High efficiency cyclotron trap assisted positron moderator

TL;DR

This paper presents a novel cyclotron trap assisted positron tungsten moderator that significantly improves efficiency in converting broad-spectrum positrons into mono-energetic eV beams, with potential for even higher performance.

Contribution

It introduces a new moderator design achieving nearly 100-fold higher efficiency than previous tungsten moderators, validated by simulation and experiment.

Findings

Achieved 1.8% efficiency in converting positrons to eV beams.

Demonstrated almost two orders of magnitude improvement over previous methods.

Simulations suggest further efficiency enhancements are possible with optimization.

Abstract

We report the realisation of a cyclotron trap assisted positron tungsten moderator for the conversion of positrons with a broad keV- few MeV energy spectrum to a mono-energetic eV beam with an efficiency of 1.8(2)% defined as the ratio of the slow positrons divided by the $\beta^+$ activity of the radioactive source. This is an improvement of almost two orders of magnitude compared to the state of the art of tungsten moderators. The simulation validated with this measurement suggests that using an optimised setup even higher efficiencies are achievable.

Tables

Table 1. Table 1: Endpoint energy T max subscript 𝑇 max T_{\text{max}} , half-life t 1 / 2 subscript 𝑡 1 2 t_{1/2} , β + superscript 𝛽 \beta^{+} branching Γ ​ ( β + ) Γ superscript 𝛽 \Gamma(\beta^{+}) , production target and reaction (projectile,X), maximum cross-section σ max ​ ( E σ ) subscript 𝜎 max subscript 𝐸 𝜎 \sigma_{\text{max}}(E_{\sigma}) , corresponding projectile energy E σ subscript 𝐸 𝜎 E_{\sigma} , EOB activity A EOB subscript 𝐴 EOB A_{\text{EOB}} and Φ ⋅ t ⋅ Φ 𝑡 \Phi\cdot t as µ ​ A microampere \mathrm{\SIUnitSymbolMicro A} h/ e 𝑒 e to create 1 MBq ( e 𝑒 e C is the elementary charge) for 1   µ ​ m times 1 micrometer 1\text{\,}\mathrm{\SIUnitSymbolMicro m} foils of 58 Co, 22 Na and 48 V NDS_IAEA .

Isotope	58Co	22Na	48V
$T_{\text{max}}$ / keV	475	545	695
$t_{1/2}$	70.85 d	2.602 y	15.97 d
$\Gamma \left({\beta }^{+}\right)$	14.9%	90.6%	50%
target(projectile,X)	58Ni(n${}_{\text{fast}}$,p)	27Al(p,X)	48Ti(p,n)
${\sigma }_{\text{max}}\left(E_{\sigma }\right)$	1-600 mb	44 mb	382 mb
$E_{\sigma }$	25 meV	44 MeV	12 MeV
${\rho }_{\text{target}}$ / $\text{g}/{\text{cm}}^3$	8.9	2.7	4.5
$A_{\text{EOB}}$ / kBq/($\mu A$h/$e$)	107	0.05	24
$\Phi \cdot t$ / $\mu A$h/$e$ for 1 MBq	9.4	20000	41

Equations

$$\left|\frac{p_{\parallel 0}}{p_{\perp 0}}\right|\le \sqrt{\frac{B_{\text{max}}}{B_{\text{min}}}-1}.$$

$$A_{\text{EOB}}=\text{ln}(2)\cdot \frac{{\rho }_{\text{target}}\cdot d\cdot \sigma (E)}{t_{1/2}\cdot m_a}\cdot \Phi \cdot t$$

Full text

I Introduction

The positron and its bound state with an electron, positronium, have found many applications in physics and chemistry CharltonBook ; JeanBook . In medicine, they are used for what is probably the best known application of anti-matter in “everyday” life, the method of positron emission tomography (PET) townsend2004 . Relying on their unique sensitivity to the electronic environment, positrons serve in applied science for the characterisation of materials. For example they provide one of the most sensitive techniques to detect defect concentrations tuomisto2013 , they can be used to perform measurements of Fermi surfaces eijt2006 ; weber2015 , determine pore sizes in polymers jean2013 and nanoporous films gidley2006 . The number of applications is continuously increasing e.g. prompted by the growing complexity of advanced functional materials with multi-level porosity such as hierarchical zeolites and metal-organic frameworks oPsNC ; oPsMOFs . Studies of positron and positronium interactions with matter are also a vibrant field of research surko2005 ; laricchia2015 .

As systems made of two elementary particles with no sub-structure, positronium (Ps), including Ps-ions and Ps2 molecules, are ideal for testing bound state QED karshenboim2005 ; fee1993 ; asai2014 ; PsIon ; PsIon2 ; cassidyPs2 , fundamental symmetries vetter ; yamazaki2010 and to search for new physics PRD2007 . Work is in progress to improve on the current results, to measure the effect of gravity on antimatter using Rydberg Ps cassidyPRL2016 and to form a Ps Bose-Einstein condensate Avetissian2014 . Positrons and positronium are also essential ingredients for the production of anti-hydrogen currently being studied at CERN ALPHA ; ATRAP ; ASACUSA ; AEGIS ; GBAR .

The development of slow positron beams in the seventies greatly expanded the possibilities of this field PosBeamAppl . More recently, an additional boost was given by the advent of buffer gas traps allowing for manipulation and storage of large positron plasmas surko2015 .

There are different ways to produce positrons which include the use of accelerators Krause2008 ; Oshima2009 ; Perez2009 , nuclear reactors Falub2002 ; Hawari2011 ; Hugenschmidt2014 or ultra-intense short pulsed lasers Chen2009 . The most common and compact solution is to use radioactive isotopes that are $\beta^{+}$ emitters such as 22Na surko2015 . To form a slow positron beam the positrons from the broad keV to few MeV energy spectrum of the source have to be converted to a mono-energetic eV beam using moderators. Those can be divided into two classes: metals with a negative work function LynnAPL1985 and materials with very long diffusion lengths for positrons MillsAPL1986 . The best work function based moderators are thin single crystalline tungsten foils or tungsten meshes with efficiencies of the order of ${10}^{-4}$ Saito2002 . The most efficient moderators rely on the long diffusion length of positrons in frozen rare gases, e.g. neon has a typical efficiency of $\epsilon=$7\text{\times}{10}^{-3}$$ surko2015 .

In this paper, we present a scheme based on cyclotron trap assisted moderation that improves the amount of positrons available for the moderation process resulting in a higher efficiency.

II Principle of the cyclotron trap assisted moderation

A cyclotron trap (CT) is a magnetic bottle consisting of two coaxially identical coils separated by a given distance (see Fig. 1). By running a current in the same direction through the coils, the created magnetic field along their central axis has a maximum value $B_{\text{max}}$ at the center of each coil and a local minimum $B_{\text{min}}$ between them. This leads to the confinement of charged particles if their momenta perpendicular $p_{\perp}$ and parallel $p_{\parallel}$ to the coil axis satisfy the relation (assuming adiabatic invariance):

[TABLE]

These particles then travel back and forth between the two coils on spiral trajectories along the trap axis.

In 1960, Gibson et al. Gibson1960 , reported the confinement of positrons in a “mirror machine”. In the eighties Simons:1988fz ; Eades:1989vk , L. M. Simons proposed a CT with a thin foil placed in its middle to be used as an energy degrader for slowing down anti-protons and negative muons Simons:1993aa to keV energies. This scheme has been used in the recent measurement of the proton charge radius with muonic-hydrogen Pohl2010 . W. B. Waeber et al. Shi1994 tried to implement the same approach for degrading positrons to energies of a few keV before their extraction and subsequent moderation outside the CT to form a mono-energetic beam. However, due to their very challenging extraction scheme they could not reach the very promising theoretical predictions and this project was discontinued Gerola1995 ; Gerola1995NIMA .

In the setup presented here, all the involved steps, i.e. the positron emission, the energy degradation, the moderation and the extraction are performed inside the cyclotron trap. The source, an activated $1\text{\,}\mathrm{\SIUnitSymbolMicro m}$ thick titanium foil, and the moderator, a $1\text{\,}\mathrm{\SIUnitSymbolMicro m}$ thick single crystal tungsten (110) foil are matched and placed in the center of the cyclotron trap. This allows to greatly increase the amount of positrons available for moderation. The trapped positrons lose energy each time they pass through the foils. Once they have been degraded to energies of a few keV they thermalise in the foils and can be re-emitted as slow positrons. The very narrow energy spread, due to the negative work function of tungsten, guarantees that slow positrons can be extracted with an efficiency close to $100\text{\,}\mathrm{\char 37\relax}$ from the trap (see Eq. 1) when applying a small electric field.

III Experimental setup

The experimental setup is schematically illustrated in Fig. 2. The sources for this experiment were 48V created by irradiation of $1\text{\,}\mathrm{\SIUnitSymbolMicro m}$ Ti foils exploiting the reaction 48Ti(p,n)48V with 8 MeV protons from the ETHZ TANDEM accelerator and with 18 MeV protons using the external beam line of the IBA 18/9 medical cyclotron located at the Inselspital in Bern, Switzerland CAARIpaper .

Calculations of the yield, confirmed by multiple Ti foil irradiations, show a good agreement for the end-of-bombardment activity $A_{\text{EOB}}$ in the thin target approximation:

[TABLE]

with the target density $\rho_{\text{target}}$, thickness $d$, cross section $\sigma(E)$, projectile flux $\Phi$, irradiation time $t$, half-life $t_{1/2}$ and atomic mass $m_{\text{a}}$ of the target material. Those values are reported in Table 1.

The half-life of 48V is 16 days which is not ideal for continuous operation of a positron beam. However, developments are underway that should allow one to achieve 10 MBq activities of the foils in less than 1 day irradiation using solid target stations usually employed for the production of radioisotopes with medical cyclotrons. Therefore, 48V is interesting for targeted measurements. For long term operation, better choices for the $\beta^{+}$ emitter are 58Co or 22Na with half-lives of 70 days and 2.6 years respectively. Preliminary attempt to produce 58Co via irradiation of 58Ni foils were performed at the SINQ spallation source of the Paul Scherrer Institute (PSI) but only a very limited activity of few kBq was achieved. In fact this reaction is suppressed for thermal neutrons and ideally one would use a fast reactor since the cross section for 58Ni(n,p) becomes appreciable only for neutrons above 0.5 MeV. Moreover, 58Co has a high capture cross-section for thermal neutrons, thus in this case the produced positron emitting isotope is depleted. The production of a 22Na source has a higher threshold (see Table 1) and to achieve comparable activities requires about 1000 times more protons on target than the 48V production. The production of up to 20 MBq 22Na sources by irradiation of $125\text{\,}\mathrm{\SIUnitSymbolMicro m}$ aluminum foils with 72 MeV protons has been demonstrated in the past at PSI beamNIMA ; cugPhD . With commercial 70 MeV cyclotrons for isotope production cyclotron2010 , 1 MBq sources on $1\text{\,}\mathrm{\SIUnitSymbolMicro m}$ foils could be produced in 10 days of irradiation with $80\text{\,}\mathrm{\SIUnitSymbolMicro A}$ currents. An important feature of activated thin metal foils is that those are vacuum compatible and the radioactive isotopes are well bound inside the foil and thus are ideal in terms of radiation safety.

The $1\text{\,}\mathrm{\SIUnitSymbolMicro m}$ tungsten moderator was purchased from the Dept. of Physics and Astronomy of the University of Aarhus, Denmark and annealed $2\times 15$ minutes through electron bombardment shortly before mounting it in the setup. For the slow positron extraction a 96% transmission tungsten mesh was used. The cyclotron trap is formed by two identical water cooled coils that were re-used from an experiment at PSI WEBmagnet after removal of the iron yoke and refurbishing. The maximal characteristic values of the CT running with a current of 650 A are $B_{\text{max}}=2.559(2)$ kG and $B_{\text{min}}=0.544(2)$ kG corresponding to a magnetic field ratio of 4.704(17). The typical energy distribution of the moderator used in this experiment is $\Delta E_{\parallel,\text{mod}}\approx 1$ eV Vehanen:1983aa ; firstmoderation ; Appl.Phys.Lett.51.1862 . Due to this energy spread not all slow positrons can escape from the trap. In order to maximize the extraction efficiency a grid has been added to produce a 200 V/cm electric field between moderator and grid.

To reduce the background from the annihilation in the source and from unmoderated positrons that could reach the detector, a 1 m long 100 G solenoid guides the positrons away from the CT (see Fig. 2).

Due to the limited activity of the source available for this experiment we selected an electron multiplier (EM) to detect the slow positrons since it has smaller dark counts ($<$ 1 count/s) compared to micro-channel plate detectors (MCPs). The drawback is that EMs are very sensitive to magnetic fields and therefore the positrons have to be extracted from the guiding field used for their transport. This was realized by terminating the magnetic field with Mu-metal shielding. Simulations with SIMION and COMSOL were used to optimise the extraction efficiency to values close to 100%. This was confirmed experimentally by using the ETHZ slow positron beam beamNIMA .

IV Simulation

To design the cyclotron trap assisted positron moderator we performed a detailed simulation with Geant 4 Agostinelli2003 . The CT magnetic field maps were created with COMSOL and Matlab. Geant 4 was validated to reproduce the correct positron stopping profiles Dryzek2008 but does not include positron diffusion and the physics of the moderation process. Therefore, the simulation does not predict the moderation efficiency. To estimate it, we count the fraction of positrons stopping near the surface, in the so-called ejection layer ($\approx$ 100 nm). In fact, those are the ones that have a probability to diffuse to the surface and be emitted as moderated positrons due to their negative work function in tungsten MillsReview1988 .

The simulation suggests that the extraction efficiency by applying +100 V on the source/moderator, with the grid at ground potential, is close to the 94 % transmission of the grid. The number of fast positrons contributing to the background is expected to be below $10^{-4}$. The simulation of our proof of principle setup for which 2 Ti foils of $1\text{\,}\mathrm{\SIUnitSymbolMicro m}$ thickness where used in order to increase the available positron activity, predicts moderation efficiency of the order of 1 %.

Figures 3 and 4 illustrate the basic principle of assisted positron moderation with a CT. The overall advantage of the trap can be seen in Fig. 3. Without a CT just the positrons in the low energy tail of the beta spectrum will stop inside the foil (black area in Fig. 3). Of those, only the small fraction stopping in the ejection layer will actually get moderated. With the CT, trapped higher energetic positrons that did not stop in the first pass through the foil will have a chance to stop in one of the subsequent passages thus a part of the beta spectrum that is normally lost can be recycled (white area in Fig. 3). The overall enhancement for stopping positrons is a factor of 5. The fact that the moderation efficiency actually improves by a much larger factor is illustrated in Fig. 4. The contribution of mirrored positrons (white area), in the ejection layer on the moderator surface opposite to the source, is enhanced compared to the case where no CT is used (black area). This mimics the so-called reflection “geometry” which is known to have a higher slow positron yield Williams2015 .

The magnetic field of the CT used in this experiment is not strong enough to radially confine all the high energy positrons. The total amount of mirrored positrons are around 66% for a magnetic field ratio of about 5. As can be seen in Fig. 3, only 30 % of the them finally stop (white area) in the foils and the others escape (grey area). This is due to forward scattering at the foils. Simulations suggest that with a higher magnetic field ratio and a single source foil, even higher efficiencies are achievable with cyclotron trap assisted positron moderation.

V Results

To measure the background due to the unmoderated positrons and photons reaching the detector, the source and the moderator are kept at ground potential while the extraction grid is biased to +100 V in order to block the moderated positrons. In this configuration, 1 count/s was detected in the electron multiplier. In the extraction mode, +100 V are applied on the moderator while the grid is at ground, the number of counts in this case was 40 s*-1*. The difference of counts between these two configurations, after correcting for the 70(3) % detection efficiency of the electron multiplier, is the number of moderated positrons. At the time of the experiment the positron activity was $3.2(1)$ kBq, measured with a germanium detector and a calibration source. The division of the counts in the extraction mode by the total positron activity gives a moderation efficiency of the order of $\epsilon\approx 1.8(2)$ % in fair agreement with what has been estimated from the simulation results.

VI Conclusions

The scheme presented here improves the positron moderation of state of the art tungsten moderators by almost two orders of magnitude. It can therefore produce the same output intensity from a much weaker radioactive source. It also yields a factor of two improvement compared to rare gas moderators but is operationally considerably simpler. The simulation validated with the measurement predicts that with this technique, using an optimised setup, higher efficiencies can be achieved. Therefore, this technique combined with a few MBq $\beta^{+}$ source on a $1\text{\,}\mathrm{\SIUnitSymbolMicro m}$ foil would result in a positron flux of $10^{4}$ positrons/s which is the typical value achieved with standard tungsten moderator based beams. This opens the possibility to envisage a widespread use of positron beams which are currently available only in few specialized laboratories around the world. Furthermore, this scheme could be used to increase the moderation efficiency and the yield at high intensity positron facilities thus allowing for further advances in the positron and positronium field.

Acknowledgements.

This work has been supported by the Swiss National Science Foundation under the grant number 200020_156756. We would like to thank the PSI and ETH Zurich IPP workshops for their support.