow positron beam generated by the electron LINAC (40 MeV, approximately 300 W) at AIST. The accelerated electron beam was dumped onto a tantalum converter, and the derived positrons were moderated by using a tungsten foil assembly arranged in a grid shape to produce a slow positron beam [27]. The positrons formed 0.5 µs square pulses at a repetition rate of 40 Hz (reflecting the structure of the electron beam). A solenoid field of 6 mT magnetically transported a positron beam with a maximum intensity of approximately 6 × 10 6 positrons/s (2 × 10 5 positrons/pulse) and an elliptical shape (major axis: about 10 mm, minor axis: about 5 mm), to a SiC-based positron trap. The transport energy of 150 eV was controlled via the voltage of the moderator (tungsten foil).
A SiC-based positron trap was constructed by incorporating a SiC device into an electromagnetic trap used for the buffer-gas trap [19,28]. Figure 1(a) shows a schematic of the trap system. The main components included a multi-ring electrode, a cooling gas (CF 4 ) outlet and a center-hole SiC remoderator. The multi-ring electrode was situated in a uniform magnetic field of 60 mT formed by a magnetic solenoid coil, while the gas outlet and the SiC remoderator were situated near the coil end (50 mT). The multi-ring electrode was a coaxial array of cylindrical electrodes with an inner diameter of 60 mm, with one of the electrodes close to the center segmented into four parts in the azimuthal direction to apply 90 • -phase-shifted sine waves to the electrodes (rotating electric field). Potential configurations for the accumulation of positrons were formed by applying arbitrary voltages to each electrode. The vacuum of the trap system was maintained at a base pressure of 1 × 10 −6 Pa by using turbomolecular pumps and a cryo-pump (Ulvac Cryogenics Inc., CRYO-U8H). The remoderators used in this demonstration were commercial 10 mm-square n-type 4H-SiC (0001) wafers made by Xiamen Powerway Advanced Materials. The wafer surfaces were processed by using chemical mechanical polishing. The resistivity of the wafers was 15-28 mΩ cm, enabling us to apply a voltage to the surface. Following the previous report [26], the pristine wafers were used without any treatment. To eject accumulated positrons downstream from the trap, four wafers were staggered and arranged in a clover shape to form a center hole, as shown in figure 1(b). The hole was designed to be a 2 mm square through which accumulated positrons with a diameter of less than 1 mm passed without particle loss. The position of the SiC remoderator (and its center hole) was adjusted by using an XYZ-linear stage with a precision of 0.01 mm.
In the first step, the positron beam injected into the trap (with flowing CF 4 cooling gas) passed through a pipe with an inner diameter of 23 mm and the multi-ring electrode to impinge onto the center-hole 4H-SiC in back-reflection geometry. Since the beam size in the trap was expected to be less than 3 mm in diameter, the beam loss by hitting with the cell and electrode was not observed. Furthermore, the positron beam with 150 eV was not reflected by a trap potential used in this demonstration, implying the lossless beam injection into the trap. Note that the incoming positron beam may have been affected by collisions between it and the CF 4 gas; however, the effect was considered negligible in our gas-pressure range [29]. A fraction of the positrons impinging on the SiC was remoderated and then re-emitted from the surface with an energy of approximately 2 eV (due to the positron work function) [24][25][26]. The re-emitted positrons were trapped in the potential barrier formed in front of the SiC with the CF 4 cooling gas. A rotating electric field [30,31] was applied to the accumulated positrons to drift the positrons toward the center of the trap axis (radial compression). Finally, the accumulated positrons were extracted through the hole in the SiC and dumped onto a phosphor screen 24 mm in diameter and biased at −1.4 kV. The screen was located at a magnetic flux density of 6 mT. The shape of the positron beam was monitored by imaging the fluorescence from the phosphor screen with a charge-coupled device (CCD) camera. The annihilation gamma rays of the positrons from the phosphor screen were also detected by a plastic scintillator coupled to a photomultiplier tube (Hamamatsu, H6614-70). The signal waveforms were averaged over 200 shots and recorded using a digital oscilloscope (Lecroy, WaveRunner 64Xi). Then, they were integrated with respect to time to estimate the annihilation signal intensity. Figure 2 shows the electrostatic potential on the central axis of the trap used for positron accumulation, calculated by finite-element analysis. A series of operations from trapping to extraction was executed in four steps corresponding to different electric potential configurations, Φ 1 -Φ 4 . First of all, before entering the pulsed positron beam from the LINAC into the trap, a Φ 1 configuration was varied to that of Φ 2 . Then the positron beam impinged onto the SiC in the Φ 2 configuration. The positrons re-emitted from the SiC headed upstream and 'bounce' off of the upstream potential barrier. To prevent them from re-impinging onto the SiC, the voltage applied to the SiC was rapidly raised (Φ 2 → Φ 1 ) by using a transistor switching circuit (Toshiba, 2SC5171). Since the bounce frequency of 2 eV positrons is approximately 1.4 MHz, a positron pulse with a temporal width of 0.5 µs became trapped in the potential well (the details are described in appendix A). Here, if positrons were trapped inside the well without any energy loss process, they could be re-incident onto the SiC when the SiC voltage was dropped at the next beam injection (Φ 1 → Φ 2 ). Therefore, CF 4 gas was present in the trap system to cool the temporarily trapped positrons, so that they were accumulated at the bottom of the well with a depth of about 1.5 V. These trapping operations repeated at each beam injection to accumulate positrons (Φ 1 → Φ 2 → Φ 1 ). After the accumulation procedure, the potential was floated up (Φ 1 → Φ 3 ), and the positrons were extracted by dumping the downstream barrier using a high-speed MOS-FET switching circuit (ON Semiconductor, EL7104CSZ-T7), which was synchronized with the dumping of the SiC voltage (Φ 3 → Φ 4 ). The rotating electric field was driven to compress the positrons in the well throughout the operations.

Results and discussion
The various parameters of the SiC-based trapping scheme were optimized. Figure 3 shows the overall trapping efficiency of the positrons as a function of CF 4 partial pressure, which was controlled by using a variable leak valve and monitored with a Bayard-Alpert (BA) gauge connected to the six-way cross chamber (shown in figure 1). The time to accumulate multiple positron pulses from the LINAC was 0.1 s. The overall efficiency was calculated by S t / (NS i ), in which S t is the annihilation signal of the extracted positrons from the trap, S i is the annihilation signal of the single incoming pulse from the LINAC, and N is the shot number of the incoming pulse during the accumulation time (N = 4). This number depends on the number of positrons that can be extracted through the hole of the SiC and thus forms a lower bound on the number trapped. As will be shown below, under optimal conditions (CF 4 pressure, rotating electric field frequency/amplitude), the positron cloud is compressed to be smaller than the hole, and for those cases the number trapped is exactly equal to the number passed through the hole. During measurement, the rotating electric field with an optimal condition (frequency: 3.66 MHz, amplitude: 3.6 V) was driven. The efficiency increased as the CF 4 pressure increased and then leveled off slightly above 10 −3 Pa. Also, at high pressures close to 10 −2 Pa, the efficiency slightly decreased, likely because of the positron annihilation in the gas. The admittance of the CF 4 gas plays a crucial role in this scheme for trapping positrons. The CF 4 gas acts as a cooling medium not only for positrons caught in the potential well Φ 2 but also for heated positrons during compression by the rotating electric field (described later). The main reason to use CF 4 gas is its large inelastic cross sections ranging from 0.2 to 2 eV owing to its vibrational excitations (positrons lose 0.16 eV per collision by the dominant excitation of ν 3 modes) [32,33]. This energy range is well suited to cool the positrons of approximately 2 eV re-emitted from the SiC remoderator. The time constant τ c of positron thermalization in the CF 4 atmosphere is estimated from the previously obtained pressure-normalized time constant [34] to be 0.6 ms at 1 × 10 −3 Pa and room temperature (300 K). Therefore, the thermalization time (e.g. 5τ c ) is expected to be 3 ms, which is short enough to cool positrons during the interval of the positron beam injection (25 ms). On the other hand, this cooling process does not make sense at the pressure of, e.g. 10 −4 Pa, at which the efficiency falls off significantly, even though the thermalization time is still short enough. The pressure dependence shown in figure 3 can be governed by the balance between the CF 4 gas cooling and the heating produced by the rotating electric field. The GBAR Collaboration used the cooling gases SF 6 and CO 2 for their SiC-based positron trap [21], although the performances of these gases do not differ considerably from that of CF 4 gas [30]. In addition to these gas cooling methods, positrons can be cooled down via synchrotron radiation with a high-field trap (>1 T). However, due to the high cost of superconducting magnets and the magnetic mirror limiting positron injection into the trap, it was not adapted in this demonstration.
The response of the positrons accumulated in the trap to the rotating electric field was also investigated. Compression by the rotating electric field, the so-called rotating wall technique, is essential to extract the accumulated positrons through the hole in the SiC. Ninety degree-phase-shifted sine waves were applied to the segmented electrodes, forming a rotating electric field in the potential well. Figure 4(a) shows the overall trapping efficiency of the positrons as a function of the rotating-field frequency, f, with a CF 4 pressure of 1.1 × 10 −3 Pa. The amplitude was fixed at 3.6 V and the accumulation time was 0.1 s. Upon tuning the frequency to approximately 3.7 MHz, the accumulated positrons were spatially compressed and extracted downstream through the small hole in the SiC remoderator, resulting in an increase in the efficiency. The rotating-field compression is also considered to improve the trapping efficiency in the accumulation stage. The frequency response indicates that compression by the rotating field occurs resonantly within ±0.5 MHz. The resonance frequency is close to the axial bounce frequency of positrons in the confinement potential well, f z = 3.6 MHz, as estimated by the shape of the harmonic potential near the bottom of the well. Considering this frequency characteristic, compression is likely to be caused by the mechanism in a single particle regime [31], which has a resonant response similar to that observed. This mechanism can be described as motional sideband cooling with an asymmetric dipolar rotating field in the presence of a cooling gas [35]. In this regime, rapid compression (millisecond timescale) can be achieved by applying a large-amplitude rotating electric field. The efficiency as a function of the peak-to-peak amplitude, V pp , applied to the segmented electrodes was also investigated at a frequency of 3.66 MHz as shown in figure 4(b). An amplitude larger than 4 V was required to obtain the maximum efficiency (good compression). Conversely, for amplitudes exceeding 4 V, the efficiency decreased as the amplitude increased. This behavior may be attributed to the strong electric field kicking positrons out of the potential well (heating). Figure 5 shows the annihilation signal of extracted positrons as a function of the filling time t of the positron beam in the accumulation stage in figure 2(a). The rotating electric field (f = 3.66 MHz, V pp = 3.6 V) was driven during measurement, with a CF 4 pressure of 1.1 × 10 −3 Pa. The signal was normalized to that of the single incoming pulse from the LINAC, i.e. S t /S i . The signal increased monotonically with t up to roughly 4 s and then saturated. The blue line in the figure is the fit using a time evolution function of accumulated positrons, , where A is the normalization constant and τ is the time constant of the number of positrons in the trap. τ is determined to be 2.6 s from the fit. The annihilation lifetime of positrons in the CF 4 atmosphere of this experiment (1 × 10 −3 Pa) is calculated to be approximately 10 s [36], so the particle loss in the trap was likely caused not only by positron annihilation in the CF 4 atmosphere but also by spatial expansion of the accumulated positrons during the longer storage, which reduced the extraction efficiency through the hole. Thus, the present trapping scheme works efficiently for short accumulations (e.g. 1 s), which is similar to the two-stage buffer-gas trap [37]. This scheme can produce a controllable-burst beam with a repetition rate from 1 to 40 Hz and positron cooling in the first stage. Long-term storage of a large number of positrons, e.g. 10 9 -10 10 e + , requires another accumulator [37,38] designed to stack positrons from the SiC trap.
The spatial profiles of the extracted positrons were measured by dumping the beam onto a phosphor screen monitored with a CCD camera. The fluorescent profiles were integrated over 60 s. Figures 6(a) and (b) show the profiles of the incoming positron beam positioned on and off the trap central axis, respectively, taken with the SiC remoderator offline. Since the repetition rate of the LINAC was 40 Hz, the profiles contain an integrated signal for 2400 positron pulses. The XY position of the incoming beam was controlled by steering coils located upstream of the trap. Figures 6(c) and (d) show profiles of the extracted positrons from the trap using the on-and off-axis beams, respectively. The accumulation time of multiple positron pulses from the LINAC was set to 0.1 s and the cycle from the accumulation to the extraction was repeated (10 Hz). Hence the profiles contain an integrated signal for 600 cycles with the incoming beam background through the center hole of 2400 pulses. The rotating electric field, with f = 3.66 MHz and V pp = 3.6 V, was driven to compress the positrons throughout the cycles, with a CF 4 pressure of 1.1 × 10 −3 Pa. The red frames in the figures outline the center hole of the SiC remoderator projected onto the screen and enlarged by the ratio of the square root of the magnetic flux density at the remoderator (50 mT) to that at the screen (6 mT). For both conditions, the positrons were sufficiently compressed by the rotating field to pass through the center hole. The beam diameter was 2 mm full width at half maximum on the screen. The halo around the extracted beam in figure 6(c) is attributed to the incoming beam passing through the center hole. A fraction of the incoming beam passed through the hole, f t , was estimated by taking the ratio of the annihilation signals at the screen when the SiC was online and offline. Note that, when the SiC was online, an annihilation signal at the SiC was additive, and hence this contribution was evaluated and subtracted from the signal at the screen. Therefore, a fraction of the incoming beam impinged onto the SiC, f i = 1 − f t , was estimated to be 67 ± 3%. To avoid such particle loss, the incoming beam was deflected off-axis, as shown in figure 6(b), in which case f i = 97 ± 4%. Although the incoming beam was not centered on the axis, accumulated positrons were drifted toward the axis by the rotating electric field and then extracted through the hole. These incident methods are selected on a case-by-case basis; when the incident beam size is much larger than the hole, the beam should be on the central axis because the fraction passing through the hole is sufficiently small compared with the whole. Conversely, when the beam size is comparable to or smaller than the hole, the beam should be off center so that the whole beam impinges on the SiC.
The trapping efficiency of the present trapping scheme was also assessed based upon the annihilation signals at the screen. The overall efficiency is given by ε = S t / (NS i ), as already mentioned. Under optimal conditions (f = 3.66 MHz, V pp = 3.6 V, CF 4 pressure = 1.1 × 10 −3 Pa), with an accumulation time of 0.1 s, the efficiencies for the on-and off-axis beams were estimated to be 17 ± 1% and 26 ± 1%, respectively. Here, S t and S i were measured four times for both beam conditions, and the ε values and the synthetic uncertainties were calculated from each mean value and each standard deviation, respectively. To assess the efficiency of our trapping scheme, the overall efficiency can be described as where ε t is the trapping efficiency of the positron beam entering the SiC. Since the combination of the SiC and CF 4 gas is used as the energy-dumper instead of N 2 buffer gas, we define ε t as the product of the SiC remoderation efficiency and the trapping/cooling efficiency by CF 4 gas. Using the aforementioned values of f i and τ , as well as an accumulation time of t = 0.1 s, the trappingefficiencies for the on-and off-axis beams were 26 ± 2% and 28 ± 2%, respectively. These trapping efficiencies are five to six times greater than that obtained for the LINAC-base beams with the buffer gas [17][18][19] and are comparable to that for radioisotope-based beam accumulation with a buffer-gas trap [13]. One of the factors limiting the trapping efficiency may be the moderation efficiency of the 4H-SiC remoderator. The efficiency of the SiC wafers used in this demonstration was estimated by the retarding potential method (the details are described in appendix B) [26]. The efficiency for an incident energy of 150 eV was 46 ± 2%. Since the moderation efficiency depends strongly on the crystalline quality of the materials and thus on the concentration of defects, which serve as positron-trapping sites, epitaxially grown films with low-carrier densities are leading candidates for semiconductor remoderators. High remoderation efficiencies of 63%-65% were reported for positrons with an energy of 1 keV incident on epitaxially grown films of 4H-SiC [26] and 6H-SiC [23]. This high efficiency can be maintained even at low energies of less than 1 keV [21], although an epithermal component may be included. Therefore, if an epitaxially grown 4H-SiC film was used in our trap system, a trapping efficiency of approximately 40% might be expected.

Conclusion
In conclusion, we have demonstrated the efficient trapping of a LINAC-based positron beam and its extraction by using a center-hole SiC remoderator. This was done by first trapping re-moderated positrons from SiC with CF 4 gas cooling, then spatially compressing the accumulated positrons by using a rotating electric field and then extracting the positrons through a hole in the SiC. Thanks to the high remoderation efficiency of 4H-SiC, a trapping efficiency in the higher 20% range was achieved under optimal conditions, the entire cloud of positrons could be extracted through the hole in the SiC. Note that a SiC-based positron trap is only suitable for trapping pulsed beams with pulse widths less than a few microseconds, since the positrons re-emitted from the SiC must be caught in a pulsed manner. Thus, the SiC-based trap is suitable for the microsecond pulsed positron beams supplied by LINAC-based facilities such as CERN AD (GBAR Collaboration) [14], KEK IMSS SPF [15], and AIST [16]. In application, the trap system can serve as an efficient converter of a LINAC-based positron beam to a controllable, high-quality burst beam, and can store a large number of positrons (10 9 -10 10 e + ) when used in combination with another accumulator.

Data availability statement
The data that support the findings of this study are available upon reasonable request from the authors.

Appendix B
We estimated the moderation efficiency of the SiC remoderator using the retarding potential method. The experimental setup was modified for this purpose as shown in figure B1 (a). A scintillation detector was placed on the side of the coil, so that it could detect annihilation gamma-rays from the SiC, and it was surrounded by lead blocks to shield gamma-rays from surroundings. A pipe with a bias voltage of V R , placed in front of the MRE, was used to repel re-emitted positrons instead of being used as the buffer-gas cell in [19]. The incoming positron beam passed through the pipe and then impinged onto the SiC grounded. Re-emitted positrons were repelled by the retarding voltage if their parallel energies were lower than that and impinged onto the SiC again. The signal of the annihilation gamma-rays from the SiC was measured as a function of V R . Figure B1 (b) shows the result for a positron incident energy of 150 eV. The signal increased steeply as V R increased and became saturated because all re-emitted positrons were repelled. The annihilation signal was normalized to the saturated value, S s . We estimated the moderation efficiency using the equation 1 − S 0 /S s , where S 0 is the signal at the V R = 0 limit. The efficiency for an incident energy of 150 eV was 46 ± 2%. Furthermore, we estimated the parallel energy distribution of the re-emitted positrons from the signal curve. Assuming its distribution was Gaussian, data were fitted with an error function (blue curve), , where C is a constant; and µ and σ are the mean value and standard deviation of the Gaussian, respectively. The distribution parameters were derived to be µ =2.1 ± 0.2 eV and σ =1.5 ± 0.3 eV, respectively. The value of µ is comparable to the absolute value of the positron work function for SiC [22][23][24][25][26]. The energy spread (σ) is slightly larger than the reported value (∼1 eV) for an incident energy of 1 keV [26]. This may be attributed to the epithermal positron component due to the incident energy as low as 150 eV.